Experimental Evidence of Trigger Strategies in Repeated Games

Abstract

In the infinitely repeated Prisoner's Dilemma game with complete information, there are two popular Nash Equilibrium strategies. One such strategy is to not cooperate in every period, which is both a Nash Equilibrium in the one-shot game and a subgame-perfect Nash Equilibrium in the repeated game. Another strategy, known as the 'grim trigger strategy', consists of cooperating in the first stage, and in any subsequent stage, k, if the outcome of k-1 preceding stages has been mutual cooperation, then cooperate, otherwise, do not cooperate. Essentially, this leads to never cooperating, once the other player has not cooperated. In a repeated game, but not infinitely repeated game, with a probability, p, of game continuation, there exists a critical p, p{c}, at which this trigger strategy is also a subgame perfect equilibrium (the so-called Folk Theorem). This paper explicitly models such a game and then performs a laboratory experiment with real subjects to understand to what extent the grim trigger strategy is observed in practice. We find that players generally do not adopt trigger strategies for values of p