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Note Perfect folk theorems. Does public randomization matter?

Author

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  • Wojciech Olszewski

    () (Dept. of Econ., Warsaw Univ., ul. Dluga 44/50, 00-241 Warsaw, Poland)

Abstract

I consider two player games, where player 1 can use only pure strategies, and player 2 can use mixed strategies. I indicate a class of such games with the property that under public randomization both the discounted and the undiscounted finitely repeated perfect folk theorems do hold, but the discounted theorem does not without public randomization. Further, I show that the class contains games such that without public randomization the undiscounted theorem does not hold, as well as games such that without public randomization the undiscounted theorem does hold.

Suggested Citation

  • Wojciech Olszewski, 1998. "Note Perfect folk theorems. Does public randomization matter?," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 147-156.
  • Handle: RePEc:spr:jogath:v:27:y:1998:i:1:p:147-156 Note: Received March 1996/Revised version 1997
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    References listed on IDEAS

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    1. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    2. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February.
    3. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    4. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, pages 834-847.
    5. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136 World Scientific Publishing Co. Pte. Ltd..
    6. Alcantud, J. C. R., 2002. "Non-binary choice in a non-deterministic model," Economics Letters, Elsevier, vol. 77(1), pages 117-123, September.
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    Cited by:

    1. Yuichi Yamamoto, 2010. "The use of public randomization in discounted repeated games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 431-443, July.
    2. Gonzalez-Diaz, Julio, 2006. "Finitely repeated games: A generalized Nash folk theorem," Games and Economic Behavior, Elsevier, vol. 55(1), pages 100-111, April.
    3. Bo Chen & Satoru Fujishige, 2013. "On the feasible payoff set of two-player repeated games with unequal discounting," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 295-303, February.

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