Drew Fudenberg

Emergence of cooperation and evolutionary stability in finite populations.

To explain the evolution of cooperation by natural selection has been a major goal of biologists since Darwin. Cooperators help others at a cost to themselves, while defectors receive the benefits of altruism without providing any help in return. The standard game dynamical formulation is the ‘Prisoners Dilemma’, in which two players have a choice between cooperation and defection. In the repeated game, cooperators using direct reciprocity cannot be exploited by defectors, but it is unclear how such cooperators can arise in the first place. In general, defectors are stable against invasion by cooperators. This understanding is based on traditional concepts of evolutionary stability and dynamics in infinite populations. Here we study evolutionary game dynamics in finite populations. We show that a single cooperator using a strategy like ‘tit-for-tat’ can invade a population of defectors with a probability that corresponds to a net selective advantage. We specify the conditions required for natural selection to favour the emergence of cooperation and define evolutionary stability in finite populations.

The Folk Theorem with Imperfect Public Information

The authors study repeated games in which players observe a public outcome that imperfectly signals the actions played. They provide conditions guaranteeing that any feasible, individually rational payoff vector of the stage game can arise as a perfect equilibrium of the repeated game with sufficiently little discounting. The central condition requires that there exist action profiles with the property that, for any two players, no two deviations--one by either player--give rise to the same probability distribution over public outcomes. The results apply to principal-agent, partnership, oligopoly, and mechanism-design models, and to one-shot games with transferable utilities. Copyright 1994 by The Econometric Society.

Rules of Thumb for Social Learning

This paper studies agents who consider the experiences of their neighbors in deciding which of two technologies to use. We analyze two learning environments, one in which the same technology is optimal for all players and another in which each technology is better for some of them. In both environments, players use exogenously specified rules of thumb that ignore historical data but may incorporate a tendency to use the more popular technology. In some cases these naive rules can lead to fairly efficient decisions in the long run, but adjustment can be slow when a superior technology is first introduced.

Winners don’t punish

A key aspect of human behaviour is cooperation. We tend to help others even if costs are involved. We are more likely to help when the costs are small and the benefits for the other person significant. Cooperation leads to a tension between what is best for the individual and what is best for the group. A group does better if everyone cooperates, but each individual is tempted to defect. Recently there has been much interest in exploring the effect of costly punishment on human cooperation. Costly punishment means paying a cost for another individual to incur a cost. It has been suggested that costly punishment promotes cooperation even in non-repeated games and without any possibility of reputation effects. But most of our interactions are repeated and reputation is always at stake. Thus, if costly punishment is important in promoting cooperation, it must do so in a repeated setting. We have performed experiments in which, in each round of a repeated game, people choose between cooperation, defection and costly punishment. In control experiments, people could only cooperate or defect. Here we show that the option of costly punishment increases the amount of cooperation but not the average payoff of the group. Furthermore, there is a strong negative correlation between total payoff and use of costly punishment. Those people who gain the highest total payoff tend not to use costly punishment: winners don’t punish. This suggests that costly punishment behaviour is maladaptive in cooperation games and might have evolved for other reasons.

Positive Interactions Promote Public Cooperation

Carrots Are Better Than Sticks The challenge of dealing with freeloaders—who benefit from a common good but refuse to pay their “fair share” of the costs—has often been met in theoretical and laboratory studies by sanctioning costly punishment, in which contributors pay a portion of their benefit so that freeloaders lose theirs. Rand et al. (p. 1272; see the news story by Pennisi and the cover) added a private interaction session after each round of the public goods game during which participants were allowed to reward or punish other members of their group. The outcome showed that reward was as effective as punishment in maintaining a cooperative mindset, and doing so via rewarding interactions allowed the entire group to prosper because less is lost to the costs of punishing. Reward is as good as punishment to promote cooperation, costs less, and increases the share out of resources up for grabs. The public goods game is the classic laboratory paradigm for studying collective action problems. Each participant chooses how much to contribute to a common pool that returns benefits to all participants equally. The ideal outcome occurs if everybody contributes the maximum amount, but the self-interested strategy is not to contribute anything. Most previous studies have found punishment to be more effective than reward for maintaining cooperation in public goods games. The typical design of these studies, however, represses future consequences for today’s actions. In an experimental setting, we compare public goods games followed by punishment, reward, or both in the setting of truly repeated games, in which player identities persist from round to round. We show that reward is as effective as punishment for maintaining public cooperation and leads to higher total earnings. Moreover, when both options are available, reward leads to increased contributions and payoff, whereas punishment has no effect on contributions and leads to lower payoff. We conclude that reward outperforms punishment in repeated public goods games and that human cooperation in such repeated settings is best supported by positive interactions with others.

Short-term contracts and long-term agency relationships

Abstract Long-term contracts are valuable only if optimal contracting requires commitment to a plan today that would not otherwise be adopted tomorrow. We show that commitments are unnecessary, and hence short-term contracts are sufficient if (1) all public information can be used in contracting, (2) the agent can acess a bank on equal terms with the principal, (3) recontracting takes place with common knowledge about technology and preferences and (4) the frontier of expected utility payoffs generated by the set of incentive-compatible contracts is downward sloping at all times.

Reputation and Equilibrium Selection in Games with a Patient Player

A single, long-run player plays a simultaneous-move stage game against a sequence of opponents who only play once, but observe all previous play. If there is a positive prior probability that the long-run player will always play the pure strategy he would most like to commit himself to (his Stackleberg strategy), then his payoff in any Nash equilibrium exceeds a bound that converges to the Stackleberg payoff as his discount factor approaches one. When the stage game is not simultaneous move, this result must be modified to account for the possibility that distinct strategies of the long-run player are observationally equivalent. Copyright 1989 by The Econometric Society.

Self-Confirming Equilibrium

In a self-confining equilibrium, each players strategy is a best response to his beliefs about the play of his opponents and each players beliefs are correct along the equilibrium path of play. Thus, if a self-confirming equilibrium occurs repeatedly, no player ever observes play that contradicts his beliefs, even though beliefs about play at off-path information sets need not be correct. The authors characterize the ways in which self-confirming equilibria and Nash equilibria can differ and provide conditions under which self-confirming equilibria correspond to standard solution concepts. Copyright 1993 by The Econometric Society.

Moral hazard and renegotiation in agency contracts

The authors modify the standard principal-agent model with oral hazard by allowing the contract to be renegotiated after the agents choice of action and before the observation of the actions consequences. In equilibrium, the agent randomizes over effort levels. The optimal contract gives the agent a menu of compensation schemes: safe ones intended for low-effort workers and risky ones for those whose effort is high. The optimal contract may give the agent a positive rent, in contrast to the case without renegotiation. Copyright 1990 by The Econometric Society.

Word-of-mouth learning

This paper analyzes a model of rational word-of-mouth learning, in which successive generations of agents make once-and-for-all choices between two alternatives. Before making a decision, each new agent samples N old ones and asks them which choice they used and how satisfied they were with it. If (a) the sampling rule is “unbiased” in the sense that the samples are representative of the overall population, (b) each player samples two or more others, and (c) there is any information at all in the payoff observations, then in the long run every agent will choose the same thing. If in addition the payoff observation is sufficiently informative, the long-run outcome is efficient. We also investigate a range of biased sampling rules, such as those that over-represent popular or successful choices, and determine which ones favor global convergence towards efficiency.