Turn Taking: Intertemporal Cooperation and Symmetry through Intratemporal Asymmetry *

Turn taking is observed in many field and laboratory settings captured by various widely-studied 2x2 games. This paper develops a repeated game model that allows us to systematically investigate turn-taking behavior in many 2x2 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 a subgame-perfect equilibrium with TTIR strategy exists and is unique. Regarding testable implications of the model, we show that while in general an increase in the “degree of conflict ” of the stage game increases the expected number of periods in reaching the turn-taking path, there exist conditions under which the opposite result occurs