Using turn taking to achieve intertemporal cooperation and symmetry in infinitely repeated 2 × 2 games |
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Authors: | Sau-Him Paul Lau Vai-Lam Mui |
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Institution: | (2) Department of Economics, The Pennsylvania State University, University Park, USA;(3) Faculty of Economics, University of Cambridge, Cambridge, UK; |
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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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