We consider a task of scheduling with a common deadline on a single machine. Every player reports to a scheduler the length of his job and the scheduler needs to finish as many jobs as possible by the deadline. For this simple problem, there is a truthful mechanism that achieves maximum welfare in dominant strategies. The new aspect of our work is that in our setting players are uncertain about their own job lengths, and hence are incapable of providing truthful reports (in the strict sense of the word). For a probabilistic model for uncertainty our main results are as follows. 1) Even with relatively little uncertainty, no mechanism can guarantee a constant fraction of the maximum welfare. 2) To remedy this situation, we introduce a new measure of economic efficiency, based on a notion of a fair share of a player, and design mechanisms that are @math -fair. In addition to its intrinsic appeal, our notion of fairness implies good approximation of maximum welfare in several cases of interest. 3) In our mechanisms the machine is sometimes left idle even though there are jobs that want to use it. We show that this unfavorable aspect is unavoidable, unless one gives up other favorable aspects (e.g., give up @math -fairness). We also consider a qualitative approach to uncertainty as an alternative to the probabilistic quantitative model. In the qualitative approach we break away from solution concepts such as dominant strategies (they are no longer well defined), and instead suggest an axiomatic approach, which amounts to listing desirable properties for mechanisms. We provide a mechanism that satisfies these properties.
Forgiveness: Forgiveness is an important concept in social studies. It has also been recently adopted in designing computational systems, such as reputation systems @cite_20 . Another line of research that introduces a notion of forgiveness is the study of evolution of cooperation @cite_14 ; indeed, the famous Tit-for-Tat strategy can be viewed as employing proportional punishment and forgiveness. While game theory does not deal explicitly with forgiveness, some classical solution concepts do incorporate a possibility of error on behalf of players. A well known example is that of trembling hand perfect equilibrium (see @cite_8 ). It defines rational behavior of a player as a limit to which best responses converge once the probability of accidental" irrational behavior on behalf of other players tends to 0.
@cite_14 @cite_20 @cite_8
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Pro-social punishment and exclusion are common means to elevate the level of cooperation among unrelated individuals. Indeed, it is worth pointing out that the combined use of these two strategies is quite common across human societies. However, it is still not known how a combined strategy where punishment and exclusion are switched can promote cooperation from the theoretical perspective. In this paper, we thus propose two different switching strategies, namely, peer switching that is based on peer punishment and peer exclusion, and pool switching that is based on pool punishment and pool exclusion. Individuals adopting the switching strategy will punish defectors when their numbers are below a threshold and exclude them otherwise. We study how the two switching strategies influence the evolutionary dynamics in the public goods game. We show that an intermediate value of the threshold leads to a stable coexistence of cooperators, defectors, and players adopting the switching strategy in a well-mixed population, and this regardless of whether the pool-based or the peer-based switching strategy is introduced. Moreover, we show that the pure exclusion strategy alone is able to evoke a limit cycle attractor in the evolutionary dynamics, such that cooperation can coexist with other strategies.Pro-social punishment and exclusion are common means to elevate the level of cooperation among unrelated individuals. Indeed, it is worth pointing out that the combined use of these two strategies is quite common across human societies. However, it is still not known how a combined strategy where punishment and exclusion are switched can promote cooperation from the theoretical perspective. In this paper, we thus propose two different switching strategies, namely, peer switching that is based on peer punishment and peer exclusion, and pool switching that is based on pool punishment and pool exclusion. Individuals adopting the switching strategy will punish defectors when their numbers are below a threshold and exclude them otherwise. We study how the two switching strategies influence the evolutionary dynamics in the public goods game. We show that an intermediate value of the threshold leads to a stable coexistence of cooperators, defectors, and players adopting the switching strategy in a well-mixed pop... In the prevention and resolution of conflicts in social contexts, an important step is to understand how different emotions and empathic traits are linked to punishment behaviors. Unfortunately, few paradigms exist to study these phenomena. Here, we developed the Inequality Game (IG) as an economic and verbal interaction paradigm in which participants are faced with an “unfair other” as opposed to a “fair other” and subsequently have the opportunity to engage in a range of social behaviors. These social behaviors include cooperative or competitive economic choices and nice or derogatory verbal behavior toward the unfair and fair other. Participants could thus engage in punishment or forgiveness behavior toward the unfair other as well as in cooperative or aggressive behavior toward the fair other. We validated the IG through multimodal measures comprising the assessment of personality traits, emotions (by means of facial expressions and self-reports), arousal (by means of skin conductance responses), physical effort (force exertion), and behavioral reactions. Second, we examined the influence of emotions and empathy-related traits on punishment behavior. With regard to emotions, we observed a positive relation between malicious joy and punishment behavior. This result highlights the role of reward-related mechanisms in favoring punishment behavior. In addition, different empathic traits had opposing effects on antisocial behavior. Whereas personal distress predicted aggressive verbal behavior, perspective taking and empathic concern predicted a reduction in punishment behavior. Empathic traits also modulated emotional experience and person evaluations, such that perspective taking was related to more positive affect (less frowning and more smiling) and a more favorable evaluation of the unfair other. The current data validate the IG, reveal that malicious joy is positively related to punishment behavior, and show that different types of empathic traits can have opposing effects on antisocial behavior as well as on related emotions and person evaluations. We propose a novel online learning method for minimizing regret in large extensive-form games. The approach learns a function approximator online to estimate the regret for choosing a particular action. A no-regret algorithm uses these estimates in place of the true regrets to define a sequence of policies. We prove the approach sound by providing a bound relating the quality of the function approximation and regret of the algorithm. A corollary being that the method is guaranteed to converge to a Nash equilibrium in self-play so long as the regrets are ultimately realizable by the function approximator. Our technique can be understood as a principled generalization of existing work on abstraction in large games; in our work, both the abstraction as well as the equilibrium are learned during self-play. We demonstrate empirically the method achieves higher quality strategies than state-of-the-art abstraction techniques given the same resources. The concept of fair division is as old as civil society itself. Aristotle's "equal treatment of equals" was the first step toward a formal definition of distributive fairness. The concept of collective welfare, more than two centuries old, is a pillar of modern economic analysis. Reflecting fifty years of research, this book examines the contribution of modern microeconomic thinking to distributive justice. Taking the modern axiomatic approach, it compares normative arguments of distributive justice and their relation to efficiency and collective welfare. The book begins with the epistemological status of the axiomatic approach and the four classic principles of distributive justice: compensation, reward, exogenous rights, and fitness. It then presents the simple ideas of equal gains, equal losses, and proportional gains and losses. The book discusses three cardinal interpretations of collective welfare: Bentham's "utilitarian" proposal to maximize the sum of individual utilities, the Nash product, and the egalitarian leximin ordering. It also discusses the two main ordinal definitions of collective welfare: the majority relation and the Borda scoring method. The Shapley value is the single most important contribution of game theory to distributive justice. A formula to divide jointly produced costs or benefits fairly, it is especially useful when the pattern of externalities renders useless the simple ideas of equality and proportionality. The book ends with two versatile methods for dividing commodities efficiently and fairly when only ordinal preferences matter: competitive equilibrium with equal incomes and egalitarian equivalence. The book contains a wealth of empirical examples and exercises.