Yuval Heller

Three Steps Ahead

Experimental evidence suggest that people only use 1-3 iterations of strategic reasoning, and that some people systematically use less iterations than others. In this paper, we present a novel evolutionary foundation for these stylized facts. In our model, agents interact in finitely repeated Prisoners Dilemma, and each agent is characterized by the number of steps he thinks ahead. When two agents interact, each of them has an independent probability to observe the opponents type. We show that if this probability is not too close to 0 or 1, then the evolutionary process admits a unique stable outcome, in which the population includes a mixture of “naive” agents who think 1 step ahead, and “sophisticated” agents who think 2-3 steps ahead.

Observations on Cooperation

We study stable behavior when players are randomly matched to play a game, and before the game begins each player may observe how his partner behaved in a few interactions in the past. We present a novel modeling approach and we show that strict Nash equilibria are always stable in such environments. We apply the model to study the Prisoners Dilemma. We show that if players only observe past actions, then defection is the unique stable outcome. However, if players are able to observe past action profiles, then cooperation is also stable. Finally, we present extensions that study endogenous observation probabilities and the evolution of preferences.We study environments in which agents are randomly matched to play a Prisoner’s Dilemma, and each player observes a few of the partner’s past actions against previous opponents. We depart from the existing related literature by allowing a small fraction of the population to be commitment types. The presence of committed agents destabilizes previously proposed mechanisms for sustaining cooperation. We present a novel intuitive combination of strategies that sustains cooperation in various environments. Moreover, we show that under an additional assumption of stationarity, this combination of strategies is essentially the unique mechanism to support full cooperation, and it is robust to various perturbations. Finally, we extend the results to a setup in which agents also observe actions played by past opponents against the current partner, and we characterize which observation structure is optimal for sustaining cooperation.

Instability of Belief-Free Equilibria

Various papers have presented folk-theorem results that yield efficiency in the repeated Prisoners Dilemma with imperfect private monitoring. I present a mild equilibrium refinement that requires robustness against small perturbations in the behavior of potential opponents, and I show that only defection satisfies this mild refinement among all the equilibria in the existing literature, unless one assumes either (1) communication among the players, or (2) sufficient correlation between the private signals (conditional on the action-profile).Various papers have presented folk theorem results for repeated games with private monitoring that rely on belief-free equilibria. I show that these equilibria are not robust against small perturbations in the behavior of potential opponents. Specifically, I show that essentially none of the belief-free equilibria is evolutionarily stable, and that in generic games none of these equilibria is neutrally stable. Moreover, in a large family of games (which includes many public good games), the belief-free equilibria fail to satisfy even a very mild stability refinement.

THE ENDOWMENT EFFECT AS BLESSING: THE ENDOWMENT EFFECT AS BLESSING

We study the idea that seemingly unrelated behavioral biases can coevolve if they jointly compensate for the errors that any one of them would give rise to in isolation. We suggest that the “endowment effect” and the “winners curse” could have jointly survived natural selection together. We develop a new family of “hybrid‐replicator” dynamics. Under such dynamics, biases survive in the population for a long period of time even if they only partially compensate for each other and despite the fact that the rational types payoff is strictly larger than the payoffs of all other types.

The Endowment Effect as a Blessing

We study the idea that seemingly unrelated behavioral biases can coevolve if they jointly compensate for the errors that any one of them would give rise to in isolation. We pay specific attention to barter trade of the kind that was common in prehistoric societies, and suggest that the “endowment effect” and the “winners curse” could have jointly survived natural selection together. We first study a barter game with a standard payoff-monotone selection dynamics, and show that in the long run the population consists of biased individuals with two opposed biases that perfectly offset each other. In this population, all individuals play the barter game as if they were rational. Next we develop a new family of “hybrid-replicator” dynamics. We show that under such dynamics, biases survive in the population for a long period of time even if they only partially compensate for each other and despite the fact that the rational types payoff is strictly larger than the payoffs of all other types.Experimental evidence and field data suggest that agents hold two seemingly unrelated biases: failure to account for the fact that the behavior of others reflects their private information (“winners curse”), and a tendency to value a good more once it is owned (“endowment effect”). In this paper we propose that these two phenomena are closely related: the biases fully compensate for each other in various economic interactions, and induce an “as-if rational” behavior. We pay specific attention to barter trade, of the kind that was common in prehistoric societies, and suggest that the endowment effect and the winners curse could have jointly survived natural selection together.

Social Learning and the Shadow of the Past

In various environments new agents may base their decisions on observations of actions taken by a few other agents in the past. In this paper we analyze a broad class of such social learning processes, and study under what circumstances the initial behavior of the population has a lasting effect. Our results show that this question strongly depends on the expected number of actions observed by new agents. Specifically, we show that if the expected number of observed actions is: (1) less than one, then the population converges to the same behavior independently of the initial state; (2) between one and two, then in some (but not all) environments there are decision rules for which the initial state has a lasting impact on future behavior; and (3) more than two, then in all environments there is a decision rule for which the initial state has a lasting impact.

Promises and Endogenous Reneging Costs

We present a novel theoretical mechanism that explains the capacity for non-enforceable communication about future actions to improve efficiency. We explore a two-player partnership game where, before choosing a level of effort to exert on a joint project, each player makes a cheap talk promise to their partner about their own future effort. We allow agents to incur a psychological cost of reneging on their promises. We demonstrate a strong tendency for evolutionary processes to select agents who incur intermediate costs of reneging, and show that these intermediate costs induce second-best optimal outcomes.

When Is Social Learning Path-Dependent?

In various environments new agents may base their decisions on observations of actions taken by a few other agents in the past. In this paper we analyze a broad class of such social learning processes, and study under what circumstances the initial behavior of the population has a lasting effect. Our results show that this question strongly depends on the expected number of actions observed by new agents. Specifically, we show that if the expected number of observed actions is: (1) less than one, then the population converges to the same behavior independently of the initial state; (2) between one and two, then in some (but not all) environments there are learning rules for which the initial state has a lasting impact on future behavior; and (3) more than two, then in all environments there is a learning rule for which the initial state has a lasting impact.