As African swine fever (ASF) continues to expand geographically, supplementary control strategies are needed to reduce disease risk and impact in affected areas. Full depopulation is central to current ASF control efforts, and its efficacy depends on surveillance and timely disease reporting, while resulting in large losses regardless of the producers' efforts to promptly detect, report, and contain the disease. This disconnect between prompt detection and reporting, and subsequent farm losses, can deter producers to invest in ASF detection and control. Alternative approaches are needed to incentivize individual producers to invest in early detection and reporting. We postulate that commercial swine farms may be effectively partitioned in separate units, or subpopulations, to which biosecurity, surveillance and control can be applied. The suggested Partitioning framework relies on three main components: 1. external and internal biosecurity to reduce the risk of ASF introduction and maintain separate subpopulations; 2. cost-effective on-farm ASF surveillance to enhance early detection; 3. response plans at the unit level, including culling of affected subpopulations, and demonstration of freedom from disease on the remaining ones. With such Partitioning approach, individual producers may reduce ASF risk on a farm and in the region, while also reducing ASF outbreak losses via targeted depopulation of affected units. It requires relevant legislation to incorporate the notion of within-farm subpopulations and provide a regulatory framework for targeted depopulation and substantiation of disease freedom. Its design should be tailored to fit individual farms. Partitioning can be an effective public-private partnership approach for ASF risk reduction. It should be driven by industry, as its benefits are accrued mainly by individual producers, but regulatory oversight is key to ensure proper implementation and avoid further disease spread. Partitioning's value is greatest for producers in ASF-affected regions, but ASF-free areas could also benefit from it for preparedness and early detection. It could also be adapted to other transboundary animal diseases and can be implemented as a stand-alone program or in conjunction with other efforts such as zoning and compartmentalization. Partitioning would contribute to the improved resilience and sustainability of the global pork industry and will benefit consumers and society through improved food security and animal welfare. African swine fever (ASF) is one of the most devastating diseases of pigs, associated with high mortality rates and dramatic economic losses , 2. Its Given the unprecedented spread of the disease, public concerns about animal culling, and in the absence of a “silver bullet” to control ASF, there is a need to consider additional control approaches based on public-private partnerships (PPP). Acknowledging this, the Food-and-Agriculture Organization (FAO) of the United Nations and the OIE launched in 2020 a new initiative for the global control of ASF  that higCreating cost-effective solutions that incentivize individual producers to invest in surveillance, early detection, and prompt reporting of ASF.Implementing effective alternatives to full farm depopulation in case of an ASF outbreak, that is in line with appropriate supporting legislation.In this paper, we propose an industry-led PPP initiative for ASF-affected areas to incentivize individual producers to invest in risk management measures, and thus enhance ASF prevention and control. Typically, commercial swine farms are organized in units  that could be “partitioned” into spatially and epidemiologically separate subpopulations. On this premise, we propose a Partitioning framework focused on on-farm activities for prevention, early detection, and control of ASF at the level of these subpopulations. This approach would require a legal basis and endorsement by the competent authority (CA). Here we describe the rationale for the Partitioning approach, outline its three main components and show its value to various stakeholders. We discuss how it can be implemented as a stand-alone effort or in complement to other programs, particularly in areas where ASF is present in domestic pig populations and with barriers to the implementation of current ASF control strategies.ASF represents an increasing risk for pig producers worldwide. Current ASF and TADs control guidelines typically include culling of all animals in infected herds, cleaning and disinfection, movement control, and contact tracing , 18, 19.Governments and the OIE have established approaches to enhance early detection and mitigation of ASF risks, such as zoning or compartmentalization—which are particularly relevant for the purpose of international trade , 30. BotThe abovementioned programs focus on reducing the economic impact of ASF from specific disease-free sectors of the industry. However, in line with laws and policies in places in most countries, an ASF outbreak in a participating farm typically results in its full depopulation regardless of the extent of infection on the farm. There is thus an opportunity for supplementing these existing strategies with an approach that incentivizes producers to invest in early detection and timely reporting in return for allowing for the depopulation of only affected units in the farm location. A growing number of experts support the development of these alternatives to mass depopulation , 8, 32. This type of on-farm risk management is already a possibility for some non-notifiable and/or endemic diseases, such as porcine reproductive and respiratory syndrome (PPRS) in the U.S . In the We propose a voluntary framework to improve detection and control of ASF  - such approach is possible if it can be shown that the investment is cost-effective for producers and that there is no increase in disease spread risk. This Partitioning framework for cost-effective risk management of ASF by individual producers relies on maintaining separate animal units via good external and internal biosecurity, conducting on-farm surveillance and early reporting, and in case of outbreak, coordinating with CAs for the safe targeted depopulation of affected units and demonstration of freedom in other units.As explained earlier, a typical commercial swine farm can be “partitioned” into epidemiological units i.e., separate subpopulations. The OIE defines an epidemiological unit as a “group of animals (...) that share approximately the same likelihood of exposure to a pathogenic agent,” and an outbreak as the “occurrence of one or more cases in an epidemiological unit” . What coPartial depopulation strategies for ASF are currently being implemented in ASF-affected areas in Asia , 45. In Farm biosecurity: prevention of disease introduction and on-farm spread via external and internal biosecurity practices. This objective may be aided by decision-support tools to prioritize and harmonize efforts on individual farms.Optimization of cost-effective on-farm surveillance, informed by modeling early detection, and prevention of disease spread between epidemiological units.Preparedness for prompt response and control in case of disease introduction into farm unit(s). A response plan must be prepared and in line with government requirements for targeted depopulation, including notification of authorities and close collaboration for the implementation of safe targeted depopulation, as well as monitoring and demonstration of disease freedom on separate units. This monitoring plan can also be supported by modeling.The Partitioning framework contains components that should be part of any ASF prevention and control strategy  as well as items more specific to the Partitioning framework which we further discuss below.Biosecurity comprises procedures and practices both to prevent disease introduction into a farm , and to reduce the risk of disease transmission between areas of a farm . Most existing biosecurity tools' emphasis is on external biosecurity . While eMany biosecurity guidance and scoring tools exist but they are not always well adopted, and/or compliance by staff is not always observed. They can indeed be cumbersome, and the efficacy of separate biosecurity measures is not well measured –54. For In addition, biosecurity measured by an overall score fails to distinguish a farm that performs well in almost all aspects but very poorly on a few biosecurity measures from a farm that performs fairly well across all biosecurity aspects. Ultimately, the weakest links can affect the overall biosecurity  of a farm , hence tBecause understanding the reasons for control measures increases compliance , the appOne could question the credibility of internal biosecurity in case of an ASF outbreak because the external biosecurity failed. However, there are many external biosecurity aspects that also involve other stakeholders who may not have the same protocols or incentives for compliance , possibly resulting in biosecurity breaches. In contrast, internal biosecurity can be more tightly controlled as it relies on on-farm procedures for the movement of animals, people, and equipment between production units. Finally, other activities such as on-farm surveillance and demonstrating disease freedom following an outbreak will complement internal biosecurity measures to document effective Partitioning of units, as discussed hereafter.In Partitioning, the objective of on-farm ASF surveillance is to improve time to ASF detection and decrease the probability of further spread to additional units on the farm. Commercial swine farms typically conduct clinical monitoring for several targeted diseases, and additional surveillance such as ASF diagnostic tests may also be in place in ASF-affected areas. But under most ASF control programs, early detection and reporting results in full farm depopulation. Early detection may even be associated with additional losses for the individual producer: it implies contacting the CA as soon as suspect—and typically unspecific—signs are noticed and being imposed a standstill while waiting for laboratory results. Some of these suspicions may be caused by other conditions —even more so as they rely on early and unspecific signs—and in such cases, activities resume once the farm is confirmed negative. As pork production relies on a flow of animals between buildings, from the gestation unit to the farrowing unit to grower and finisher barns before shipping to slaughterhouses, a standstill results in units being backed up and crowded, and a disruption of the gestation and farrowing units. The hog market crisis earlier in the Covid-19 pandemic , 58 provWith Partitioning, an early detection of ASF incursion results in the implementation of control measures before the disease spreads to other units on the farm and thus the reduction of losses thanks to targeted depopulation—providing the other units are proven to remain free of disease. Successfully containing the infection can also be easier when it is limited to a subset of the farm.Although early detection can reduce outbreak costs—animal losses, cleaning, and disinfection, potential loss of trade partners, time until recovery, etc., conducting additional active on-farm surveillance for early detection as part of Partitioning also has direct costs: staff time to conduct regular clinical monitoring, biological samples, diagnostic kits, and laboratory analysis. In addition, the probability of false positives will increase with additional surveillance, with subsequent costs. On-farm surveillance for Partitioning relies on clinical signs and/or regular sampling and testing for preclinical detection. ASF symptoms are unspecific, especially those during the early phases of an ASF outbreak or in CSF-endemic areas, and although ASF diagnostic tests have good performance, they are imperfect. For example, due to their lower specificity, the use of antigen detection ELISA and pen-side tests or isothermal assays for preclinical detection would lead to false positives –64. AlsoA plan of action in case of ASF suspicion must be prepared in compliance with relevant CA regulations. Its implementation must be coordinated with the CAs, who are ultimately responsible for overseeing the official control program .The response plan needs to be precise and actionable so that it can be activated immediately following a suspected case. The definition of an ASF suspect should be pre-defined, and once notified, a farm-level standstill protocol activated until the laboratory confirmation is available. If the outbreak is confirmed, depopulation of the infected epidemiological units will be carried out as required by the CA. This action will be complemented by cleaning and disinfection, reinforced biosecurity, and on-farm surveillance to mitigate the risk that the disease spreads to other units. In addition, substantiation of freedom from disease will be conducted in the remaining units before the standstill can be lifted for these units. CAs would specify requirements to achieve a desired target minimum detection level in the epidemiological units being monitored and specify the diagnostic test(s) that can be used for this purpose. Modeling can support the development of such response plans, especially for designing cost-effective monitoring plans during the standstill period and for demonstrating freedom of disease following an outbreak.This third component is the one for which appropriate legislation and a clear regulatory framework is required. The definition of what constitutes an epidemiological unit needs to be clear, as well as the requirements for reporting, and procedures to determine the extent of on-farm depopulation as well as to demonstrate disease freedom on other units, etc. As mentioned previously, this regulatory clarity will allow producers to make an informed decision on whether to invest in Partitioning.Partitioning should largely be funded by individual producers, but requires a clear regulatory framework in line with supporting legislation. Regulatory certainty gives individual producers a financial motivation to invest in measures to meet such requirements, in exchange for the possibility to reduce their losses. Partitioning is therefore a good example of a PPP effort, in which the public and private sectors work together to efficiently reduce disease risk . We beliThe following aspects should be considered when designing a Partitioning program:Tailoring Partitioning to individual situations: the higher the sensitivity of on-farm surveillance, the earlier the detection, but also the higher the costs for individual producers, as discussed previously. On-farm surveillance should account for the large diversity of production systems and will thus need to be customized to each farm to be cost-effective. Partitioning protocols should also be tailored to consider disease incidence, farm type, structure and management, access to laboratory diagnostics, economic situation, potential for investment, attitude toward risk, etc. For example, producers may decide to go beyond the minimum requirements set by the CA, depending on their individual cost-benefits, appetite for risk, and investment capacity. Also, not all swine farms, nor units on a swine farm are equal, and options for control measures to prevent spread between units will vary depending on the type of units considered. For instance, it is generally easier to restrict movements in growing and finishing units than it is in sow units, where animals are regularly moved back and forth between gestation and farrowing units.Requirements to establish freedom from disease following an outbreak: while ASF-affected units will be depopulated, other units will have to be shown to be free of infection following standards from the CA, to avoid further disease spread. Such standards need to consider the balance between the confidence in the disease-free status of epidemiological units and its cost: setting the monitoring standards too low could result in ASF spreading undetected to other units or farms, with a negative impact on all stakeholders, but setting them too high will increase the costs of Partitioning and reduce the net economic incentive for producers to invest in Partitioning.Balancing the costs and benefits to the CA: Establishing requirements for Partitioning and safe targeted depopulation with demonstration of disease freedom will result in additional rules and procedures for the CA, and implementation will involve coordination with producers. Conversely, the widespread adoption of Partitioning can result in a reduction of ASF circulation overall, and better allocation of the CAs resources. The burden of this additional complexity would also have to be balanced against the benefits of Partitioning to the various stakeholders , Eastern and southern Africa , Russian Federation, and the Caribbean . However, with the increasing spread of ASF worldwide, Partitioning can also have value in free areas under increased ASF risk of introduction, for preparedness and to increase the chance of early detection when ASF is introduced into a new area, before it further spreads. A good example for this are protection zones recognized by OIE , such asFewer CA resources for compensation of producer's losses, including those from culled animals, result in greater economic value of Partitioning to individual producers.The value of Partitioning also increases where the overall structure of the pork industry is complex and/or less centrally organized, making it difficult to initially meet the requirements for a compartmentalization effort or other certification programs. Partitioning can be a step toward these larger efforts.For producers who are already part of (an)other control effort(s), the marginal benefits of Partitioning may be lower, but the investments and costs needed to join will likely also be lower.Partitioning is more valuable for farms with larger numbers of separate production units, and smaller epidemiological units relative to the overall size of the farm. This is because the potential reduction in a producer's loss compared to full depopulation is greater compared to farms where animals are housed in a few units. However, such benefits of smaller epidemiological units would need to be weighed against the higher costs of internal biosecurity and on-farm surveillance that this may cause.We propose Partitioning as a cost-effective framework to help producers reduce their risk of ASF introduction as well as their losses in case of ASF outbreak. If widely adopted, it can also reduce the overall size of an ASF epidemic in a country or region. Given the continued expansion of ASF worldwide and the challenges with existing control efforts, there is a need for alternative disease management and control approaches that allow producers to better handle disease risk and impact in an endemic area or during an active epidemic. Partitioning would be particularly relevant in areas where ASF is present in domestic pig populations, and where there are barriers to the implementation of existing control measures relying on full depopulation. In addition, as mass depopulation is becoming increasingly unacceptable to the public, Partitioning can also help address animal welfare, sustainability, and food security concerns.While this paper focused on ASF, the Partitioning framework can be used to manage other TADs. As biosecurity measures and required investments are similar for other TADs, applying the Partitioning framework to multiple TADs would result in a greater return on investment for producers.Partitioning requires a legal basis so that CAs can provide a regulatory framework for the recognition of within-farm epidemiological units and requirements for targeted depopulation and substantiation of disease freedom. There is a need for organizations setting international standards as well as CAs to consider such notions and discuss guiding principles for their implementation. As illustrated by the change from mass culling to partial depopulation in China, this is becoming urgent given the ongoing global spread of ASF, the limitations in the implementation of current control strategies relying on stamping-out policies, and public concern regarding the welfare and sustainability issues of mass culling .In many ASF-affected countries, producers have started implementing partial depopulation , 26–28. With the growing demand for animal protein and increasing need for sustainability in food systems, new effective disease control approaches that result in less waste due to mass depopulation are needed. Partitioning offers an approach that can be as effective as current control methods while also resulting in an increased sustainability of the pork industry and better public perception of outbreak management.Better on-farm risk management, including on-farm surveillance and early reporting, will increase when the economic incentives of individual producers are aligned with that of competent authorities , 70, sucWhile Partitioning may initially be of most interest to larger commercial swine farms that are organized in separate production units, the concept of cost-effective disease risk management associated with Partitioning can also be used for smaller producers. For example, it could provide them with a better economic incentive to invest in measures to separate animals of higher economic value from the rest of the herd. In addition, any additional investment by larger producers in early surveillance and reporting will also, indirectly, benefit smaller producers through ASF spread reduction in the region. The use of Partitioning by larger farm will also likely result in improvements in technology and practices, such that it will become more affordable and accessible over time, for increasingly smaller producers.This paper describes the overall concept of Partitioning, and more detailed descriptions of its main components will be provided in separate articles. Biosecurity is key to the prevention of ASF risk, but the design and implementation of a biosecurity plan can be challenging for individual producers. In a forthcoming paper, we describe an approach for helping producers prioritize biosecurity measures and align both external and internal biosecurity as part of the Partitioning framework. Second, what constitutes a cost-effective on-farm ASF surveillance program will vary depending on multiple factors, including the farm considered and its epidemiological context. Other factors that need to be considered include the costs of testing, the overall sensitivity and specificity of the surveillance, benefits of finding a true-positive ASF case, as well as costs due to false positive or false negative results. Modeling to support the design of on-farm surveillance for Partitioning is being conducted. Early results were reported by Pouzou , but morWe hope that this paper will provide a basis for further research and discussions and contribute to the development and implementation of alternative strategies and tools to reduce ASF risk, such as the proposed Partitioning framework.SC, HG, and FZ designed the project and conceived the presented idea. SC and HG wrote the first version of the manuscript. All authors provided critical feedback and helped shape the research and manuscript.This work was supported by Section 108 Foreign Currency Program  from the USDA FAS.SC, FZ, JP, and HG are employed by EpiX Analytics LLC. All authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


In economic unethical decision-making experiments, one important methodological investigation is what types of contexts should be used to frame the instructions. Within the experimental economics community, using neutral-context instructions instead of loaded-context instructions is the mainstream practice. Because the loaded contexts may impact behavior in an unpredictable manner and therefore, put experimental control at risk. Nevertheless, using the loaded-context instructions could be advantageous in several ways. A properly framed context can help to facilitate learning and gain ecological validity. The challenge is whether we can identify when and why the loaded context may alter behavior. In this paper, we aim to test if being familiar with a loaded context can systematically influence unethical decisions in a bribery game. We conduct a laboratory bribery game experiment with three different treatments: the neutral-context treatment, the familiar-context treatment, and the unfamiliar-context treatment. Using the neutral-context treatment as a benchmark, we find that participants in the familiar-context treatment express stronger negative attitudes toward corruption. Attitudes toward unethical behavior are the same in the neutral-context treatment and the unfamiliar-context treatment. Behaviorally, the participants in the familiar-context treatment are much less likely to engage in corrupt activities. The neutral-context treatment and the unfamiliar-context treatment produce the same behavioral outcome. Over the past three decades, the study of unethical decision making has received increasing attention. In laboratory economic experiments, one commonly used technique to investigate the underlying motivation of unethical behavior is to put a decision maker in a position where he or she must decide whether to engage in economically rational but dishonest practices. In such experiments, an important methodological debate is whether one should frame the experimental instruction with neutral context or loaded context .Within the experimental economics community, framing the instruction with neutral context is the mainstream practice. It is generally agreed that altering the experimental context could have profound effects on unethical decisions. The bone of contention is whether such effects are predictable. Many past studies have contributed to this heated and ongoing debate, yet little consensus has been reached. For instance, it is presumably that context plays a major role in determining people’s decisions in bribery games—calling participants “Public officers” and “Firm owners” instead of “Player 1” and “Player 2” may lead to divergent behavioral outcomes. As a matter of fact, a considerable amount of evidence has been found to support this conjecture . HoweverThe question we address in this paper is whether the effect of context is always unpredictable. In particular, we use a laboratory bribery game as an example to examine what kind of experimental context may influence unethical decisions in a systematic, predictable way.Past studies in bribery games examine the distinctions between two types of contexts: either neutral context  or loaded context (framed with a specific background story). However, we consider such a dichotomous view insufficient: Not all the loaded contexts have the same impact on decisions. Extensive evidence suggests that emotional responses triggered by the context alter people’s behavior. It is worthwhile to take account of how people’s real-life experiences may influence their perceptions of the loaded contexts, which in turn, affect decision.From the psychology literature, All the above studies lead to the point that emotion and context jointly determine behavior. In the realm of unethical decision-making, we argue that an evocative context may alter people’s reasoning and behavior by increasing the emotional charge. For instance, in bribery games, unethical behaviors typically impose negative externalities to the society, which might bring the individual with considerable psychological costs. Adopting the evocative context may make the psychological costs more salient. When people are facing scenarios that evoke strong (negative) emotional responses, they are more likely to think about the negative consequences of their decision. Accordingly, their behaviors in the lab can better reflect what they may do in naturally occurring environments in their everyday life.In the current study, we aim to test if being familiar with a loaded context can systematically influence unethical decisions in a bribery game. In particular, we put forward that a loaded context that is closely related to the decision maker’s real-life experience is more likely to orient her to associate the hypothetical scenario with her self-concept, and therefore, evoke strong emotional responses. Consequently, the decision maker is more likely to perceive it as the “evocative context” . The decision maker is more engaged with the task and is likely to devote more attention to her decisions. Moreover, the moral standard and social norms embedded in such a context are more salient to the individual. Actions that violate certain moral obligations or injunctive norms would bring the decision maker with considerable psychological costs. Behaviorally, the decision maker is less likely to engage in dishonest practices.Hypothesis 1. Unethical behaviors should be less likely to happen in the evocative context, as compared with the meaningful context and the neutral context.On the other hand, a loaded context that is distant from the individual’s real-life experience is more likely to be perceived as the “meaningful context” . Although the meaningful context is constructed with a specific scenario, it doesn’t evoke strong emotions or significant psychological responses—It leads the decision maker to be unattached to the task. The moral standards and social norms in a meaningful (yet remote) context are ambiguous, or vague to the individual. The ambiguity in the moral standard plus the lack of personal involvement make it easier to find external justifications for a dishonest practice. To escape from the aversive state and strive for self-consistency, people would rationalize their unethical decisions. The reasoning can possibly be: “This is just a game; I would not do that in real life” , or “I’m curious about what the consequences are for choosing this; let me try it out.” Because neither the meaningful context nor the neutral context evokes strong emotions, the psychological cost of engaging in dishonest behavior should be similar in these two conditions. Thus, we would expect the meaningful context and the neural context drives similar behavioral outcome.Hypothesis 2. The meaningful context and the neutral context will lead to similar behavioral outcomes.While people’s behaviors are observable, the motives of the behaviors are not. In the field of social psychology, it has been widely accepted that behavior is guided by attitudes e.g., . In the The experiment is conducted at the school of business in Jianghan University . The experimental procedure is reviewed and approved by the research ethics committee at Jianghan University. To recruit participants, we distribute recruitment flyer to students during their self-study sessions. Students who are interested in participating will response to our recruit email on the flyer. The experimenter then sends them the electronic copy of the information sheet. Potential participants can take as much time as they need to make the decision. For students who decided to participate, we send them the invitation with detailed time and location.Upon arrival, the students will first receive the consent form, and then orally indicate whether they agree to participant. Informed consent is obtained from all participants. Next, the participant will be randomly assigned with a unique experimental identification number. This number will be used to track their decisions and responses during the experiment. Since all data are collected anonymously, we do not ask the participants to provide signed consent.In total, 340 students , which consisted of freshmen or sophomores, participated in the experiment. Among the 340 participants, 250 of them  are randomly invited to our lab to play a bribery game and followed by a short questionnaire asking about their decisions and reasoning in the game. For the rest of the 90 students , we conduct an independent attitude survey to obtain the perceived attitudes toward unethical behaviors in each game context. All data is collected anonymously. It is very important to note that each participant only participates in either the bribery game plus the corresponding questionnaire, or the attitude survey.1.To run the bribery game, we conduct 13 sessions with either 10 or 20 participants in each. It takes approximately 60 min (including check-in and payment processing) to run one session. All the sessions are conducted with computer-based materials, which are developed using z-tree . During We use a laboratory bribery game to simulate a decision-making scenario in which unethical behavior may occur. All the 250 participants who participate in the bribery game are randomized into 25 groups with ten participants in each.player 1 below), the other five participants play as granter . Each player 1 applies for five different grants ; each player 2 is in charge of allocating the 1,000 game points among the five player 1s. In addition, each player 1 is randomly paired with a player 2. Prior to the player 2’s point allocation decision, the two participants in a pair can interact with each other. We adopt a fixed-partner design to allow repeated interactions between the paired players. All the interactions are anonymous. After the role assignment, the participants start to make decisions. The process is as follow:In the beginning of the game, each participant is randomly assigned with a role. Within a group, five participants play as applicants . If violating the game rules, then the player 1 in the pair earns 1,000 points, and the other player 1s earn nothing.•After all the allocation decisions have been made, the player 1 sees feedback on how the points are allocated.•The game repeats for 15 periods with fixed partners. At the end of period 15, all participants will be reassigned with a different role, and then paired with a strange partner. The new pairs will then play the same game for another 15 periods. That is to say, if a player was the briber in the first half (period 1–15), she/he will be playing the bribee in the second half of the game (period 16–30). At the conclusion of the experiment, four periods  are randomly selected to determine the players’ payment.T denotes the number of points offered by player 1. X and Y denote the possible penalty for the player 1 and the player 2, respectively.During the iterations, a pair of participants is identified as a “rule-breaking pair” if any offer from the player 1 is accepted by the player 2. If a pair has been identified as the “rule-breaking pair” at least once, then there is a 1% chance the punishment occurs: both players’ earnings are cleared from their accounts. By the end of all the 30 periods, a lottery is played out to decide whether to punish the rule-breaking pairs. The extremely low probability reflects that most corrupt activities in reality are difficult to discover. As a matter of fact, many corrupt activities are even unobservable, and the severe penalty we impose represents the consequences arising from discovery of corrupt activities. 2. Accordingly, player 2 will play the two alternatives with the same probability (50%). Furthermore, player 2’s expected payoffs for accepting the bribe is T-Y, which is greater than 0. Therefore, player 2 will accept any bribe being offered. Given that, the expected payoffs of a player 1 who offers T points to his or her partner is (1200-2T-2X)/2, which is lower than the expected payoffs of offering nothing (1200/2 = 600). That is, not bribing is the dominant strategy for player 1. In equilibrium, player 1 does not offer a bribe to player 2, and player 2 violates the allocation rule with a probability of 50%. However, a growing literature has shown that actions that violate social norms can bring the decision maker with considerable psychological costs. We anticipate that participants’ behavior will deviate from the theoretical equilibria.Under the homo-economicus assumption, a rational decision maker is motivated by pure self-interest. The rational decision maker does not have to overcome moral qualms about unethical behavior. The theoretical equilibria of the game are not hard to obtain. Since this is a finite-repeated game, rational players will apply backward induction to solve for a unique subgame perfect Nash equilibrium. On an equilibrium path, a player 2 is indifferent between “abide by the rules” and “violate the rules”3 (the familiar-context treatment below). In the second treatment, the game is presented as a competitive bidding scenario among firms (the unfamiliar-context treatment below). In the third treatment, the game is presented in an abstract form without any specific scenario or role . Three treatments are conducted with the same bribery game framework. The treatments only vary in the experimental instructions. In the first treatment, the game is presented as a scholarship allocation scenario in a collegeSince all participants are college students, we conjecture that the college scenario is more likely to be perceived as an evocative context. Unethical decisions in this context will trigger strong emotional responses, bringing the decision maker considerable psychological costs. Consequently, corrupt conduct  should be less likely to happen in the familiar-context treatment.Another question we are curious about is whether the unfamiliar-context treatment and the neutral-context treatment may lead to different behavioral results. As discussed earlier, a meaningful but not evocative context will not trigger emotional responses. The participants in the meaningful (yet unfamiliar) context should bear the same psychological costs as in the neutral context. As a result, we conjecture that the unfamiliar-context treatment and the neutral-context treatment will produce the same behavior.4.In addition to the laboratory bribery game, we also conduct an independent attitude survey to measure students’ attitudes toward unethical behaviors. In the survey, we present the bribery relationship to the respondents, and then ask them to indicate their attitude on a 7-point Likert scale. Similar to the laboratory bribery game, the same interaction structure is framed with three different contexts . Please see the survey with familiar context below as an exampleAccording to the college policy, the academic advisor shall split the $1,000 dollars among the five applicants. That is to say, each of the applicants shall receive an award of $200.Imagine a scholarship allocation scenario in a college. In total five students applied to the same scholarship. There are 1,000 dollars available in the award pool. All the student applicants are equally qualified. However, prior to the scholarship allocation decision, one of the five students talked to the academic advisor, sent him a gift that worth $200 (secretly and privately). As return, the academic advisor announced that student as the only person who won the scholarship, distributed all $1,000 to her. All other applicants earned nothing. The interaction between the student and the academic advisor will not be discovered by others.Please select the response that indicates the degree to which you agree or disagree with the STUDENT and the ACADEMIC ADVISOR’S activities. There is no right or wrong answer, so try hard to be completely honest in your responses. You can state your opinions accurately as the information you submit will be completely confidential.Besides, we also ask the respondents to indicate their sex. To the best of our knowledge, this is the first study that use independent attitude survey to complement laboratory bribery experiment.In total 90 participants are invited to our lab to complete the survey. The 90 students are randomized into the three different contexts (with 30 respondents in each context). We adopt a between-subjects design, each respondent only participant in one of the three contexts. Given that the survey respondents and the laboratory game participants are randomly chosen from the same population, we assume that they should have similar attitudes toward unethical behaviors in the given contexts. Our design allows us to obtain measures for attitudes that are not influenced by decisions in the laboratory bribery game. Results from the attitude survey can inform us what people perceive as the “right thing to do” in each context. Ideally, the attitudes should be able to help predict people’s behavior in the bribery game experiment.F = 0.735, p = 0.482].To analyze the survey data, we take people’s attitude toward unethical conduct as the dependent variable. The first independent variable is role, which has two levels: player 1 or player 2; The second independent variable is context, which has three levels: familiar context, unfamiliar context, and neutral context. We first perform a two-way 2 (role: player 1 or player 2) × 3  mixed measures ANOVA with repeated measures on the “role” variable (because each respondent needs to indicate their attitude toward both players). The result is presented in p < 0.001). That is, people rate player 2’s unethical behavior more negatively. We also conduct a pairwise comparison between group levels to see how context impact attitudes on each role. The result . That is, player 2 is less likely to engage in corrupt activities.In general, the frequency of a player 1’s bribery attempt is 37% across all treatment, and the frequency of a player 2 violating the rule when allocating resources is 14.33%. The difference is statistically significant . No evidence suggests that the player 1’s bribery rate in the unfamiliar-context treatment is significantly different than in the neutral-context treatment (Fisher exact test p = 0.4089). p = 0.0480), and 17.27% in the neutral-context treatment . In the experiment, some of the player 1s may have selected the bribery option by mistake (or perhaps to become familiar with the game). Among all player 1s in the familiar-context treatment, 43% made bribery attempts no more than 1 time (out of 15 periods); this number is 20% in the unfamiliar-context treatment , and 25.45% in the neutral-context treatment . Moreover, the proportion of participants who constantly bribe the partners is the lowest in the familiar-context treatment (Fisher exact test p < 0.001).The frequency of a player 1’s bribery attempt is 31.13% in the familiar-context treatment, 39.81% in the unfamiliar-context treatment, and 41.83% in the neutral-context treatment. Fisher exact test results indicate that the familiar-context treatment has the lowest bribery rate .We then compare the outcomes in the unfamiliar-context treatment and the neutral-context treatment. We do not find any significant differences (proportion of participants who never offer bribe: p < 0.0001). The player 2s in the familiar-context treatment are also much more likely to abide by the rules than those in the neutral-context treatment (Fisher exact test p < 0.0001). The proportion of participants who never violate the rule is 17.50% in the unfamiliar-context treatment and 30% in the neutral-context treatment. Again, the difference is not statistically significant (Fisher exact test p = 0.147).5 about their decisions and reasoning in the bribery game. According to the questionnaire, 54% of the participants in the familiar-context treatment indicate that corrupt behaviors are typically disapproval in the college context. Among them, only 6% engaged in corruption in the experiment.Upon completion of the bribery game, all the participants are asked to complete an open-ended questionnairep < 0.0001) and 53.20% in the neutral-context treatment . Moreover, the player 2s in the familiar-context treatment are more likely to reject the bribery from the other person (p < 0.0001) and 77.12% in the neutral-context treatment .Next, we examine the interactions between the player 1 and the player 2 in a pair. We find that a reciprocal relationship between the two players is less likely to be established in the familiar-context treatment . Specifir person . In aggrIn addition, we notice that some player 2s violate the game rule without an offer from the player 1. Such behavior could be understood as “signaling.” The essence of bribery relationship is a mutual exchange of favors relying on trust and reciprocity. Since the two individuals in a pair may interact with each other repeatedly, in early stage of the game, the player 2 may have an incentive to signal the player 1 that he is interested in establishing such relationship (in the hope that the player 1 will start to offer bribe in later interactions). From To further examine whether the familiar context is inversely predicting the probability of engaging in corruption, we perform several regression analyses. In particular, consider the following random effect model:where:y1it is player 1’s bribery decision at period t. yit1 = 1 if individual i offers a payment to the other person in period t and yit1 = 0 if otherwise.familiari and unfamiliari are dummy variables, they indicate if individual i is in a particular context. We use the neutral context treatment as the compare group.malei is a dummy variable indicates if individual i is male.Uit is the individual-specific random effect .it is the error term.εα is the constant term.We first use the model above to estimate how the contexts affect player 1’s decisions, results are reported in column (1) in Following that, we conduct a similar analysis for the player 2s. In addition to the existing independent variables, we add the total amount of points being offered to the model, because player 2’s decision might be influenced by how much payment was offered. Accordingly, the model becomes:where:y2it is player 2’s decision at period t. yit2 = 1 if individual i violates the allocation rule at period t and yit2 = 0 if otherwise.offerit represents the amount of point being offered in period t.All the other independent variables are the same as in the previous model. We also change the model specification by adding periods and groups as controls. The estimation results are shown in column (5)—column (7) in As familiar male, and unfamiliar male), and then estimate the parameters. Regression results with the interaction terms are reported in column (4) and column (8) in Lastly, we are interested in if there is any interaction between the context effect and the gender effect. We then add the interaction terms of the gender and the contexts into the models . Further, we find that although both the familiar context and the unfamiliar context are heavily loaded with suggestive words and background stories, the former clearly evoke stronger emotional responses. When we compare the attitudes in the unfamiliar context and the neutral context, we do not see statistically different outcomes. Result from the pairwise comparison analysis indicates that the negative attitudes are amplified by the familiar  context among the student respondents. Moreover, we find the students hold stronger negative attitudes toward player 2’s unethical behavior. Result from the mixed measures ANOVA shows that there is no interaction effect between the context variable and the role variable. Note that the survey respondents and the bribery game participants are randomly chosen from the same population, their attitudes toward bribery should be similar. Hence, we anticipant the results from the attitude survey can help predict behavior in the lab. First of all, we anticipate that the player 2s should be less likely to engage in corrupt activities than the player 1s; Secondly, we predict that the participants in the familiar-context treatment should be less likely to engage in unethical behavior; Thirdly, we expect that the unfamiliar-context treatment and the neutral-context treatment should lead to similar behavior outcome.Findings from the laboratory bribery game confirmed all these predictions. The experimental data suggest that the possibility of engaging in unethical behavior  is obviously, in a statistical sense, the lowest in the familiar-context treatment, for both the player 1s and the player 2s. The unfamiliar-context treatment and the neutral-context treatment produce the same behavior. Observations from the bribery game, together with evidence from the attitude survey, suggest that in unethical decision-making experiments, emotional responses evoked by the context can be used to explain participants’ behavior. Since the familiar context evokes the strongest emotional responses among all the contexts, the norm-consistent behaviors  are more predictive in the familiar-context treatment than in the others.With this insight, let’s try to reconcile the mixed findings from past studies. A major limitation of the current study is that the experimental design cannot fully reveal the mechanism underlying context effect in unethical decision-making experiments. For instance, there are at least two other possible explanations for the observed results. First, it is possible that the familiar context amplifies the cognitive dissonance evoked by engaging in corrupt activities. A key element that determines the intensity of the dissonance is personal involvement—the more attention one devotes to the unethical decision, the greater the dissonance experienced. As Elliot n = 40) is still sufficient for the statistical tests we used. Unbalanced sample may also cause unequal variances between samples. To address this concern, we compared the variances of bribing decisions in the familiar-context treatment and the unfamiliar-context treatment and find no significant difference. To the second point, the unequal number of male and female is caused by both the gender imbalance of the school and our recruitment strategy. At Jianghan University (where the experiment was conducted), female students account for 60% of the student population. Moreover, due to our sampling strategy, it turned out female students are more likely to reply to our recruitment email. Although gender effect is not the main focus of this paper, it would be better if we can use a more representative sample to conduct the study. In future studies, it would be interesting to systematically explore how gender affect the ways people interpret contexts.Unbalanced sample is another limitation of this paper. In particular, the sample we collected is unbalanced in two senses: First, the number of participants in the unfamiliar-context treatment is fewer than the other two treatments ; Second, female participants account for 73% of the sample. To the first point, the highly unbalanced participant number is caused by administrative reasons that out of our control. Such sample may jeopardize the power of the statistic tests, especially when the variables of interest have different variances across treatments. The good news for us is that even in the unfamiliar-context treatment, the sample size  can give the student participants a more self-relevant, emotional experience than the unfamiliar context (bidding competition in business setting). This implies that with participants who is more familiar with the bidding competition in business setting but less familiar with academic setting, the contexts may lead to different behavior patterns. In the future, we hope to test our theory with different samples.Social scientists from different fields  apply various approaches to investigate the motivation of dishonest behavior in games, yet interdisciplinary cooperation in this area is surprisingly rare. This lack of communication may result from the disagreement on some issues concerning fundamental research methodology.Our research contributes to one of the persistent, but still far from settled questions on experimental methodology: what is the role of experimental context in laboratory unethical decision-making research? In economics, it has become standard to present the experimental tasks using the neutral-context instructions, even in the experiments that emphasize the values and ethics embedded in the context. Because people worry about the loaded-context instructions may impact behavior in an unpredictable manner. Past studies in bribery games show that the loaded context alters people’s behavior in some cases but produces the same result as the neutral context in others. Nevertheless, using loaded-context instructions has clear advantages. For instance, the participants can better learn the experimental tasks and be more engaged; the experimenters can explicitly associate the loaded contexts with the research questions to better understand participants’ motivation. By identifying factors through which the loaded context impacts behavior, we can actually use the properly framed context as a way to gain ecological validity.We do not think our results should be seen as a whole rejection of the neutral-context design approach. Instead, the point we are trying to make is that we should always keep our experimental design as simple as possible, but not simpler. In reality, moral obligation and emotional responses play vital roles in unethical decision making; therefore, it is important to simulate these non-monetary payoffs while conducting laboratory experiments. In unethical decision-making experiments, we think it is inappropriate to assume that experimental manipulation can be studied apart from the cultural and social norms that define its meaning. When the values and ethics associated with the contexts are unclear to participants, we put the ecological validity and reproducibility of the experiment at risk.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The studies involving human participants were reviewed and approved by the Jianghan University, Committee of Research Ethics. Written informed consent for participation was not required for this study in accordance with the national legislation and the institutional requirements.SW designed and conducted the experiment and performed the statistical analysis. TC and SW together wrote the manuscript. Both authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


This study was conducted according to Arksey and O'Malley's framework. To investigate the evidence on the effects of Kinect-based rehabilitation, a search was executed in five databases  from 2010 to 2020.  Thirty-three articles were finally selected by the inclusion criteria. Most of the studies had been conducted in the US (22%). In terms of the application of Kinect-based rehabilitation for stroke patients, most studies had focused on the rehabilitation of upper extremities (55%), followed by balance (27%). The majority of the studies had developed customized rehabilitation programs (36%) for the rehabilitation of stroke patients. Most of these studies had noted that the simultaneous use of Kinect-based rehabilitation and other physiotherapy methods has a more noticeable effect on performance improvement in patients.  The simultaneous application of Kinect-based rehabilitation and other physiotherapy methods has a stronger effect on the performance improvement of stroke patients. Better effects can be achieved by designing Kinect-based rehabilitation programs tailored to the characteristics and abilities of stroke patients. Stroke is the second most prevalent cause of mortality and disability worldwide. The prevalence of stroke will increase due to the aging of the population. Moreover, stroke happens in a larger number of young populations in low- and middle-income communities . It damaRehabilitation in stroke is a purposeful process to help the patients regain and retain their social, intelligence, mental, and physical abilities while also helping them perform their daily and social activities with some level of independence , 5. RehaThe use of technology in rehabilitation is increasing rapidly. One of these technologies is video games, which is known as an effective intervention in rehabilitation. Video games are a useful solution for stroke patients who are unable to perform daily activities in the real environment and also motivate and encourage people to do rehabilitation exercises and improve motor function in stroke patients . Video gAnother feature of Kinect for patients is performing rehabilitation exercises at home with no need for a physiotherapist . By provToday, serious games, especially exergames, are used by therapists as a tool for rehabilitation purposes , 27. ExeBased on the findings of systematic reviews on the clinical and technical evaluation of the Kinect sensor, the use of this rehabilitation system is acceptable due to its cost-effectiveness and adequate precision in movement tracking , 31, 32.What is the effect of Kinect-based rehabilitation systems on the performance of stroke patients?What is the main application domain of a Kinect-based rehabilitation system for stroke patients?What are the limitations of utilizing Kinect-based rehabilitation systems for stroke patients?The aim of scoping review is to determine, retrieve, and summarize the research pertinent to special issues to identify the key concepts supporting a research domain and the major sources and available evidence . ScopingThe current scoping review adopted Arksey and O'Malley's methodology . Based oEnglish articles published in peer-reviewed journals and conferences with an available full textArticles published from 1 January 2010 to 13 October 2020Articles using Kinect-based rehabilitation for stroke patientsArticles clinically evaluating and using Kinect for tracking movements and interactions in the rehabilitation systemThe main inclusion criteria for this review were as follows:Review articles, case reports, case studies or study protocols, letter to the editor, correspondences, and conference papers (absence or lack of access to the full text)Articles in languages other than EnglishArticles merely evaluating the accuracy and validity of Kinect and not clinically evaluating the use of Kinect for improving the conditions of stroke patientsArticles examining conditions other than strokeFurthermore, the most important exclusion criteria for this review were as follows:Articles were searched in five online databases . The search strategy comprised MeSH terms and other relevant keywords, and the two groups of terms were combined using Boolean operators AND and OR. The search was limited to the 2010-2020 period since Microsoft's first generation of Kinect sensors was introduced in November 2010 . The keyThe electronic search was performed in the five mentioned databases. Also, hand-searching was performed in Google Scholar, and 58 articles were retrieved. The retrieved articles were then inputted to EndNote, and the duplicates were identified and removed by using the software. Subsequently, the titles and abstracts of the articles were reviewed by two authors according to the research questions and objectives. In the next step, the full text of the papers was examined by two authors concerning the inclusion and exclusion criteria. Any disagreements between the authors were resolved by discussions.Data extraction was executed by using a form including the first author's name (reference), year of publication, country, the domain of rehabilitation, type of rehabilitation program , main findings, and technical limitations of the Kinect-based rehabilitation program. The data were obtained by two authors, and disagreements were resolved upon discussions. Finally, the data extracted from the articles were inputted to Microsoft Excel for classification, synthesis, and reporting of the results.Totally, 1196 articles were retrieved by searching in the databases. In the next step, by using EndNote, 184 duplicates were removed, and 954 articles remained. Subsequently, the titles and abstracts of the papers were reviewed, 856 papers were removed, and 98 remained. Then, the full text of the articles was examined, 64 articles were removed, and finally, 34 articles were included in this scoping review. n = 7, 22%), followed by Spain and South Korea .The data extracted from the articles were recorded in the data extraction form . The majn = 8).Following the invention of Kinect in 2010, the number of studies on the use of Kinect-based rehabilitation programs for stroke patients increased . Howevern = 22), followed by balance (n = 10), cognitive rehabilitation (n = 3), lower body (n = 2), and functional recovery (n = 2)  .In terms of the effects of Kinect-based rehabilitation programs, the majority of the studies had evaluated it as positive leading to the performance improvement of stroke patients –48. MostFurthermore, the results revealed that the use of a Kinect-based rehabilitation program increases the repetitions of the movements, improves motivation, promotes the quality of life, and enhances adherence to treatment , 61, 62.The results of this study showed that 56% of the articles were in the field of upper limb rehabilitation. Patients' movements in the study were measured using Fugl-Meyer Assessment and Brunnstrom Motor Recovery Stage, which used Kinect-based rehabilitation games to improve patients' shoulder, elbow, wrist, and finger movements and ultimately to improve daily activities. There was an increase in patients' quality of life.The results of this study showed that 26% of the articles were in the field of balance rehabilitation. In the studies studied using Box and Block Test, Barthel Index, and Berg Balance Scale, it was measured that the use of Kinect-based rehabilitation games improved patients' balance.The results of this study showed that 8% of the articles were in the field of cognitive rehabilitation. The results of the studies showed that the use of Kinect-based rehabilitation games improved patients' attention, spatial awareness, and generalized cognitive functioning.The results of this study showed that 5% of the articles were in the field of lower limb rehabilitation. In these studies, the Timed Up and Go Test and Fugl-Meyer Assessment erew used to measure lower limb movements, and the results showed that it improved lower limb movement.n = 13, 38%), while the other studies had utilized commercial Kinect-based programs . Among the studies using commercial Kinect-based programs, technical limitations mostly included not challenging enough, lack of customization to the patients' abilities, complexity and difficulty of use, dependency on the therapist due to complexity, and the content of the programs being radically different from the daily activities of stroke patients [In terms of the type of rehabilitation program used for stroke patients, the majority of the studies had designed the rehabilitation program tailored to the status and abilities of the patients (patients , 56, 68.patients , 61, 65.This scoping review investigated the effect of using Kinect-based rehabilitation systems on the performance improvement of stroke patients, the rehabilitation domain, and technical limitations. The reviewed articles were published since 2010, when Microsoft-invented Kinect was examined . The resThe most important feature of Kinect is that there is no need for any wearables during rehabilitation . This feMost studies had also mentioned that, compared to the use of routine treatment methods alone, the simultaneous application of Kinect-based rehabilitation and other physiotherapy methods has a stronger effect on the performance improvement of stroke patients. Regarding the positive outcome of simultaneous use of Kinect-based rehabilitation and other physiotherapy methods, the results of the present research are consistent with those of other papers , 74.Despite all these advantages, some studies utilizing commercial Kinect-based programs reported different effects on the performance improvement of stroke patients; the reason was the limitations of these programs such as not challenging enough, not being customized to the patients' abilities, complexity, dependency on the therapist due to the complexity of the games, and the difference between the content of the games with patients' daily activities , 57, 68.On the other hand, some studies had developed games customized to the abilities of stroke patients and reported positive effects on their motor recovery , 61, 62.To promote neural plasticity in rehabilitation programs, tailor-made rehabilitation systems are promising tools for patients. Furthermore, appropriate feedback should be provided to actively engage patients in better motor recovery. One of the essential elements in rehabilitation programs is to keep the patients motivated and engaged. In this way, caregivers should provide suitable feedback to correctly execute the exercise. The caregiver should change the different parameters of exercise to make it challenging and simultaneously possible for executing.Since the therapist cannot regularly monitor and evaluate the patient's condition in Kinect-based rehabilitation systems, using different sensors such as brain and body wearable sensors can receive more data to help better assess the patient. Captured data should be interpreted and presented by utilizing graphs to simply be understood by physicians. To enhance the efficacy of rehabilitation systems, the user interface should be designed by considering both patients' restrictions and caregivers' needs.One limitation of the current study was the diversity in the type of studies and the small samples of some studies, which pose problems in drawing definitive conclusions about the positive effects of Kinect-based rehabilitation on the motor recovery of stroke patients. Lack of access to the full text of some papers was another limitation. About the positive effect of customized Kinect-based rehabilitation programs which are tailored to the abilities of stroke patients, it is suggested more research be conducted on the design framework of such programs and their effects on the motor recovery of stroke patients. Furthermore, developing the rehabilitation systems should concentrate on a range of complex factors such as patients living environment, social environment, different challenges of daily living, and patients' skills in using various technologies. Furthermore, developing systems with a concentration on supporting personal goals and performing the rehabilitative exercise in a competitive atmosphere may increase progress over time. It will be necessary to conduct different clinical trials in large sample size, as well as different devices to determine which factors have a greater effect in achieving a better outcome. Furthermore, performing a meta-analysis study to investigate whether rehabilitation programs are beneficial in improving patients function in stroke is essential.Because of some limitations such as the costs of rehabilitation, the long distance to rehabilitation centers, lack of access to such centers, patients' motor limitations, and commute problems, patients with stroke lose motivation to follow treatment. The application of Kinect-based rehabilitation is an effective solution for creating motivation and improving adherence to rehabilitation programs in stroke patients. Kinect-based rehabilitation will be more effective on the performance improvement of these patients if used as a complementary technique in combination with other rehabilitation methods. Furthermore, to promote effects on motor recovery, it is essential to pay attention to the design of rehabilitation programs customized to the abilities of stroke patients.


Based on winning coalitions, the PHI θ index was introduced by Bertini et al. in  in algorithms to compute the PHI θ index if at least one of the players is a null player. We also discuss some relationships among the Holler index, the PHI θ index, and the gnp index  proposed by Álvarez-Mozos et al. in (This paper proposes a new representation for the Public Help Index t al. in . The goat al. in . In the literature, a power index is defined as a measure that is meant to assess the a priori power, as the influence, or as the payoff expectation of players in a simple game.θ  introduced by Bertini et al.  based on minimal winning coalitions. The PGI index was introduced by Holler . Hence, as Bertini and Stach  or the Z index introduced by Nevison (KB and Z) are not only based on winning coalitions and closely related to the Banzhaf .The PHI äuninger  index , reducing the power of others. However, considering the consumption of public goods and social help, we cannot exclude free-riders in many cases . Conventional methods that measure the voting power of players, such as the Banzhaf (θ index is solidary with weak players (not only null players), while the mentioned above indices are not.PHI  Banzhaf , Shapley Banzhaf  indices,θ index represents a solidary with the “weak” brother  proposed by Álvarez-Mozos et al.  by taking some desirable properties of power indices into account. With Sect. The rest of the paper is structured as follows. In Sect. cooperative n-person game is a pair  where n players and v is real-valued function N. Each coalition and N is called the grand coalition. Hereafter we call both  and v a game since N is inherent in the definition of v.worth of coalition S in game v. |S|= s denotes the cardinality of S, so |N|= n. A cooperative game is monotonic if A simple game is a monotonicwinning coalitions, while those with losing coalitions. By W, we denote the set of all winning coalitions in simple game . Any simple game may be unequivocally described by its set of winning coalitions. Wi stands for the set of all winning coalitions that contain player i. A simple game is proper if the following condition holds: SN, we denote the set of all simple games on N.A ee Stach , for exacritical in minimal winning coalition if all Wm, we denote the set of all minimal winning coalitions, and i.A player null player if, for all coalitions, marginal contribution of player i to null player free winning coalition if i. Like W and Wm, A player N, v) is called a weighted game and is represented by qA simple game .In this section we give the definitions of the three power indices considered in this paper: the θ  is givegnp power index  was defined in , y Holler . For allFor an axiomatic characterization of the Public Good Index, see Holler and Packel . Moreoveθ, gnp, and h) by taking these properties into consideration.In this section we provide definitions of some well-known and desirable properties of power indices in simple games. In Sect. f satisfies the following:efficiency property if, for all , the null player property if N, v) and each null player the null player removable property if, for all simple games v by eliminating the null players, the symmetry (anonymity) property if, for all simple games , each player the non-negativity property ifN, v) and the dominance  property if, for all weighted games the donation property if, for two weighted games v = v’ = the redistribution property if, for two weighted games v = v’ = v’ arising from v by the redistribution of weights  can be seen as the union of two disjoint subsets: Let us fix an k null players, we can obtain All winning coalitions with null players i is a null player in game W. Thus, in total, i takes part in i belongs to k null players belong to Let us assume that player i is a non-null player in game W, i takes part in i belongs to Now, let us assume that θ index for all From the above considerations for null and non-null players, we have We can still simplify the above formula by dividing the numerator and denominator of the first part , the above Formula  with k null players, we can easily separate the part of the power assigned by PHI θ to all null players from the part assigned to non-null players (see Corollary 1).Thanks to (1), for a given simple game (TPNP) is equal to.If If i we have The demonstration is immediate from Formula  .As a consequence of Corollary 1, we can also immediately calculate the total power assigned by the PHI TPNNP) is equal to.If The demonstration immediately follows from Formula  by summiθ and gnp as well as to show the application fields in which the θ index is suitable.In this section, we present some examples to illustrate the use of new Formula  to compaθ can be calculated from both the original formula and the new one. However, when we would like to have an algorithm to calculate the PHI θ index in an automatic way, then Formula  of a certain country. Player 1 . According to Public Help Index θ index satisfies the efficiency property  quantifies the amount of memory space that is required by an algorithm to run as a function of the length of the input  and Banzhaf . The rolLet us turn to the COVID-19 example and modify it a bit considering only two groups of players: Polish citizens, and the set of null players. The set of null players can represent groups of immigrants, unemployment, and closed businesses by COVID-19, for example. Each Polish citizen has weight equal to 1, and each null player has weight equal to 0. As was mentioned before in this kind of problem all players should have rights to have a medical service, access to the vaccine (where available), etc., and the surplus would be shared among the non-null players .θ index to share the total pandemic budget. Let us assume that in this weighted game, we have m Polish citizens (m is on the order of 37–38 millions) and k null players  that m is odd and the quota is placed at q = (m + 1)/2. Then, the game can be represented in the following way:The θ index for each player in this game are easy using both, the new and former formulas. We use Eq. (i (Polish citizen). In this example, all null player free winning coalitions must have at least m is an odd number. For each non-null player i, m is an odd number. Therefore, using Formula  = 1). Player 3 is a disabled person and can contribute nothing to any coalition. The v({i}) = 0 for each player i = 1, 2, 3. Therefore, v = 1 and v = v = 0.(“Three Brothers”). Players 1, 2, and 3 are brothers who live together. Players 1 and 2 can make a profit of one unit together  index distribution  seems to be a “better” solution in this case than that which is given by the gnp, Banzhaf, or Shapley-Shubik indices: .“Should the disabled brother leave his family?” This was a question that was posed by Nowak and Radzik (1994). If Players 1 and 2 take responsibility for their “weaker” brother (Player 3), then the PHI θ and gnp indices were born as modifications of the Holler index (h). In this section, we compare the θ, gnp, and h indices by taking the ranges of the indices and some desirable properties of the power indices into account. All of these indices have the same structure, but they based on different families of coalitions: winning coalitions (W), null player free winning coalitions (Wn−), and minimal winning coalitions (Wm), respectively. Given a player set N, each of these sets unequivocally determines the simple game and W or as an extension of The PHI h, θ, and gnp) are non-negative and relative .By definition, all of the indices considered . The h e Holler , for exai by the PHI θ index depends on the number of null players in a game . So, thθ satisfies it  are not critical in any coalition. Moreover, in game v2, we have only one null player free winning coalition: {1, 2}, which is also a unique minimal winning coalition. Thus. h, θ, and gnp indices. So, all of these indices violate the donation property.Informally, the donation property states that a player who donates votes to another player (recipient) should not increase his voting power. Bertini et al.  presenteh, θ, and gnp indices present a failure of the donation property, so they will also present a failure of the redistribution property. Moreover, Felsenthal and Machover  we can formulate the following corollary.Note that, for a given θ index a null player i can achieve in game v.The minimum PHI The demonstration immediately follows from Theorem 5.gnp index into account, we see that this index is closer to the Holler index than to the PHI θ index. The difference between these indices lies in the dominance property. Meanwhile, the θ and gnp indices differ in their null players, null player removable, and positivity properties.Table θ .Moreover, we compare the θ index for games with several levels of approval, for example. The next idea is a modification of θ to simple games with the known probability distribution over coalitions and then study the properties of the obtained index, see Freixas and Pons (One of the further developments is following the ideas of Freixas , 2020 anand Pons , for exa


Neoplasia-associated EMRCs showed a mean Ki67 labeling index of 12.6% (range 0–30%); with nuclear atypia in 16/20 (80%) cases; diffuse p16 expression in 15/20 (75%) cases; and heterogeneous ER, PR, and vimentin expression. Compared to the associated neoplasia, EMRCs showed a lower Ki67 expression (p < 0.001) and higher p16 expression (p < 0.001). No EMRC case showed mitotic activity, PTEN loss, MMR deficiency, nuclear β-catenin, p53-mutant pattern, Napsin A, or AMACR expression. No significant differences were found between neoplasia-associated and neoplasia-unassociated EMRCs. Complex metaplastic lesions showed a lower Ki67 expression than EMRCs (p = 0.044) and PTEN loss in 5/8 cases, even in the absence of nuclear atypia. In conclusion, neoplasia-associated simple EMRCs may show evident atypia and a worrisome immunophenotype, but no data support their involvement in endometrial carcinogenesis. Architectural complexity appears as a crucial factor to identify precancerous lesions.The aim of this study was to assess the relationship between endometrial metaplastic/reactive changes (EMRCs) and endometrial neoplastic lesions. Twenty cases of “simple” (without architecture complexity) EMRCs coexistent with endometrial malignant/premalignant lesions, twenty cases of neoplasia-unassociated EMRCs, and eight cases of complex metaplastic lesions were assessed by immunohistochemistry. EMRCs coexisted with endometrioid carcinoma ( The uterine endometrium is a unique tissue undergoing different phases of hormonal stimulation and may show several different types of altered differentiation, such as tubal, squamous, morular, and mucinous. A peculiar subgroup of endometrial metaplastic change, referred to as “reactive changes”, is characterized by cytoplasmic enlargement with clearing or eosinophilia, hobnail, or pseudopapillary appearance, and is typically found in the presence of ischaemia, desquamation, or hormonal imbalance ,2. ReactAll cases of EMRCs coexistent with endometrial neoplasia  and diagnosed in the April–September 2021 period were included. EMRCs were defined as endometrial glandular and/or surface epithelium showing cytoplasmic enlargement with clearing or eosinophilia, hobnail cells, cellular tufting, or pseudopapillation ; nuclear atypia was assessed based on nuclear enlargement and/or pleomorphism, loss of polarity, and evident nucleoli. Cases showing architectural complexity, such as glandular crowding and true papillation, were excluded. Eight cases of complex metaplastic lesions and 20 cases of EMRCs with no associated neoplasia, diagnosed in the same period, were included as the controls. Only hysterectomy specimens were included. All cases were reviewed by a panel of five pathologists with expertise in gynecological pathology .Immunohistochemistry was performed according to previously described methods  and invop-value < 0.05. Data analysis was performed using Statistical Package for Social Science (SPSS) 18.0 package .Dichotomous variables were compared by using Fisher’s exact test, while continuous variables were compared by using Student’s T test, with a significant n = 10), atypical endometrial hyperplasia (n = 5), clear cell carcinoma (n = 3), and serous carcinoma (n = 2) were identified (p = 0.741); PR showed a score 1–2 in 14/20 EMRCs (70%) and 9/20 associated neoplasia (45%), with no significant difference (p = 0.200).Twenty EMRCs associated with endometrioid carcinoma ; in two cases, the Ki67 LI of EMRCs was equal to or higher than that of the coexistent neoplasia (p = 1). Fifteen out of twenty EMRCs (75%) showed a diffuse expression of p16, out of which five (25%) were block-type (p < 0.001). No case of EMRC shared the immunohistochemical markers of the associated neoplasia, including PTEN loss (n = 10) (n = 4), p53 mutant-type expression (n = 4), β-catenin nuclear expression (n = 2), Napsin A positivity (n = 3), and AMACR positivity (n = 2). However, two EMRC cases showed a p53 expression in >50% of cells, mimicking a wild-type pattern (p = 0.044); no complex metaplasia case showed p16 block-type expression. The immunohistochemical features of all the included specimens are reported in Ki67 levels were also heterogeneous, with LI varying from 0% to 30%; the mean LI level was significantly lower in EMRC than in associated neoplasia  c, MMR de pattern d. Moreov pattern ; complexThis study showed that neoplasia-associated EMRCs often display nuclear atypia with a diffuse p16 expression, a p53 expression that may mimic a mutant pattern, and a variably increased Ki67 LI; however, these EMRCs showed neither a mitotic activity nor any marker of endometrial carcinogenesis. Moreover, neoplasia-associated EMRCs did not differ from neoplasia-unassociated EMRCs. On the other hand, complex metaplastic lesions showed PTEN loss, even in the absence of evident nuclear atypia and of a high Ki67 expression.The wide spectrum of morphologic alterations encountered in endometrial pathology has long since caused diagnostic issues. The first study that addressed the issue of endometrial metaplasia was conducted by Hendrickson and Kempson in 1980. The authors reported several different metaplastic changes that might mimic malignancy; they proposed classifying endometrial metaplasia into seven categories: morular/squamous, papillary, ciliated/tubal, eosinophilic, mucinous, hobnail, and clear cell . SubsequPrevious studies assessed the association between EMRCs and carcinogenesis. EMRCs may superimpose to atypical hyperplasia and endometrioid carcinoma; in these cases, architectural complexity is crucial to identify premalignant/malignant lesions . RegardiWe found that neoplasia-associated EMRCs can show evident nuclear atypia with nucleomegaly, pleomorphism, and nucleolation; such atypia might rise the suspicion of serous carcinoma. This issue has prompted several authors to assess immunohistochemical markers to differentiate between the two entities. While most authors have reported that the immunophenotypes of EMRCs and serous carcinoma are completely different, other authors have reported that it is overlapping ,13,14,15Therefore, EMRCs may show a combination of nuclear atypia and altered immunophenotyped, which may be worrisome to pathologists; this highlights that immunohistochemistry should be interpreted carefully in these lesions. However, mitotic activity was not observed in any EMRC. Furthermore, we assessed several markers of endometrial carcinoma, including PTEN loss MMR deficiency, nuclear β-catenin expression , p53-mutant-pattern (a marker of serous carcinoma), Napsin A, and AMACR positivity (confirmatory markers of clear cell carcinoma) , and nonIt should be remarked that EMRCs may be heterogeneous with regard to morphological and immunophenotypical features. For instance, immunohistochemical markers such as p16, p53, and Ki67 may be highly expressed in some glands and not in other ones within the same EMRC area. Such heterogeneity may be crucial to differentiate EMRCs from malignant/premalignant lesions. Therefore, submitting additional sections can be helpful when only little foci of EMRCs are observed and the morphological/immunophenotypical features are worrisome. The submission of the entire endometrial cavity appears appropriate in cases of complex metaplastic lesions, given their analogies with atypical endometrial hyperplasia.The main limitation of our study is the lack of follow-up data, as all included specimens were derived from hysterectomies. Determining the biological behavior of EMRCs clearly is impossible for cases that already have a coexistent neoplasia. Regarding neoplasia-unassociated EMRCs, long-term follow-up data from the literature suggest that they do not evolve into overt premalignant/malignant lesions . FurtherEMRCs that accompany endometrial carcinoma and AEH may show evident nuclear atypia and an aberrant phenotype that might mimic serous carcinoma; however, the lack of mitotic activity and of carcinogenesis-related markers and the similarity with neoplasia-unassociated EMRCs support that they are benign reactive change. By contrast, complex metaplastic lesions often show PTEN loss, even in the absence of evident atypia and of increased proliferation, supporting that architectural complexity is a crucial factor to define the premalignant potential of EMRCs. Further studies are encouraged in this field, with particular regard to the precursors of non-endometrioid carcinomas.