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

Published on Feb 1, 2012in Theory and Decision
· DOI :10.1007/S11238-011-9249-4
Sau-Him Paul Lau13
Estimated H-index: 13
(HKU: University of Hong Kong),
Vai-Lam Mui13
Estimated H-index: 13
(Monash University)
Abstract
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.
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