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Decision Making and Games with Vector Outcomes

Author

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  • Park Jaeok

    (School of Economics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul03722, Korea)

Abstract

In this paper, we study decision making and games with vector outcomes. We provide a general framework where outcomes lie in a real topological vector space and the decision maker’s preferences over outcomes are described by a preference cone, which is defined as a convex cone satisfying a continuity axiom. Further, we define a notion of utility representation and introduce a duality between outcomes and utilities. We provide conditions under which a preference cone is represented by a utility and is the dual of a set of utilities. We formulate a decision-making problem with vector outcomes and study optimal choices. We also consider games with vector outcomes and characterize the set of equilibria. Lastly, we discuss the problem of equilibrium selection based on our characterization.

Suggested Citation

  • Park Jaeok, 2020. "Decision Making and Games with Vector Outcomes," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 20(1), pages 1-14, January.
    • Handle: RePEc:bpj:bejtec:v:20:y:2020:i:1:p:14:n:14
    DOI: 10.1515/bejte-2018-0170
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    More about this item

    Keywords

    decision making; duality; games; incomplete preferences; utility representation; vector outcomes;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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