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


  • Voorneveld, Mark

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


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.

Suggested Citation

  • Voorneveld, Mark, 2003. "Probabilistic choice in games: properties of Rosenthal's t-solutions," SSE/EFI Working Paper Series in Economics and Finance 542, Stockholm School of Economics, revised 20 Dec 2003.
  • Handle: RePEc:hhs:hastef:0542

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    1. 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, January.
    2. Rosenthal, Robert W, 1989. "A Bounded-Rationality Approach to the Study of Noncooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 273-291.
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    Cited by:

    1. 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.
    2. Paola Manzini & Marco Mariotti, 2014. "Stochastic Choice and Consideration Sets," Econometrica, Econometric Society, vol. 82(3), pages 1153-1176, May.
    3. Tsakas, Elias & Voorneveld, Mark, 2009. "The target projection dynamic," Games and Economic Behavior, Elsevier, vol. 67(2), pages 708-719, November.
    4. repec:spr:compst:v:74:y:2011:i:2:p:147-161 is not listed on IDEAS
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.

    More about this item


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

    JEL classification:

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

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