A Review of Case-Based Decision Theory <s> CBDT Model and Its Evolution <s> This paper suggests that decision-making under uncertainty is, at least partly, case-based. We propose a model in which cases are primitive, and provide a simple axiomatization of a decision rule that chooses a "best" act based on its past performance in similar cases. Each act is evaluated by the sum of the utility levels that resulted from using this act in past cases, each weighted by the similarity of that past case to the problem at hand. The formal model of case-based decision theory naturally gives rise to the notions of satisficing decisions and aspiration levels. <s> BIB001 </s> A Review of Case-Based Decision Theory <s> CBDT Model and Its Evolution <s> In the light of the case-based decision theory (CBDT), this paper proposes that the attributes' weights corresponding to different acts should also be different. Based on this idea, the concept of case similarity with alterable weights is put forward, a decision-making method introduced, and optimization model for weights setting presented. Meanwhile, this method is applied to the case of examining vehicles' technical state under accident, and it proves effective. <s> BIB002 </s> A Review of Case-Based Decision Theory <s> CBDT Model and Its Evolution <s> We experimentally investigate the disposition of decision makers to use case-based reasoning as suggested by Hume (An enquiry concerning human understanding, 1748 ) and formalized by case-based decision theory (Gilboa and Schmeidler in Q J Econ 110:605–639, 1995 ). Our subjects face a monopoly decision problem about which they have very limited information. Information is presented in a manner which makes similarity judgements according to the feature matching model of Tversky (Psychol Rev 84:327–352, 1977 ) plausible. We provide subjects a “history” of cases. In the $$2\times 2$$ 2 × 2 between-subject design, we vary whether information about the current market is given and whether immediate feedback about obtained profits is provided. The results provide support for the predictions of case-based decision theory, particularly when no immediate feedback is provided. Copyright Springer Science+Business Media New York 2015 <s> BIB003 </s> A Review of Case-Based Decision Theory <s> CBDT Model and Its Evolution <s> We evaluate repeated decisions of individuals using a variant of the case-based decision theory (CBDT), where individuals base their decisions on their own past experience and the experience of neighboring individuals. Looking at a range of scenarios to determine the successful outcome of a decision, we find that for learning to occur, agents must have a sufficient number of neighbors to learn from and access to sufficiently independent information. If these conditions are not fulfilled, we can easily observe herding in cases where no best decision exists. <s> BIB004 </s> A Review of Case-Based Decision Theory <s> CBDT Model and Its Evolution <s> This paper starts out from the proposition that case-based decision theory (CBDT) is an appropriate tool to explain human decision behavior in situations of structural ignorance. Although the developers of CBDT suggest its reality adequacy, CBDT has not yet been tested empirically very often, especially not in repetitive decision situations. Therefore, our main objective is to analyse the decision behavior of subjects in a repeated-choice experiment by comparing the explanation power of CBDT to reinforcement learning and to classical decision criteria under uncertainty namely maximin, maximax, and pessimism-optimism. Our findings substantiate a predominant significantly higher validity of CBDT compared to the classical criteria and to reinforcement learning. For this reason, the experimental results confirm the suggested reality adequacy of CBDT in repetitive decision situations of structural ignorance. <s> BIB005 </s> A Review of Case-Based Decision Theory <s> CBDT Model and Its Evolution <s> We introduce a computer program which calculates an agentʼs optimal behavior according to case-based decision theory (Gilboa and Schmeidler, 1995) and use it to test CBDT against a benchmark set of problems from the psychological literature on human classification learning (Shepard et al., 1961). This allows us to evaluate the efficacy of CBDT as an account of human decision-making on this set of problems. <s> BIB006 </s> A Review of Case-Based Decision Theory <s> CBDT Model and Its Evolution <s> Abstract In this paper, we show that Case-based decision theory, proposed by Gilboa and Schmeidler (Q J Econ 110(3):605–639, 1995), can explain the aggregate dynamics of cooperation in the repeated Prisoner’s Dilemma, as observed in the experiments performed by Camera and Casari (Am Econ Rev 99:979–1005, 2009). Moreover, we find CBDT provides a better fit to the dynamics of cooperation than does the existing Probit model, which is the first time such a result has been found. We also find that humans aspire to a payoff above the mutual defection outcome but below the mutual cooperation outcome, which suggests they hope, but are not confident, that cooperation can be achieved. Finally, our best-fitting parameters suggest that circumstances with more details are easier to recall. We make a prediction for future experiments: if the repeated PD were run for more periods, then we would be begin to see an increase in cooperation, most dramatically in the second treatment, where history is observed but identities are not. This is the first application of Case-based decision theory to a strategic context and the first empirical test of CBDT in such a context. It is also the first application of bootstrapped standard errors to an agent-based model. <s> BIB007 </s> A Review of Case-Based Decision Theory <s> CBDT Model and Its Evolution <s> Case-based decision theory (CBDT) provided a new way of revealing preferences, with decisions under uncertainty determined by similarities with cases in memory. This paper introduces a method to measure CBDT that requires no commitment to parametric families and that relates directly to decisions. Thus, CBDT becomes directly observable and can be used in prescriptive applications. Two experiments on real estate investments demonstrate the feasibility of our method. Our implementation of real incentives not only avoids the income effect, but also avoids interactions between different memories. We confirm CBDT's predictions except for one violation of separability of cases in memory. <s> BIB008
CBDT first appeared in Discussion Paper of Gilboa and Schmeidler in 1992, they believe that a case-based approach can be adopted to make decisions under uncertain scenarios, and propose an initial CBDT model  . CBDT divides cases into three aspects: Problem, Act and Result. And it also introduces three important concepts: Similarity, Utility Level and Aspiration Level. Respectively, they are used to measure the similarity between the current and the past two cases, the utility level of the past cases using the scheme and the overall expectation level after the adoption of the scheme. The Aspiration Level is the sum of the product of similarity degree and utility level, which is the decision basis of CBDT BIB001 . The final choice of CBDT decision makers is to adopt the scheme that maximizes the expectation level. Meanwhile, there are properties (hypothesis) of comparability, monotonicity, continuity, independence and invariability of similarity degree in CBDT model  -  . If the past solution has an impact on the evaluation of the current decision cases, it is necessary to introduce the "Problem-Act Pairs", with the requirement of comparing the current Problem with the solution as a whole with the past case when calculating the degree of similarity. If the decision maker has already guessed each result in the case, the similarity of the results needs to be taken into account. In some cases, the implementation scheme accomplishes not only the immediate results, but also the possible completion of the next scheme. At this point, CBDT is extended to accomplish the Case-Based Planning. In order to preferably measure the similarity among cases and make more accurate decisions, the basic CBDT model also derived two transformations: Averaged Similarity and Act Similarity BIB001  . The Utility can be measured in two ways: the outcome tradeoff approach and the case repetition approach  .  thought that there were two attributes of Aspiration Level adjustment rules: Realistic and Ambitious. The attributes of Realistic have the following characteristics: The Aspiration Level will be adjusted according to the actual performance; The adjustment conforms to the principle of "adaptability"; Adjusting the level of expectation is "optimal" in a sense. Ambitious has two meanings: Static Ambition and Dynamic Ambition. Static Ambition sets the initial level of expectations relatively high depending on the context; Dynamic Ambition means that decision makers never lose hope and the cycle of S. Y. Hu expectation level updates never stops. Gilboa and Schmeidler believe that the Aspiration Level should be realistic and dynamic ambitious, because realistic will make the Aspiration Level converge to the local optimal, and dynamic ambition plays the role of "noise", which will make decision makers choose actions that seem inferior, but converge to the global optimal in the long run  . Zeng et al. (2007) thought that each different Action had different impacts on decision-making and should be given different Weights. Based on this, they proposed the concept of Case Similarity with Alterable Weights and tested the technical status of cars in accidents BIB002 . Despite its realistic adequacy, CBDT has not been empirically tested frequently, especially in the case of repeated decisions BIB005 . Therefore, CBDT needs to be constantly improved and normalized, both theoretically and practically. Ossadnik et al. (2012) conducted an experiment with colored spheres to empirically analyze the CBDT theory, and the results showed that the decision-making of CBDT was highly effective, which also verified the adequacy of CBDT in reality in the case of repeated decision-making with unknown structure BIB005 [10]. Grosskopf et al. (2015) accomplished the experiment of monopolistic decision-making with extremely limited information in the CBR (Case-Based Reasoning) and CBDT situations respectively, and the results support the prediction of CBDT, especially in the case that timely feedback cannot be achieved BIB003 . Pape and Kurtz (2013) tested the efficacy of CBDT by using a set of benchmark questions from psychological experiments of human classified learning   . The results showed that CBDT could accurately predict these problems and empirically tested the effectiveness of CBDT BIB006 . Guilfoos and Pape (2016) applied CBDT to the repeated prisoner's dilemma problem to predict people's cooperative behavior, which empirically tested CBDT BIB007 . Bleichrodt et al. (2017) verified the observability and falsifiability of CBDT through two real estate investment cases BIB008 . Kinjo et al. (2014, 2017) believed that under certain assumptions, CBDM (case-based Decision Model) could be converted into IPM (Idea Point Model), which was verified by data from Japanese TV series, and the results were quite consistent  [17]. Zhou et al. (2003) proposed a double-layer CBDT fuzzy decision making method based on probability theory and case-based reasoning, and used the case of movie watching decision to verify it  . Han et al. (2016) proposed a mixed multi-attribute case decision method based on Regret Theory, and verified the rationality of the method by using the PX project case  . BIB004 proposed an improved model of CBDT, that is, people can make decisions based on their past experiences and those of their neighbors, and its effectiveness was tested by Monte Carlo Model BIB004 .