Cooperation in the Repeated Prisoner’s Dilemma with Local Interaction

This paper studies the repeated Prisoner’s Dilemma in a local interaction setup. We construct a sequential equilibrium in pure strategies that sustains cooperation for suffciently patient players. The strategy is embedded in an explicitly defined expectation system, which is a more compact way than machines to describe strategies in the local interaction setup, although essentially the expectation system can also be viewed as a finite state automaton. The belief system is derived by perturbing the strategy appropriately and following the principle that parsimonious explanations receive all the weight. The equilibrium has the property that after any global history, full cooperation will be restored after a finite number of periods

A Polya Urn Model of Conformity

In this paper we propose to use Polya urn processes to model the emergence of conformity in an environment where people interact with each other sequentially and indirectly, through a common physical facility. Examples include rewinding video tapes, erasing blackboards, and switching headlights, etc. We find that a minimum amount of imitation is able to generate a maximum level of conformity. We then reinterpret the result in a group imitation setup, and show that as long as groups imitate each other with positive probabilities, they will end up with the same population composition, irrespective of the initial conditions, and the imitating probabilities

Collective Behavior with Endogenous Thresholds

We endogenize the threshold points in Granovetter’s threshold model of collective behavior (Granovetter 1978). We do this in a simple model that combines strategic complementarity and private information in a dynamic setup with endogenous order of moves. Looking at Granovetter’s model in the strategic context allows us to highlight the sensitivity of collective outcomes to the timing of the games and the reversibility of the actions, and to emphasize an extra incentive for people to follow other people: to encourage more people to follow them