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Stochastic dominance equilibria in two-person noncooperative games

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  • Perea ý Monsuwé, A.

    (Quantitative Economics)

  • Peters, H.J.M.

    (Quantitative Economics)

  • Schulteis, T.J.W.

    (Quantitative Economics)

  • Vermeulen, A.J.

    (Quantitative Economics)

Abstract

Two-person noncooperative games with finitely many pure strategies and ordinal preferences over pure outcomes are considered, in which probability distributions resulting from mixed strategies are evaluated according to t-degree stochastic dominance. A t-best reply is a strategy that induces a t-degree stochastically undominated distribution, and a t-equilibrium is a pair of t-best replies. The paper provides a characterization and existence proofs of t-equilibria in terms of representing utility functions, and shows that for t becoming large-which can be interpreted as the players becoming more risk averse-behavior converges to a specific form of max-min play. More precisely, this means that in the limit each player puts all weight on a strategy that maximizes the worst outcome for the opponent, within the supports of the strategies in the limiting sequenceof t-equilibria.
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Suggested Citation

  • Perea ý Monsuwé, A. & Peters, H.J.M. & Schulteis, T.J.W. & Vermeulen, A.J., 2005. "Stochastic dominance equilibria in two-person noncooperative games," Research Memorandum 005, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2005005
    DOI: 10.26481/umamet.2005005
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    References listed on IDEAS

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    1. Swait, Joffre & Adamowicz, Wiktor, 2001. "The Influence of Task Complexity on Consumer Choice: A Latent Class Model of Decision Strategy Switching," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 28(1), pages 135-148, June.
    2. Peter C. Fishburn, 1980. "Stochastic Dominance and Moments of Distributions," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 94-100, February.
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, September.
    4. Borgers, Tilman, 1993. "Pure Strategy Dominance," Econometrica, Econometric Society, vol. 61(2), pages 423-430, March.
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    Cited by:

    1. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.
    2. Wiktor Adamowicz & David Bunch & Trudy Cameron & Benedict Dellaert & Michael Hanneman & Michael Keane & Jordan Louviere & Robert Meyer & Thomas Steenburgh & Joffre Swait, 2008. "Behavioral frontiers in choice modeling," Marketing Letters, Springer, vol. 19(3), pages 215-228, December.
    3. Singh, Sonika & Swait, Joffre, 2017. "Channels for search and purchase: Does mobile Internet matter?," Journal of Retailing and Consumer Services, Elsevier, vol. 39(C), pages 123-134.
    4. Wendel, S. & Dellaert, B.G.C., 2008. "Situation-Based Shifts in Consumer Web Site Benefit Salience: The Joint Role of Affect and Cognition," ERIM Report Series Research in Management ERS-2008-050-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    5. Hans Peters & Tim Schulteis & Dries Vermeulen, 2010. "Generalized stochastic dominance and bad outcome aversion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 285-290, July.
    6. Gummerus, Johanna & Pihlström, Minna, 2011. "Context and mobile services' value-in-use," Journal of Retailing and Consumer Services, Elsevier, vol. 18(6), pages 521-533.
    7. Roponen, Juho & Ríos Insua, David & Salo, Ahti, 2020. "Adversarial risk analysis under partial information," European Journal of Operational Research, Elsevier, vol. 287(1), pages 306-316.
    8. Chen Lin & Sriram Venkataraman & Sandy D. Jap, 2013. "Media Multiplexing Behavior: Implications for Targeting and Media Planning," Marketing Science, INFORMS, vol. 32(2), pages 310-324, March.
    9. Collier, Joel E. & Moore, Robert S. & Horky, Alisha & Moore, Melissa L., 2015. "Why the little things matter: Exploring situational influences on customers' self-service technology decisions," Journal of Business Research, Elsevier, vol. 68(3), pages 703-710.
    10. Dellaert, Benedict G.C. & Arentze, Theo & Horeni, Oliver & Timmermans, Harry J.P., 2017. "Deriving attribute utilities from mental representations of complex decisions," Journal of choice modelling, Elsevier, vol. 22(C), pages 24-38.
    11. Frank J. van Rijnsoever & Martin J. Dijst & Carolina Castaldi, 2009. "Involvement and use of multiple search channels in the automobile purchase process," Innovation Studies Utrecht (ISU) working paper series 09-06, Utrecht University, Department of Innovation Studies, revised Apr 2009.

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