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Stochastic Timing, Uniqueness, and Efficiency in Games

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Author Info

  • 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)

Abstract

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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File URL: http://www.latrobe.edu.au/__data/assets/pdf_file/0003/130917/2010.01.pdf
File Function: First version, 2010
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Bibliographic Info

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
Date of revision:
Handle: RePEc:ltr:wpaper:2010.01

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Related research

Keywords: asynchronous moves; stochastic timing; equilibrium selection; revision; asymmetric coordination games. EDIRC Provider-Institution: RePEc:edi:smlatau;

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References

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  1. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  2. Eric van Damme & Sjaak Hurkens, 2001. "Endogenous price leadership," Economics Working Papers 581, Department of Economics and Business, Universitat Pompeu Fabra.
  3. 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.
  4. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
  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. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475, October.
  7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  8. 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.
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Cited by:
  1. Jan Libich & Dat Thanh Nguyen & Petr Stehlík, 2011. "Monetary Exit Strategy and Fiscal Spillovers," CAMA Working Papers 2011-04, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.

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