This paper studies the effect of randomness in per-period matching on the long-run outcome of non-equilibrium adaptive processes. If there are many matchings between each strategy revision, the randomness due to matching will be small; our question is when a very small noise due to matching has...

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 analyze a class of imitation dynamics with mutations for games with any finite number of actions, and give conditions for the selection of a unique equilibrium as the mutation rate becomes small and the population becomes large. Our results cover the multiple-action extensions of the...

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...

This paper studies whether agents must agglomerate at a single location in a class of models of two-sided interaction. In these models there is an increasing returns effect that favors agglomeration, but also a crowding or market-impact effect that makes agents prefer to be in a market with...

This paper studies the way that word-of-mouth communication aggregates the information of individual agents. We find that the structure of the communication process determines whether all agents end up making identical choices, with less communication making this conformity more likely. Despite...

This paper shows that larger auctions are more efficient than smaller ones, but that despite this scale effect, two competing and otherwise identical markets or auction sites of different sizes can coexist in equilibrium. We find that the range of equilibrium market sizes depends on the...

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...

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...