Cooperation in the Repeated Prisoner’s Dilemma with Local Interaction

Abstract

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.