Using turn taking to achieve intertemporal cooperation and symmetry in infinitely repeated 2 × 2 games

Turn taking is observed in many field and laboratory settings captured by various widely studied 2 × 2 games. This article develops a repeated game model that allows us to systematically investigate turn‐taking behavior in many 2 × 2 games, including the battle of the sexes, the game of chicken, the game of common‐pool‐resources assignment, and a particular version of the prisoners’ dilemma. We consider the ‘turn taking with independent randomizations’ (TTIR) strategy that achieves three objectives: (a) helping the players reach the turn‐taking path, (b) resolving the question of who takes the good turn first, and (c) deterring defection. We determine conditions under which there exists a unique TTIR strategy profile that can be supported as a subgame‐perfect equilibrium. We also show that there exist conditions under which an increase in the ‘degree of conflict’ of the stage game leads to a decrease in the expected number of periods in reaching the turn‐taking path.