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Probabilistic choice in games: properties of Rosenthal's t-solutions

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  • Voorneveld, Mark

    ()
    (Dept. of Economics, Stockholm School of Economics)

Abstract

In t-solutions, quantal response equilibria based on the linear probability model as introduced in R.W. Rosenthal (1989, Int. J. Game Theory 18, 273-292), choice probabilities are related to the determination of leveling taxes. The set of t-solutions coincides with the set of Nash equilibria of a game with quadratic control costs. Increasing the rationality of the players allows them to successively eliminate higher levels of strictly dominated actions. Moreover, there exists a path of t-solutions linking uniform randomization to Nash equilibrium.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 542.

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Length: 15 pages
Date of creation: 28 Oct 2003
Date of revision: 31 Oct 2003
Handle: RePEc:hhs:hastef:0542

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Keywords: quantal response equilibrium; t-solutions; linear probability model;

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  1. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  2. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  3. Anderson, Simon P. & Goeree, Jacob K. & Holt, Charles A., 2001. "Minimum-Effort Coordination Games: Stochastic Potential and Logit Equilibrium," Games and Economic Behavior, Elsevier, vol. 34(2), pages 177-199, February.
  4. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June.
  5. Lawrence E. Blume & William R. Zame, 1993. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Game Theory and Information 9309001, EconWPA.
  6. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
  7. Jacob K Goeree & Charles A Holt, 2004. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," Levine's Working Paper Archive 618897000000000900, David K. Levine.
  8. Rosenthal, Robert W, 1989. "A Bounded-Rationality Approach to the Study of Noncooperative Games," International Journal of Game Theory, Springer, vol. 18(3), pages 273-91.
  9. Mattsson, Lars-Goran & Weibull, Jorgen W., 2002. "Probabilistic choice and procedurally bounded rationality," Games and Economic Behavior, Elsevier, vol. 41(1), pages 61-78, October.
  10. 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.
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Cited by:
  1. Paola Manzini & Marco Mariotti, 2013. "Stochastic Choice and Consideration Sets," Discussion Paper Series, Department of Economics 201303, Department of Economics, University of St. Andrews.
  2. Voorneveld, Mark & Fagraeus Lundström, Helena, 2005. "Strategic equivalence and bounded rationality in extensive form games," Working Paper Series in Economics and Finance 605, Stockholm School of Economics.
  3. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer, vol. 42(1), pages 119-156, January.
  4. Reinoud Joosten & Berend Roorda, 2008. "Generalized projection dynamics in evolutionary game theory," Papers on Economics and Evolution 2008-11, Max Planck Institute of Economics, Evolutionary Economics Group.
  5. Reinoud Joosten & Berend Roorda, 2011. "On evolutionary ray-projection dynamics," Computational Statistics, Springer, vol. 74(2), pages 147-161, October.

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