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Perfect Public Equilibrium When Players are Patient

  • Drew Fudenberg
  • David K Levine
  • Satoru Takahashi

We provide a characterization of the limit set of perfect public equilibrium payoffs of repeated games with imperfect public monitoring as the discount factor goes to one. Our result covers general stage games including those that fail a “full-dimensionality†condition that had been imposed in past work. It also provides a characterization of the limit set when the strategies are restricted in a way that endogenously makes the full-dimensionality condition fail, as in the strongly symmetric equilibrium studied by Abreu [Abreu, D., 1986. Extremal equilibria of oligopolistic supergames. J. Econ. Theory 39, 191–228] and Abreu et al. [Abreu, D., Pearce, D., Stacchetti, E., 1986. Optimal cartel equilibria with imperfect monitoring. J. Econ. Theory 39, 251–269]. Finally, we use our characterization to give a sufficient condition for the exact achievability of first-best outcomes. Equilibria of this type, for which all continuation payoffs lie on the Pareto frontier, have a strong renegotiation-proofness property: regardless of the history, players can never unanimously prefer another equilibrium.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 618897000000000865.

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Date of creation: 26 Sep 2004
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Handle: RePEc:cla:levarc:618897000000000865
Contact details of provider: Web page: http://www.dklevine.com/

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  1. Farrell, Joseph & Maskin, Eric, 1987. "Renegotiation in Repeated Games," Department of Economics, Working Paper Series qt9wv3h5jb, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  2. Fudenberg, D. & Levine, D.K., 1991. "Efficiency and Obsevability with Long-Run and Short-Run Players," Working papers 591, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Jeffrey Ely & Drew Fudenberg & David K. Levine, 2004. "When is Reputation Bad?," Harvard Institute of Economic Research Working Papers 2035, Harvard - Institute of Economic Research.
  4. Wen, Quan, 1994. "The "Folk Theorem" for Repeated Games with Complete Information," Econometrica, Econometric Society, vol. 62(4), pages 949-54, July.
  5. Maskin, Eric & Kreps, David & Fudenberg, Drew, 1990. "Repeated Games with Long-run and Short-run Players," Scholarly Articles 3226950, Harvard University Department of Economics.
  6. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  7. Susan Athey & Kyle Bagwell, 1999. "Optimal Collusion with Private Information," Working papers 99-17, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. Abreu, Dilip & Dutta, Prajit K & Smith, Lones, 1994. "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, Econometric Society, vol. 62(4), pages 939-48, July.
  9. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
  10. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-63, September.
  11. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
  12. 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.
  13. D. Fudenberg and E. Maskin., 1987. "Nash and Perfect Equilibria of Discounted Repeated Games," Economics Working Papers 8736, University of California at Berkeley.
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