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Repeated games with present-biased preferences

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  • Chade, Hector
  • Prokopovych, Pavlo
  • Smith, Lones

Abstract

We study infinitely repeated games with perfect monitoring, where players have [beta]-[delta] preferences. We compute the continuation payoff set using recursive techniques and then characterize equilibrium payoffs. We then explore the cost of the present-time bias, producing comparative statics. Unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set is not monotonic in [beta] or [delta]. Finally, we show how the equilibrium payoff set is contained in that of a repeated game with smaller discount factor.

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  • 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.
    • Handle: RePEc:eee:jetheo:v:139:y:2008:i:1:p:157-175
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    1. R. A. Pollak, 1968. "Consistent Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 201-208.
    2. Krusell, Per & Kuruscu, Burhanettin & Smith, Anthony Jr., 2002. "Equilibrium Welfare and Government Policy with Quasi-geometric Discounting," Journal of Economic Theory, Elsevier, vol. 105(1), pages 42-72, July.
    3. Matthew Rabin & Ted O'Donoghue, 1999. "Doing It Now or Later," American Economic Review, American Economic Association, vol. 89(1), pages 103-124, March.
    4. Dilip Abreu & David Pearce & Ennio Stacchetti, 2010. "Towards a Theory of Discounted Repeated Games with Imperfect Monitoring," Levine's Working Paper Archive 199, David K. Levine.
    5. 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..
    6. Steven M. Goldman, 1980. "Consistent Plans," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 533-537.
    7. Jonathan Gruber & Botond Köszegi, 2001. "Is Addiction "Rational"? Theory and Evidence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(4), pages 1261-1303.
    8. Stefano DellaVigna & M. Daniele Paserman, 2005. "Job Search and Impatience," Journal of Labor Economics, University of Chicago Press, vol. 23(3), pages 527-588, July.
    9. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    10. Kocherlakota, Narayana R., 1996. "Reconsideration-Proofness: A Refinement for Infinite Horizon Time Inconsistency," Games and Economic Behavior, Elsevier, vol. 15(1), pages 33-54, July.
    11. Dilip Abreu & David Pearce & Ennio Stacchetti, 1997. "Optimal Cartel Equilibria with Imperfect monitoring," Levine's Working Paper Archive 632, David K. Levine.
    12. 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.
    13. 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.
    14. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    15. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    16. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 391-401.
    17. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
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    15. John Duffy & Félix Muñoz-García, 2012. "Patience or Fairness? Analyzing Social Preferences in Repeated Games," Games, MDPI, vol. 3(1), pages 1-22, March.
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    23. Haan, Marco & Hauck, Dominic, 2014. "Games With Possibly Naive Hyperbolic Discounters," MPRA Paper 57960, University Library of Munich, Germany.
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    JEL classification:

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

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