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Complexity and Efficiency in Repeated Games and Negotiation

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Abstract

This paper considers the ‘negotiation game’ (Busch and Wen [4]) which combines the features of two-person alternating offers and repeated games. Despite the forces of bargaining, the negotiation game in general admits a large number of equilibria, some of which involve delay in agreement and inefficiency. In order to isolate equilibria in this game, we explicitly consider the complexity of implementing a strategy, introduced in the literature on repeated games played by automata. It turns out that when the players have a preference for less complex strategies (even at the margin) only efficient equilibria survive. Thus, complexity and bargaining in tandem may offer an explanation for co-operation in repeated games.

Suggested Citation

  • Lee, J. & Sabourian, H., 2004. "Complexity and Efficiency in Repeated Games and Negotiation," Cambridge Working Papers in Economics 0419, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:0419
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    1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
    2. Douglas Gale & Hamid Sabourian, 2005. "Complexity and Competition," Econometrica, Econometric Society, vol. 73(3), pages 739-769, May.
    3. Busch, Lutz-Alexander & Wen, Quan, 1995. "Perfect Equilibria in Negotiation Model," Econometrica, Econometric Society, vol. 63(3), pages 545-565, May.
    4. Douglas Gale & Hamid Sabourian, 2003. "Complexity and Competition, Part I: Sequential Matching," Levine's Bibliography 666156000000000199, UCLA Department of Economics.
    5. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    6. Fernandez, Raquel & Glazer, Jacob, 1991. "Striking for a Bargain between Two Completely Informed Agents," American Economic Review, American Economic Association, vol. 81(1), pages 240-252, March.
    7. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    8. Piccione, Michele, 1992. "Finite automata equilibria with discounting," Journal of Economic Theory, Elsevier, vol. 56(1), pages 180-193, February.
    9. Sabourian, Hamid, 2004. "Bargaining and markets: complexity and the competitive outcome," Journal of Economic Theory, Elsevier, vol. 116(2), pages 189-228, June.
    10. Piccione Michele & Rubinstein Ariel, 1993. "Finite Automata Play a Repeated Extensive Game," Journal of Economic Theory, Elsevier, vol. 61(1), pages 160-168, October.
    11. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    12. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    13. Binmore, K. & Piccione, M. & Samuelson, L., 1996. "Evolutionary Stability in Alternating-Offers Bargaining Games," Working papers 9603r, Wisconsin Madison - Social Systems.
    14. Binmore, Ken & Piccione, Michele & Samuelson, Larry, 1998. "Evolutionary Stability in Alternating-Offers Bargaining Games," Journal of Economic Theory, Elsevier, vol. 80(2), pages 257-291, June.
    15. Kalyan Chatterjee & Hamid Sabourian, 2000. "Multiperson Bargaining and Strategic Complexity," Econometrica, Econometric Society, vol. 68(6), pages 1491-1510, November.
    16. Piccione, M. & Rubinstein, A., 1992. "Finite Automata Play A Repeated Extensive Game," Papers 5-92, Tel Aviv.
    17. Haller, Hans & Holden, Steinar, 1990. "A letter to the editor on wage bargaining," Journal of Economic Theory, Elsevier, vol. 52(1), pages 232-236, October.
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    Keywords

    negotiation game; repeated game; bargaining; complexity; bounded rationality; automaton;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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