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

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  • Mark Voorneveld

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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  • Mark Voorneveld, 2006. "Probabilistic Choice in Games: Properties of Rosenthal’s t-Solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 105-121, April.
    • Handle: RePEc:spr:jogath:v:34:y:2006:i:1:p:105-121
    DOI: 10.1007/s00182-005-0003-4
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    Cited by:

    1. Alberto Vesperoni, 2016. "A contest success function for rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 905-937, December.
    2. Reinoud Joosten & Berend Roorda, 2011. "On evolutionary ray-projection dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 147-161, October.
    3. Paola Manzini & Marco Mariotti, 2014. "Stochastic Choice and Consideration Sets," Econometrica, Econometric Society, vol. 82(3), pages 1153-1176, May.
    4. Tsakas, Elias & Voorneveld, Mark, 2009. "The target projection dynamic," Games and Economic Behavior, Elsevier, vol. 67(2), pages 708-719, November.
    5. Paola Manzini & Marco Mariotti, 2014. "Stochastic Choice and Consideration Sets," Econometrica, Econometric Society, vol. 82(3), pages 1153-1176, May.
    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.
    7. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 119-156, January.
    8. Roy Allen & John Rehbeck, 2021. "A Generalization of Quantal Response Equilibrium via Perturbed Utility," Games, MDPI, vol. 12(1), pages 1-16, March.
    9. Ellison, Glenn & Fudenberg, Drew & Imhof, Lorens A., 2016. "Fast convergence in evolutionary models: A Lyapunov approach," Journal of Economic Theory, Elsevier, vol. 161(C), pages 1-36.
    10. Voorneveld, Mark & Fagraeus Lundström, Helena, 2005. "Strategic equivalence and bounded rationality in extensive form games," SSE/EFI Working Paper Series in Economics and Finance 605, Stockholm School of Economics.

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    More about this item

    Keywords

    Quantal response equilibrium; t-solutions; Linear probability model; Bounded rationality;
    All these keywords.

    JEL classification:

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

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