Rationalizable partition-confirmed equilibrium (RPCE) describes the steady state outcomes of rational learning in extensive-form games, when rationality is common knowledge and players observe a partition of the terminal nodes. RPCE allows players to make inferences about unobserved play by...

We extend the folk theorem of repeated games to two settings in which players' information about others' play arrives with stochastic lags. In our first model, signals are almost-perfect if and when they do arrive, that is, each player either observes an almost-perfect signal of period-t play...

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...

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...

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...

The theory of learning in games studies how, which and what kind of equilibria might arise as a consequence of a long-run non-equilibrium process of learning, adaptation and/or imitation. If agents’ strategies are completely observed at the end of each round, and agents are randomly...

We study the experimental play of the repeated prisoner’s dilemma when intended actions are implemented with noise. In treatments where cooperation is an equilibrium, subjects cooperate substantially more than in treatments without cooperative equilibria. In all settings there was...