Either/Or: Best reply versus dominance

Sudhir A. Shah
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Sudhir A. Shah: Department of Economics, Delhi School of Economics

No 318, Working papers from Centre for Development 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. The results admit action and state spaces that are sub-sets of abstract topological vector spaces. The generality of this setting significantly expands the set of applications of the dualities 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 mixed extension of a many-player game. The formalism also allows applications beyond the game-theoretic setting, such as the characterisation of various welfare-theoretic notions of efficient outcomes in terms of the best reply properties of the outcomes. Key Words: duality, best reply, internal-best reply, strong dominance, weak dominance, efficiency JEL Codes: JC72, D81

Pages: 28 pages
Date: 2021-11
New Economics Papers: this item is included in nep-gth
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