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Bounded Memory, Reputation, and Impatience

Author

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  • Benjamin Sperisen

    () (Department of Economics, Tulane University)

Abstract

Reputation models typically assume players have full memory, yet in many applications this does not hold. This paper studies incomplete information games where players observe only finitely many recent periods, deriving a recursive characterization of the equilibrium payoff set that captures both stationary and previously unexplored non-stationary equilibria, as well as tools for studying purifiable (i.e. robust to payoff perturbations) equilibria. These tools are applied to a product choice game. For 1-period memory, I obtain the exact minimum and maximum purifiable equilibrium payoffs for almost all discount factors and prior beliefs on an "honest" firm type. For long memory, I characterize the minimum purifiable non-stationary equilibrium payoff and unique stationary payoff. In both cases, incomplete information and non-stationary behavior qualitatively change the equilibrium payoff set. These results hold for fixed discount factors independent of prior beliefs, and so do not require extreme patience.

Suggested Citation

  • Benjamin Sperisen, 2016. "Bounded Memory, Reputation, and Impatience," Working Papers 1602, Tulane University, Department of Economics.
  • Handle: RePEc:tul:wpaper:1602
    as

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    File URL: http://repec.tulane.edu/RePEc/pdf/tul1602r.pdf
    File Function: First Version, March 2016
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    References listed on IDEAS

    as
    1. Doraszelski, Ulrich & Escobar, Juan, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    2. Liu, Qingmin & Skrzypacz, Andrzej, 2014. "Limited records and reputation bubbles," Journal of Economic Theory, Elsevier, vol. 151(C), pages 2-29.
    3. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, March.
    4. Monte, Daniel, 2013. "Bounded memory and permanent reputations," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 345-354.
    5. Ekmekci, Mehmet, 2011. "Sustainable reputations with rating systems," Journal of Economic Theory, Elsevier, vol. 146(2), pages 479-503, March.
    6. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    7. Benjamin Sperisen, 2015. "Bad Reputation under Bounded and Fading Memory," Working Papers 1527, Tulane University, Department of Economics.
    8. 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.
    9. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2009. "Repeated games with one-memory," Journal of Economic Theory, Elsevier, vol. 144(1), pages 312-336, January.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Reputation; bounded memory; purifiability; product choice game;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

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