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Repeated games with voluntary information purchase

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  • Flesch, János
  • Perea, Andrés

Abstract

We consider discounted repeated games in which players can voluntarily purchase information about the opponents' actions at past stages. Information about a stage can be bought at a fixed but arbitrary cost. Opponents cannot observe the information purchase by a player. For our main result, we make the usual assumption that the dimension of the set FIR of feasible and individually rational payoff vectors is equal to the number of players. We show that, if there are at least three players and each player has at least four actions, then every payoff vector in the interior of the set FIR can be achieved by a Nash equilibrium of the discounted repeated game if the discount factor is sufficiently close to 1. Therefore, nearly efficient payoffs can be achieved even if the cost of monitoring is high. We show that the same result holds if there are at least four players and at least three actions for each player. Finally, we indicate how the construction can be extended to sequential equilibrium.

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  • Flesch, János & Perea, Andrés, 2009. "Repeated games with voluntary information purchase," Games and Economic Behavior, Elsevier, vol. 66(1), pages 126-145, May.
    • Handle: RePEc:eee:gamebe:v:66:y:2009:i:1:p:126-145
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    References listed on IDEAS

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    1. Ichiro Obara, "undated". "Endogenous Monitoring," UCLA Economics Online Papers 398, UCLA Department of Economics.
    2. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
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    4. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    5. Miyagawa, Eiichi & Miyahara, Yasuyuki & Sekiguchi, Tadashi, 2008. "The folk theorem for repeated games with observation costs," Journal of Economic Theory, Elsevier, vol. 139(1), pages 192-221, March.
    6. Roy Radner, 1986. "Repeated Partnership Games with Imperfect Monitoring and No Discounting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 43-57.
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    Cited by:

    1. Lehrer, Ehud & Solan, Eilon, 2018. "High frequency repeated games with costly monitoring," Theoretical Economics, Econometric Society, vol. 13(1), January.
    2. Hino, Yoshifumi, 2019. "An efficiency result in a repeated prisoner’s dilemma game under costly observation with nonpublic randomization," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 47-53.
    3. repec:kbb:dpaper:2011-44 is not listed on IDEAS
    4. Hino, Yoshifumi, 2018. "A folk theorem in infinitely repeated prisoner's dilemma with small observation cost," MPRA Paper 90381, University Library of Munich, Germany.
    5. Miyahara, Yasuyuki & Sekiguchi, Tadashi, 2013. "Finitely repeated games with monitoring options," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1929-1952.
    6. Awaya, Yu, 2014. "Community enforcement with observation costs," Journal of Economic Theory, Elsevier, vol. 154(C), pages 173-186.
    7. Hino, Yoshifumi, 2018. "A folk theorem in infinitely repeated prisoner's dilemma with small observation cost," MPRA Paper 96010, University Library of Munich, Germany, revised 13 Sep 2019.
    8. Miklós-Thal, Jeanine & Schumacher, Heiner, 2013. "The value of recommendations," Games and Economic Behavior, Elsevier, vol. 79(C), pages 132-147.
    9. Fujiwara-Greve, Takako & Okuno-Fujiwara, Masahiro & Suzuki, Nobue, 2012. "Voluntarily separable repeated Prisonerʼs Dilemma with reference letters," Games and Economic Behavior, Elsevier, vol. 74(2), pages 504-516.
    10. Yasuyuki Miyahara & Tadashi Sekiguchi, 2016. "Finitely Repeated Games with Automatic and Optional Monitoring," Discussion Papers 2016-12, Kobe University, Graduate School of Business Administration.

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