The dual self-model of self-control with one-period lived short-run selves is excessively sensitive to the timing of shocks and to the interpolation of additional “noaction†time periods in between the dates when decisions are made. We show that when short-run selves have a random...

The most widely used economic models of social preferences are specified only for certain outcomes. There are two obvious methods of extending them to lotteries. If we do so by expected utility theory, so that the independence axiom is satisfied, our results imply that the resulting preferences...

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...

We explore the extent to which altruism, as measured by giving in a dictator game (DG), accounts for play in a noisy version of the repeated prisoner's dilemma. We find that DG giving is correlated with cooperation in the repeated game when no cooperative equilibria exist, but not when...

One of the main problems impeding the evolution of cooperation is partner choice. When information is asymmetric (the quality of a potential partner is known only to himself), it may seem that partner choice is not possible without signaling. Many mutualisms, however, exist without signaling,...

This paper studies repeated games with imperfect public monitoring where the play- ers are uncertain both about the payoff functions and about the relationship between the distribution of signals and the actions played. We introduce the concept of perfect public ex post equilibrium (PPXE), and...

We examine the long-term implication of two models of learning with recency bias: recursive weights and limited memory. We show that both models generate similar beliefs and that both have a weighted universal consistency property. Using the limited-memory model we produce learning procedures...

This note characterizes the impact of adding rare stochastic mutations to an “imitation dynamic,†meaning a process with the properties that absent strategies remain absent, and non-homogeneous states are transient. The resulting system will spend almost all of its time at the...

The repeated Prisoner's Dilemma is usually known as a story of tit-for-tat (TFT). This remarkable strategy has won both of Robert Axelrod's tournaments. TFT does whatever the opponent has done in the previous round. It will cooperate if the opponent has cooperated, and it will defect if the...

We derive a simplified version of the model of Fudenberg and Levine, 2006 and Fudenberg and Levine, 2011 and show how this approximate model is useful in explaining choice under risk. We show that in the simple case of three outcomes, the model can generate indifference curves that “fan...