Download PDF

Theory and Decision

, Volume 72, Issue 2, pp 167–188 | Cite as

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

Open Access
Article
First Online:

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.

Keywords

Conflict Coordination Turn taking Intertemporal cooperation 

JEL Classification

C70 C72 
Download to read the full article text

Notes

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.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. Athey S., Bagwell K. (2008) Collusion with persistent cost shocks. Econometrica 76: 493–540CrossRefGoogle Scholar
  2. Bergerud E. M. (1993) Red thunder, tropic lightning: The world of a combat division in Vietnam. Westview Press Inc, BoulderGoogle Scholar
  3. Berkes F. (1992) Success and failure in marine coastal fisheries of Turkey. In: Bromley D. W. (eds) Making the commons work: Theory, practice, and policy. Institute for Contemporary Studies, San Francisco, pp 161–182Google Scholar
  4. Bhaskar V. (2000) Egalitarianism and efficiency in repeated symmetric games. Games and Economic Behavior 32: 247–262CrossRefGoogle Scholar
  5. Bornstein G., Budescu D., Zamir S. (1997) Cooperation in intergroup, N-person, and two-person games of chicken. Journal of Conflict Resolution 41: 384–406CrossRefGoogle Scholar
  6. Dixit A., Skeath S. (1999) Games of strategy. W. W. Norton & Company, New YorkGoogle Scholar
  7. Friedman J. W. (1994) Introduction and overview. In: Friedman J. W. (eds) Problems of coordination in economic activity. Kluwer Academic Publishers, Boston, pp 3–15CrossRefGoogle Scholar
  8. Harrison G., Hirshleifer J. (1989) An experimental evaluation of weakest link/best shot models of public goods. Journal of Political Economy 97: 201–225CrossRefGoogle Scholar
  9. Helbing D., Schönhof M., Stark H.-U., Holyst J. A. (2005) How individuals learn to take turns: Emergence of alternating cooperation in a congestion game and the prisoner’s dilemma. Advances in Complex Systems 8: 87–116CrossRefGoogle Scholar
  10. Kaplan, T. R., & Ruffle, B. J. (2007). Which way to cooperate? Working paper. University of Exeter and Ben-Gurion UniversityGoogle Scholar
  11. Lau S.-H. P., Mui V.-L. (2008) Using turn taking to mitigate coordination and conflict problems in the repeated battle of the sexes game. Theory and Decision 65: 153–183CrossRefGoogle Scholar
  12. Luce R. D., Raiffa H. (1957) Games and decisions: Introduction and critical survey. Wiley, New YorkGoogle Scholar
  13. Ostrom E. (1990) Governing the commons: The evolution of institutions for collective action. Cambridge University Press, New YorkGoogle Scholar
  14. Ostrom, E., Gardner, R., & Walker, J. (with A. Agrawal, W. Blomquist, E. Schlager, and S. Y. Tang). (1994). Rules, games, and common-pool resources. Ann Arbor: University of Michigan Press.Google Scholar
  15. Prisbrey, J. (1992). Cooperation in reciprocity games and in the voluntary contributions mechanism. Ph.D. Dissertation, California Institute of Technology.Google Scholar
  16. Skrzypacz A., Hopenhayn H. (2004) Tacit collusion in repeated auctions. Journal of Economic Theory 114: 153–169CrossRefGoogle Scholar
  17. Ward H. (1998) A game theoretic analysis of the politics of taking it in turns. British Journal of Political Science 28: 355–387CrossRefGoogle Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.School of Economics and FinanceUniversity of Hong KongPokfulamHong Kong
  2. 2.Department of EconomicsMonash UniversityClaytonAustralia

Personalised recommendations