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Stubbornness, Power, and Equilibrium Selection in Repeated Games with Multiple Equilibria

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  • Kjell Hausken

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Abstract

Axelord’s [(1970), Conflict of Interest, Markham Publishers, Chicago] index of conflict in 2 × 2 games with two pure strategy equilibria has the property that a reduction in the cost of holding out corresponds to an increase in conflict. This article takes the opposite view, arguing that if losing becomes less costly, a player is less likely to gamble to win, which means that conflict will be less frequent. This approach leads to a new power index and a new measure of stubbornness, both anchored in strategic reasoning. The win probability defined as power constitutes an equilibrium refinement which differs from Harsanyi and Selten’s [(1988), A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge] refinement. In contrast, Axelrod’s approach focuses on preferences regarding divergences from imaginary outmost rewards that cannot be obtained jointly. The player who is less powerful in an asymmetric one-shot game becomes more powerful in the repeated game, provided he or she values the future sufficiently more than the opponent. This contrasts with the view that repetition induces cooperation, but conforms with the expectation that a more patient player receives a larger share of the pie. Copyright Springer Science+Business Media, LLC 2007

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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 62 (2007)
Issue (Month): 2 (March)
Pages: 135-160

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Handle: RePEc:kap:theord:v:62:y:2007:i:2:p:135-160

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Web page: http://www.springerlink.com/link.asp?id=100341

Related research

Keywords: conflict; discounting; equilibrium refinement; equilibrium selection; power index; repeated game; stubbornness incentive; C72; D74;

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  1. Hausken, Kjell, 2005. "The battle of the sexes when the future is important," Economics Letters, Elsevier, vol. 87(1), pages 89-93, April.
  2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
  3. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  4. Hirshleifer, Jack, 1995. "Anarchy and Its Breakdown," Journal of Political Economy, University of Chicago Press, vol. 103(1), pages 26-52, February.
  5. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
  6. Grossman, Herschel I, 1991. "A General Equilibrium Model of Insurrections," American Economic Review, American Economic Association, vol. 81(4), pages 912-21, September.
  7. Mohr, Matthias & Hausken, Kjell, 1996. "Conflict, interest and strategy: A risk limit approach to conflict," MPIfG Discussion Paper 96/7, Max Planck Institute for the Study of Societies.
  8. Skaperdas, Stergios & Syropoulos, Constantinos, 1996. "Can the shadow of the future harm cooperation?," Journal of Economic Behavior & Organization, Elsevier, vol. 29(3), pages 355-372, May.
  9. 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.
  10. Harsanyi,John C., 1986. "Rational Behaviour and Bargaining Equilibrium in Games and Social Situations," Cambridge Books, Cambridge University Press, number 9780521311830.
  11. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  12. R J Johnston, 1978. "On the measurement of power: some reactions to Laver," Environment and Planning A, Pion Ltd, London, vol. 10(8), pages 907-914, August.
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