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The Condorcet Paradox Revisited

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  • P. Jean-Jacques Herings

    (Maastricht University)

  • Harold Houba

    (VU University Amsterdam)

Abstract

We analyze the simplest Condorcet cycle with three players and three alternatives within a strategic bargaining model with recognition probabilities and costless delay. Mixed consistent subgame perfect equilibria exist whenever the geometric mean of the agents' risk coefficients, ratios of utility differences between alternatives, is at most one. Equilibria are generically unique, Pareto efficient, and ensure agreement within finite expected time. Agents propose best or second-best alternatives. Agents accept best alternatives, may reject second-best alternatives with positive probability, and reject otherwise. For symmetric recognition probabilities and risk coefficients below one, agreement is immediate and each agent proposes his best alternative.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 10-026/1.

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Date of creation: 01 Mar 2010
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Handle: RePEc:dgr:uvatin:20100026

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Web page: http://www.tinbergen.nl

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Keywords: Bargaining; Condorcet Paradox; Consistent Subgame Perfect Equilibrium; Risk Aversion; Compromise Prone;

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  3. Chatterjee, Kalyan & Bhaskar Dutta & Debraj Ray & Kunal Sengupta, 1993. "A Noncooperative Theory of Coalitional Bargaining," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 60(2), pages 463-77, April.
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  6. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  7. Herings,P. Jean-Jacques & Peeters,Ronald J.A.P, 2000. "Stationary Equilibria in Stochastic Games: Structure, Selection, and Computation," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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  9. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, Econometric Society, vol. 47(5), pages 1085-1112, September.
  10. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, Elsevier, vol. 100(2), pages 191-219, October.
  11. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 90-123, May.
  12. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262582384, December.
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