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Restricted feedback in long term relationships

Author

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  • Doraszelski, Ulrich
  • Escobar, Juan F.
Abstract
This paper studies long term relationships, modeled as repeated games, with restricted feedback. Players condition current play on summary statistics of past play rather than the entire history, as may be the case in online markets. Our state strategy equilibrium framework allows for arbitrary restrictions on strategies. We derive a recursive characterization for the set of equilibrium payoffs similar to that of Abreu, Pearce, and Stacchetti (1986, 1990) [2,3] for perfect public equilibria and show that the set of equilibrium payoffs is the largest fixed point of a monotone operator. We use our characterization to derive necessary and sufficient conditions for efficient trade in a repeated product choice game where costumers condition their purchase decisions only on the last performance signal.

Suggested Citation

  • Doraszelski, Ulrich & Escobar, Juan F., 2012. "Restricted feedback in long term relationships," Journal of Economic Theory, Elsevier, vol. 147(1), pages 142-161.
    • Handle: RePEc:eee:jetheo:v:147:y:2012:i:1:p:142-161
    DOI: 10.1016/j.jet.2011.11.013
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    References listed on IDEAS

    as
    1. Cole, Harold L. & Kocherlakota, Narayana, 2001. "Dynamic Games with Hidden Actions and Hidden States," Journal of Economic Theory, Elsevier, vol. 98(1), pages 114-126, May.
    2. Glenn Ellison, 1994. "Cooperation in the Prisoner's Dilemma with Anonymous Random Matching," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(3), pages 567-588.
    3. Tristan Tomala & Jerome Renault & Marco Scarsini, 2007. "A Minority Game with Bounded Recall," Post-Print hal-00538967, HAL.
    4. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    5. Michihiro Kandori, 1992. "The Use of Information in Repeated Games with Imperfect Monitoring," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 581-593.
    6. , & ,, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    7. Ekmekci, Mehmet, 2011. "Sustainable reputations with rating systems," Journal of Economic Theory, Elsevier, vol. 146(2), pages 479-503, March.
    8. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-465, Autumn.
    9. Jérôme Renault & Marco Scarsini & Tristan Tomala, 2007. "A Minority Game with Bounded Recall," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 873-889, November.
    10. Cole, Harold L. & Kocherlakota, Narayana R., 2005. "Finite memory and imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 53(1), pages 59-72, October.
    11. Drew Fudenberg & David M. Kreps & Eric S. Maskin, 1990. "Repeated Games with Long-run and Short-run Players," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(4), pages 555-573.
    12. Cheng Wang, 1995. "Dynamic Insurance with Private Information and Balanced Budgets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(4), pages 577-595.
    13. Daron Acemoglu & James A. Robinson, 2001. "A Theory of Political Transitions," American Economic Review, American Economic Association, vol. 91(4), pages 938-963, September.
    14. V. Bhaskar, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 135-149.
    15. Atkeson, Andrew, 1991. "International Lending with Moral Hazard and Risk of Repudiation," Econometrica, Econometric Society, vol. 59(4), pages 1069-1089, July.
    16. Johannes Hörner & Wojciech Olszewski, 2009. "How Robust is the Folk Theorem?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(4), pages 1773-1814.
    17. Fernandes, Ana & Phelan, Christopher, 2000. "A Recursive Formulation for Repeated Agency with History Dependence," Journal of Economic Theory, Elsevier, vol. 91(2), pages 223-247, April.
    18. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    19. repec:dau:papers:123456789/6381 is not listed on IDEAS
    20. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    21. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
    22. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    23. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    24. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, March.
    25. Drew Fudenberg & David K. Levine, 2009. "Repeated Games with Frequent Signals," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(1), pages 233-265.
    26. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    27. Chade, Hector & Prokopovych, Pavlo & Smith, Lones, 2008. "Repeated games with present-biased preferences," Journal of Economic Theory, Elsevier, vol. 139(1), pages 157-175, March.
    28. Christopher Phelan & Ennio Stacchetti, 2001. "Sequential Equilibria in a Ramsey Tax Model," Econometrica, Econometric Society, vol. 69(6), pages 1491-1518, November.
    29. George J. Mailath & Wojciech Olszewski, 2008. "Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring, Third Version," PIER Working Paper Archive 10-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 02 Mar 2010.
    30. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, June.
    31. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2009. "Repeated games with one-memory," Journal of Economic Theory, Elsevier, vol. 144(1), pages 312-336, January.
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    More about this item

    Keywords

    Repeated games; Restricted feedback; Product choice game;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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