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Repeated Games with Bonuses

Author

Listed:
  • G. Schoenmakers

    (Maastricht University)

  • J. Flesch

    (Maastricht University)

  • F. Thuijsman

    (Maastricht University)

  • O. J. Vrieze

    (Maastricht University)

Abstract

This paper deals with 2-player zero-sum repeated games in which player 1 receives a bonus at stage t if he repeats the action he played at stage t−1. We investigate the optimality of simple strategies for player 1. A simple strategy for player 1 consists of playing the same mixed action at every stage, irrespective of past play. Furthermore, for games in which player 1 has a simple optimal strategy, we characterize the set of stationary optimal strategies for player 2.

Suggested Citation

  • G. Schoenmakers & J. Flesch & F. Thuijsman & O. J. Vrieze, 2008. "Repeated Games with Bonuses," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 459-473, March.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:3:d:10.1007_s10957-007-9318-6
    DOI: 10.1007/s10957-007-9318-6
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    References listed on IDEAS

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    1. K. J. Arrow, 1971. "The Economic Implications of Learning by Doing," Palgrave Macmillan Books, in: F. H. Hahn (ed.), Readings in the Theory of Growth, chapter 11, pages 131-149, Palgrave Macmillan.
    2. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832, Elsevier.
    3. Joosten Reinoud & Peters Hans & Thuijsman Frank, 1995. "Unlearning by Not Doing: Repeated Games with Vanishing Actions," Games and Economic Behavior, Elsevier, vol. 9(1), pages 1-7, April.
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    Cited by:

    1. Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2021. "Repeated Games with Switching Costs: Stationary vs History-Independent Strategies," AMSE Working Papers 2129, Aix-Marseille School of Economics, France.
    2. Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2021. "Repeated Games with Switching Costs: Stationary vs History-Independent Strategies," Working Papers halshs-03223279, HAL.
    3. Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2024. "The Price of History-Independent Strategies in Games with Inter-Temporal Externalities," Dynamic Games and Applications, Springer, vol. 14(5), pages 1317-1332, November.
    4. Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2022. "Folk Theorems in Repeated Games with Switching Costs," Working Papers hal-03888188, HAL.
    5. Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2021. "Repeated Games with Switching Costs: Stationary vs History Independent Strategies," Papers 2103.00045, arXiv.org, revised Oct 2021.

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