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Zero-Sum Revision Games

Author

Listed:
  • Gensbittel, Fabien
  • Lovo, Stefano
  • Renault, Jérôme
  • Tomala, Tristan

Abstract

In a zero-sum asynchronous revision game, players can revise their actions only at exogenous random times. Players’ revision times follow Poisson processes, independent across players. Payoffs are obtained only at the deadline by implementing the last prepared actions in the ‘component game’. The value of this game is called revision value. We characterize it as the unique solution of an ordinary differential equation and show it is continuous in all parameters of the model. We show that, as the duration of the game increases, the limit revision value does not depend on the initial position and is included between the min-max and max-min of the component game. We fully characterize the equilibrium in 2?2 games. When the component game minmax and maxmin differ, the revision game equilibrium paths have a wait-and-wrestle structure: far form the deadline, players stay put at sur-place action profile, close to the deadline, they take best responses to the action of the opponent.

Suggested Citation

  • Gensbittel, Fabien & Lovo, Stefano & Renault, Jérôme & Tomala, Tristan, 2017. "Zero-Sum Revision Games," TSE Working Papers 17-751, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:31319
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    Cited by:

    1. Zhuohan Wang & Dong Hao, 2022. "Characterizing Agent Behavior in Revision Games with Uncertain Deadline," Games, MDPI, vol. 13(6), pages 1-13, November.
    2. Pierre Bernhard & Marc Deschamps, 2021. "Dynamic Equilibrium with Randomly Arriving Players," Dynamic Games and Applications, Springer, vol. 11(2), pages 242-269, June.
    3. Roy, Nilanjan, 2023. "Fostering collusion through action revision in duopolies," Journal of Economic Theory, Elsevier, vol. 208(C).
    4. Sofia Moroni, 2019. "Existence of trembling hand perfect and sequential equilibrium in games with stochastic timing of moves," Working Paper 6757, Department of Economics, University of Pittsburgh.
    5. Yevgeny Tsodikovich, 2021. "The worst-case payoff in games with stochastic revision opportunities," Annals of Operations Research, Springer, vol. 300(1), pages 205-224, May.
    6. Dong Hao & Qi Shi & Jinyan Su & Bo An, 2021. "Cooperation, Retaliation and Forgiveness in Revision Games," Papers 2112.02271, arXiv.org, revised Oct 2022.
    7. Sofia Moroni, 2020. "Existence of Trembling hand perfect and sequential equilibrium in Stochastic Games," Working Paper 6837, Department of Economics, University of Pittsburgh.

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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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