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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Acknowledgments
We are grateful to Stephen Chiu, Simon Grant, Xianming Zhou, two anonymous referees, and seminar participants at the Australian National University, City University of Hong Kong, McGill University, Monash University, Purdue University, and University of Hong Kong for helpful comments, and to Daniel Kelly and Philip Ng for excellent research assistance. We thank the Research Grants Council of Hong Kong (project HKU7223/04H) for financial support.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Lau, SH.P., Mui, VL. Using turn taking to achieve intertemporal cooperation and symmetry in infinitely repeated 2 × 2 games. Theory Decis 72, 167–188 (2012). https://doi.org/10.1007/s11238-011-9249-4
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DOI: https://doi.org/10.1007/s11238-011-9249-4