Selfishness Level of Strategic Games

We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be offered to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated to the price of stability and the price of anarchy and is invariant under positive linear transformations of the payoff functions. Also, it naturally applies to other solution concepts and other forms of games. We study the selfishness level of several well-known strategic games. This allows us to quantify the implicit tension within a game between players' individual interests and the impact of their decisions on the society as a whole. Our analyses reveal that the selfishness level often provides a deeper understanding of the characteristics of the underlying game that influence the players' willingness to cooperate. In particular, the selfishness level of finite ordinal potential games is finite, while that of weakly acyclic games can be infinite. We derive explicit bounds on the selfishness level of fair cost sharing games and linear congestion games, which depend on specific parameters of the underlying game but are independent of the number of players. Further, we show that the selfishness level of the $n$-players Prisoner's Dilemma is $c/(b(n-1)-c)$, where $b$ and $c$ are the benefit and cost for cooperation, respectively, that of the $n$-players public goods game is $(1-\frac{c}{n})/(c-1)$, where $c$ is the public good multiplier, and that of the Traveler's Dilemma game is $\frac{1}{2}(b-1)$, where $b$ is the bonus. Finally, the selfishness level of Cournot competition (an example of an infinite ordinal potential game, Tragedy of the Commons, and Bertrand competition is infinite.Comment: 34 page

Selfishness Level of Strategic Games

We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be added to the players' payoffs to ensure that a Nash equilibrium of the resulting game is also its social optimum. This notion is unrelated to that of price of stability. We compute the selfishness level for some selected games. In particular, the selfishness level of finite ordinal potential games is finite, while that of a Cournot competition oligopoly game and Tragedy of the Commons game is infinite. We also provide an estimate on the selfishness level of linear congestion games and fair cost sharing games

“Economic man” in cross-cultural perspective: Behavioral experiments in 15 small-scale societies

Researchers from across the social sciences have found consistent deviations from the predictions of the canonical model of self-interest in hundreds of experiments from around the world. This research, however, cannot determine whether the uniformity results from universal patterns of human behavior or from the limited cultural variation available among the university students used in virtually all prior experimental work. To address this, we undertook a cross-cultural study of behavior in ultimatum, public goods, and dictator games in a range of small-scale societies exhibiting a wide variety of economic and cultural conditions. We found, first, that the canonical model – based on self-interest – fails in all of the societies studied. Second, our data reveal substantially more behavioral variability across social groups than has been found in previous research. Third, group-level differences in economic organization and the structure of social interactions explain a substantial portion of the behavioral variation across societies: the higher the degree of market integration and the higher the payoffs to cooperation in everyday life, the greater the level of prosociality expressed in experimental games. Fourth, the available individual-level economic and demographic variables do not consistently explain game behavior, either within or across groups. Fifth, in many cases experimental play appears to reflect the common interactional patterns of everyday life

Comparative Statics of Altruism and Spite

The equilibrium outcome of a strategic interaction between two or more people may depend on the weight they place on each other’s payoff. A positive, negative or zero weight represents altruism, spite or complete selfishness, respectively. Paradoxically, the real, material payoff in equilibrium for a group of altruists may be lower than for selfish or spiteful groups. However, this can only be so if the equilibria involved are unstable. If they are stable, the total (equivalently, average) payoff can only increase or remain unchanged with an increasing degree of altruism.Altruism, spite, comparative statics, strategic games, stability of equilibrium

Reputation or Reciprocity? An Experimental Investigation

Recent evidence highlights the importance of social norms in many economic relations. However, many of these relationships are long-term and provide repeated game incentives for performance. We experimentally investigate interaction effects of reciprocity and repeated game incentives in two treatments (one-shot and repeated) of a gift-exchange game. In both treatments we observe reciprocity, which is strengthened in the repeated game. A detailed analysis shows that in the repeated game some subjects imitate reciprocity. Thus, reciprocity and repeated game incentives reinforce each other. Observed behaviour is robust against experience. We conclude that a long-term interaction is a reciprocity-compatible contract enforcement device.Reciprocity, reputation, repeated games, incomplete contracts

Moral Sentiments and Material Interests behind Altruistic Third-Party Punishment

Social norms are ubiquitous in human life. Their role is essential in allowing cooperation to prevail, despite the presence of incentives to free ride. As far as norm enforcement devices are concerned, it would be impossible to have widespread social norms if second parties only enforced them. However, both the quantitative relevance and the motivations underlying altruistic punishment on the part of ‘unaffected’ third parties are still largely unexplored. This paper contributes to shed light on the issue, by means of an experimental design consisting of three treatments: a Dictator Game Treatment, a Third-Party Punishment Game Treatment (Fehr and Fischbacher, 2004) and a Metanorm Treatment, that is a variant of the Third-party Punishment Game where the Recipient can punish the third party. We find that third parties are willing to punish dictators (Fehr and Fischbacher, 2004; Ottone, 2008) and, in doing so, they are affected by ‘reference-dependent fairness’, rather than by the ‘egalitarian distribution norm’. By eliciting players’ normative expectations, it turns out that all of them expect a Dictator to transfer something – not half of the endowment. Consequently, the Observers’ levels of punishment are sensitive to their subjective sense of fairness. A positive relation between the level of punishment and the degree of negative subjective unfairness emerges. Subjective unfairness also affects Dictators’ behaviour: their actual transfers and their ideal transfer are not significantly different. Finally, we interestingly find that third parties are also sensitive to the receivers’ (credible) threat to punish them: as the Dictator’s transfer becomes lower and lower than the Observer’s ideal transfer, the Observer’s reaction is – other things being equal – significantly stronger in the Metanorm Treatment than in the Third-Party Punishment Game Treatment. Hence, despite their being to some extent genuinely nonstrategically motivated, also third parties – like second parties – are sensitive to the costs of punishing.Third-Party Punishment, Moral Sentiments, Material Interests, Subjective Unfairness, Social Norms

Social preferences: from the experimental lab to economic theory

We present a wide collection of experiments which show how human behavior deviates substantially with respect to the predictions derived from standard homo economicus assumptions. Then we review the theoretical literature that this evidence has stimulated. In particular some models are found to be consistent with evidence from a large set of games. As fundamental differences exist among these proposals, new experiments were devised to contrast their effectiveness in predicting behavior. We argue that inequality aversion models are to be preferred to intention based models because the additional predictive power the latter may have comes at a very high cost of complexity. We also find that equality considerations are more relevant than efficiency motives in most economically relevant settings. Results are not conclusive and this gives scope to further research over these issues.Prisoner's dilemma; public good games; social preference models

At the Mercy of the Prisoner Next Door. Using an Experimental Measure of Selfishness as a Criminological Tool

Do criminals maximise money? Are criminals more or less selfish than the average subject? Can prisons apply measures that reduce the degree of selfishness of their inmates? Using a tried and tested tool from experimental economics, we cast new light on these old criminological questions. In a standard dictator game, prisoners give a substantial amount, which calls for more refined versions of utility in rational choice theories of crime. Prisoners do not give less than average subjects, not even than subjects from other closely knit communities. This speaks against the idea that people commit crimes because they are excessively selfish. Finally those who receive better marks at prison school give more, as do those who improve their marks over time. This suggests that this correctional intervention also reduces selfishness.experiment, Crime, Prison, Dictator Game, Hurdle Model