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Probabilistic Choice in Games: Properties of Rosenthal’s t-Solutions

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  • Mark Voorneveld

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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

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 34 (2006)
Issue (Month): 1 (April)
Pages: 105-121

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Handle: RePEc:spr:jogath:v:34:y:2006:i:1:p:105-121

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Keywords: Quantal response equilibrium; t-solutions; Linear probability model; Bounded rationality;

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References

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  1. Lawrence E. Blume & William R. Zame, 1993. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Game Theory and Information 9309001, EconWPA.
  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. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June.
  4. 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.
  5. Jacob K. Goeree & Charles A. Holt, 2000. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," Virginia Economics Online Papers 333, University of Virginia, Department of Economics.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
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Citations

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Cited by:
  1. Herings, P. Jean-Jacques & Peeters, Ronald, 2006. "Homotopy Methods to Compute Equilibria in Game Theory," Research Memorandum 046, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Tsakas, Elias & Voorneveld, Mark, 2007. "The target projection dynamic," Working Paper Series in Economics and Finance 670, Stockholm School of Economics, revised 13 Aug 2007.
  3. 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.
  4. Reinoud Joosten & Berend Roorda, 2011. "On evolutionary ray-projection dynamics," Computational Statistics, Springer, vol. 74(2), pages 147-161, October.
  5. Paola Manzini & Marco Mariotti, 2013. "Stochastic Choice and Consideration Sets," Discussion Paper Series, Department of Economics 201303, Department of Economics, University of St. Andrews.
  6. Reinoud Joosten & Berend Roorda, 2008. "Generalized projection dynamics in evolutionary game theory," Papers on Economics and Evolution 2008-11, Philipps University Marburg, Department of Geography.

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