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Stochastic Timing, Uniqueness, and Efficiency in Games

Listed author(s):
  • Suren Basov


    (Department of Economics and Finance, La Trobe University)

  • Jan Libich


    (Department of Economics and Finance, La Trobe University)

  • Petr Stehlík


    (University of West Bohemia)

In existing game theoretic settings the timing of moves is deterministic, i.e. they occur with certainty at a pre-specified time. To add more realism we propose a framework in which, after an initial simultaneous move in time t = 0, one player gets to revise his action with positive probability at some time 0. Since the initial action of the opponent can be observed, and payoffs accrue over time, the set-up constitutes a dynamic extension of the Stackelberg leadership concept. Allowing for an arbitrary timing distribution, and using both sub game perfection and stochastic stability, we derive the necessary and sufficient conditions under which our dynamic revision game has a unique efficient outcome even if the underlying normal form game has no efficient Nash, or multiple ones. Intuitively, the fact that a player is less likely to move than the opponent may serve as a commitment device. Therefore, if the revision opportunity is expected to arrive sufficiently early then the committed players initial cost of mis-coordination or conflict will be more than compensated by ensuring his preferred outcome after the opponents revision. The framework allows, among other things, to address the issue of equilibrium selection in games in which traditional equilibrium selection approaches fail such as the Battle of the Sexes and the Game of Chicken. It also offers some insights into the debate about Pareto-dominance versus risk-dominance.

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Paper provided by School of Economics, La Trobe University in its series Working Papers with number 2010.01.

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Length: 14 pages
Date of creation: 2010
Handle: RePEc:ltr:wpaper:2010.01
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  1. van Damme, Eric & Hurkens, Sjaak, 2004. "Endogenous price leadership," Games and Economic Behavior, Elsevier, vol. 47(2), pages 404-420, May.
  2. Sherrill Shaffer, 2004. "Licensing Requirements as a Coordination Mechanism for Entry," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 24(3), pages 285-299, 05.
  3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  4. Jan Libich & Petr Stehlik, 2008. "Fiscal Rigidity In A Monetary Union: The Calvo Timing And Beyond," CAMA Working Papers 2008-22, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  5. Suren Basov & Vladimir Smirnov & Andrew Wait, 2007. "Market Niche, Flexibility And Commitment," Manchester School, University of Manchester, vol. 75(1), pages 122-130, 01.
  6. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
  7. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  8. Joseph Farrell, 1987. "Cheap Talk, Coordination, and Entry," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 34-39, Spring.
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