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Computing Equilibria in Discounted 2 × 2 Supergames

  • Kimmo Berg

    ()

  • Mitri Kitti
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    This article examines the subgame perfect pure strategy equilibrium paths and payoff sets of discounted supergames with perfect monitoring. The main contribution is to provide methods for computing and tools for analyzing the equilibrium paths and payoffs in repeated games. We introduce the concept of a first-action feasible path, which simplifies the computation of equilibria. These paths can be composed into a directed multigraph, which is a useful representation for the equilibrium paths. We examine how the payoffs, discount factors and the properties of the multigraph affect the possible payoffs, their Hausdorff dimension, and the complexity of the equilibrium paths. The computational methods are applied to the 12 symmetric strictly ordinal 2 × 2 games. We find that these games can be classified into three groups based on the complexity of the equilibrium paths. Copyright Springer Science+Business Media, LLC. 2013

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    File URL: http://hdl.handle.net/10.1007/s10614-011-9308-5
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    Article provided by Society for Computational Economics in its journal Computational Economics.

    Volume (Year): 41 (2013)
    Issue (Month): 1 (January)
    Pages: 71-88

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    Handle: RePEc:kap:compec:v:41:y:2013:i:1:p:71-88
    Contact details of provider: Web page: http://www.springerlink.com/link.asp?id=100248

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    1. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, 07.
    2. George J. Mailath & Ichiro Obara & Tadashi Sekiguchi, . "The Maximum Efficient Equilibrium Payoff in the Repeated Prisoners' Dilemma," Penn CARESS Working Papers 83719e84b6825736ffcfdfacb, Penn Economics Department.
    3. Hannu Salonen & Hannu Vartiainen, 2007. "Valuating Payoff Streams under Unequal Discount Factors," Discussion Papers 16, Aboa Centre for Economics.
    4. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    5. 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.
    6. Cronshaw, Mark B, 1997. "Algorithms for Finding Repeated Game Equilibria," Computational Economics, Society for Computational Economics, vol. 10(2), pages 139-68, May.
    7. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
    8. 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.
    9. Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-22, July.
    10. Mitri Kitti, 2011. "Conditionally Stationary Equilibria in Discounted Dynamic Games," Dynamic Games and Applications, Springer, vol. 1(4), pages 514-533, December.
    11. 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.
    12. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March.
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