Abstract
In real life games, a player’s belief about the consequence of a strategy is often ambiguous due to out-of-control factors in the environment where the games are played. However, existing work cannot handle this situation. To address the issue, we introduce a new kind of games, called ambiguous games, and incorporate human cognitive factors of ambiguity aversion and minimising regret to propose a concept of solution to such a game. Moreover, we also study how ambiguity degrees of belief about payoffs impact the outcomes of a game, and find the condition under which a player should release more or less ambiguous information to his opponents.
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References
Bade, S.: Electoral Competition with Uncertainty Averse Parties. Games and Economic Behavior 72(1), 12–29 (2011)
Clemente, M., Fernandez, F.R., Puerto, J.: Pareto-Optimal Security Strategies in Matrix Games with Fuzzy Payoffs. Fuzzy Sets and Systems 176(1), 36–45 (2011)
Dubois, D., Prade, H.: A Note on Measures of Specificity for Fuzzy Sets. International Journal of General Systems 10(4), 279–283 (1985)
Ellsberg, D.: Risk, Ambiguous, and the Savage Axioms. Quarterly Journal of Economics 75(4), 643–669 (1961)
Gintis, H.: The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences. Princeton University Press, Princeton (2009)
Gurnani, H., Shi, M.: A Bargaining Model for a First-Time Interaction under Asymmetric Beliefs of Supply Reliability. Management Science 56(2), 865–880 (2006)
Halpern, J.Y., Pass, R.: Iterated Regret Minimization: A New Solution Concept. Games and Economic Behavior 74(1), 184–207 (2012)
Harsanyi, J.C.: Games with Incomplete Information Played by “Bayesian” Players, Part I. The Basic Model. Management Science 3(14), 159–182 (1967)
Kozhan, R.: Non-Additive Anonymous Games. International Journal of Game Theory 40(2), 215–230 (2011)
Larbani, M.: Solving Bimatrix Games with Fuzzy Payoffs by Introducing Nature as a Third Player. Fuzzy Sets and Systems 160(5), 657–666 (2009)
Levi, I.: Why Indeterminate Probability Is Rational. Journal of Applied Logic 7(4), 364–376 (2009)
Li, C., Zhang, Q.: Nash Equilibrium for Fuzzy Non-Cooperative Games. Fuzzy Sets and Systems 176(1), 46–55 (2011)
Mallozzi, L., Sclazo, V., Tijs, S.: Fuzzy Interval Cooperative Games. Fuzzy Sets and Systems 165(1), 98–105 (2011)
Ma, W., Xiong, W., Luo, X.: A D-S Theory Based AHP Decision Making Approach with Ambiguous Evaluations of Multiple Criteria. In: Anthony, P., Ishizuka, M., Lukose, D. (eds.) PRICAI 2012. LNCS, vol. 7458, pp. 297–311. Springer, Heidelberg (2012)
Mertens, J.F., Neyman, A.: Stochastic Games. International Journal of Game Theory 10(2), 53–66 (1981)
Myerson, R.B.: Refinements of the Nash Equilibrium Concept. International Journal of Game Theory 15(2), 133–154 (1978)
Nash, J.: Non-Cooperative Games. The Annals of Mathematics 54(2), 286–295 (1951)
Rahwan, T., Michalak, T., Wooldridge, M., Jennings, N.R.: Anytime Coalition Structure Generation in Multi-Agent Systems with Positive or Negative Externalities. Artificial Intelligence 186, 95–122 (2012)
Rothe, J.: Uncertainty Aversion and Equilibrium in Normal Form Games (2010), http://eprints.lse.ac.uk/37542/1/Uncertainty_aversion_and_equilibrium_in_normal_form_gameslsero.pdf
Selten, R.: A Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games. International Journal of Game Theory 4(1), 25–55 (1975)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Snow, A.: Amgibuity and the Value of Information. Journal of Risk and Uncertainty 40(2), 133–145 (2010)
Strat, T.M.: Decision Analysis Using Belief Functions. International Journal of Approximate Reasoning 4(5-6), 391–418 (1990)
Xiong, W., Luo, X., Ma, W.: An Expected Utility Interval Theory for Decision-Making under Uncertainty of Ambiguity: To Avoid Ambiguity and Minimise Regret. Fuzzy Sets and Systems. Technique Report, Institute of Logic and Cognition, Sun Yatsen Univerisity (submitted 2012)
Zorich, V.A.: Mathematical Analysis I. Springer, Heidelberg (2004)
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Xiong, W., Luo, X., Ma, W. (2012). Games with Ambiguous Payoffs and Played by Ambiguity and Regret Minimising Players. In: Thielscher, M., Zhang, D. (eds) AI 2012: Advances in Artificial Intelligence. AI 2012. Lecture Notes in Computer Science(), vol 7691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35101-3_35
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DOI: https://doi.org/10.1007/978-3-642-35101-3_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35100-6
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