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Games under Ambiguous Payoffs and Optimistic Attitudes

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  • Wei Xiong

Abstract

In real‐life games, the consequence or payoff of a strategy profile and a player′s belief about the consequence of a strategy profile are often ambiguous, and players may have different optimistic attitudes with respect to a strategy profile. To handle this problem, this paper proposes a decision rule using the Hurwicz criterion and Dempster‐Shafer theory. Based on this rule, we introduce a new kind of games, called ambiguous games, and propose a solution concept that is appropriate for this sort of games. Moreover, we also study how the beliefs regarding possible payoffs and optimistic attitudes may affect the solutions of such a game. To illustrate our model, we provide an analysis of a scenario concerning allocating resource of defending and attacking in military contexts.

Suggested Citation

  • Wei Xiong, 2014. "Games under Ambiguous Payoffs and Optimistic Attitudes," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:531987
    DOI: 10.1155/2014/531987
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    References listed on IDEAS

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    1. Jian Xiong & Xu Tan & Ke-wei Yang & Ying-wu Chen, 2013. "Fuzzy Group Decision Making for Multiobjective Problems: Tradeoff between Consensus and Robustness," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, August.
    2. Atsushi Kajii & Takashi Ui, 2005. "Incomplete Information Games With Multiple Priors," The Japanese Economic Review, Japanese Economic Association, vol. 56(3), pages 332-351, September.
    3. Jian Xiong & Xu Tan & Ke-wei Yang & Ying-wu Chen, 2013. "Fuzzy Group Decision Making for Multiobjective Problems: Tradeoff between Consensus and Robustness," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Jürgen Eichberger & David Kelsey, 2011. "Are the treasures of game theory ambiguous?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 313-339, October.
    5. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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