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Bounded Memory, Reputation, and Impatience

Listed author(s):
  • Benjamin Sperisen

    ()

    (Department of Economics, Tulane University)

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.

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File URL: http://econ.tulane.edu/RePEc/pdf/tul1602r.pdf
File Function: First Version, March 2016
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Paper provided by Tulane University, Department of Economics in its series Working Papers with number 1602.

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Date of creation: Mar 2016
Handle: RePEc:tul:wpaper:1602
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Web page: http://econ.tulane.edu

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  1. Liu, Qingmin & Skrzypacz, Andrzej, 2014. "Limited records and reputation bubbles," Journal of Economic Theory, Elsevier, vol. 151(C), pages 2-29.
  2. 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.
  3. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, 03.
  4. Ekmekci, Mehmet, 2011. "Sustainable reputations with rating systems," Journal of Economic Theory, Elsevier, vol. 146(2), pages 479-503, March.
  5. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2009. "Repeated games with one-memory," Journal of Economic Theory, Elsevier, vol. 144(1), pages 312-336, January.
  6. Monte, Daniel, 2013. "Bounded memory and permanent reputations," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 345-354.
  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. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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