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Games with Incomplete Preferences
Juho Kokkala supervisors Prof. Raimo P. Hämäläinen Dr. Tech. Kai Virtanen Systems Analysis Laboratory Aalto University School of Science and Technology
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Games with Incomplete Preferences
Normal-form non-cooperative game with 2-N players Strategy set for each player i Preference relation over outcomes for player i Incomplete: players may be indecisive between some outcomes Common knowledge of strategy sets and preferences Bade (2005): Each Nash equilibrium of this game is a Nash equilibrium of a completion of the game
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Rationalizable Strategies
Rationality: players select only nondominated strategies Strategy s dominates strategy s’ if it yields a preferred outcome no matter what the opponents play Common knowledge of rationality, no additional assumptions → Rationalizable strategies (Pearce 1984, Bernheim 1984) Kokkala J., Virtanen K., and Poropudas J.: Rationalizable strategies in games with incomplete preferences Manuscript in preparation No new rationalizable strategies appear when preference information is added
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Special case of games with incomplete preferences Vector-valued payoff
Multicriteria Games Special case of games with incomplete preferences Vector-valued payoff Player i desires to maximize Preferences represented by weights related to (e.g., Shapley 1959) Our manuscript Incomplete preference information represented by a set of feasible weights Preference programming (Hämäläinen and Salo 1995) Player i prefers outcome over outcome if Restricting the set of feasible weights corresponds to additional preference information Nondominated strategies Rationalizable strategies
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References S. Bade: Nash equilibrium in games with incomplete preferences, Economic Theory, 26(2): , 2005 B.D. Bernheim: Rationalizable strategic behavior, Econometrica, 52(4): , 1984 D.G. Pearce: Rationalizable strategic behavior and the problem of perfection, Econometrica, 52(4): , 1984 A. Salo and R.P. Hämäläinen: Preference programming through approximate ratio comparisons, European Journal of Operational Research, 82(3): , 1995 L.S. Shapley: Equilibrium points in games with vector payoffs, Naval Research Logistics Quarterly, 6(1):57-61, 1959
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