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General dualities between best replies and undominated actions

Author

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  • Sudhir A. Shah

    (Department of Economics, Delhi School of Economics)

Abstract

The central results of this paper are dualities between actions in a decision problem that are not strongly (resp., weakly) dominated over a state space and actions that are best (resp., internal-best) replies to a state. These results hold for action and state spaces that are subsets of abstract topological vector spaces, which significantly expands their set of applications in comparison to their predecessors. This is demonstrated in the game theoretic setting by applying the dualities to a player’s decision problem in an abstract many-player game as well as in the s-additive, the absolutely continuous, and the finitely additive mixed extensions of many-player games; the third extension is applicable to discontinuous games. In all these applications, the noncooperative nature of the games is preserved by disallowing correlated decision-making by the players. The results also allow welfare theoretic applications such as the characterisation of various notions of efficient outcomes in terms of the best reply properties of the outcomes. JEL classification: C72, D81 Key words: duality, best reply, internal-best reply, strong domi-nance, weak dominance, Pareto efficiency, Utilitarian efficiency

Suggested Citation

  • Sudhir A. Shah, 2023. "General dualities between best replies and undominated actions," Working papers 337, Centre for Development Economics, Delhi School of Economics.
    • Handle: RePEc:cde:cdewps:337
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    References listed on IDEAS

    as
    1. Alexander Zimper, 2005. "Equivalence between best responses and undominated strategies: a generalization from finite to compact strategy sets," Economics Bulletin, AccessEcon, vol. 3(7), pages 1-6.
    2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    3. Zimper, Alexander, 2005. "Equivalence between best responses and undominated," Papers 05-08, Sonderforschungsbreich 504.
    4. repec:ebl:ecbull:v:3:y:2005:i:7:p:1-6 is not listed on IDEAS
    5. van Damme, E.E.C., 1983. "Refinements of the Nash Equilibrium Concept," Other publications TiSEM 116b3ec4-be4d-48c2-ad1b-8, Tilburg University, School of Economics and Management.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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