Category of strategic games and presheaf corresponding solution concepts or welfare criteria

Tomohiko Kawamori

Papers from arXiv.org

Abstract: We define a category of strategic games in which a morphism is a pair of a map between sets of players and a map between sets of strategy profiles with specific properties, and we show that this category is well-defined. Three cases are considered for the maps between sets of strategy profiles: they may be order-preserving, order-reflecting or order-embedding with respect to each player's preference relation. We define a presheaf on the category of games valued in a category of sets that sends each strategic game to a set of strategy profiles, and we present equivalent conditions for this presheaf to be well-defined. Two cases are considered for the morphisms in the category of sets: they may be relations or maps. We define a presheaf that sends each strategic game to the set of Nash equilibria (resp.\ Pareto efficient strategy profiles), and we show that this presheaf is well-defined if and only if the maps between sets of strategy profiles are order-reflecting or order-embedding (resp.\ the maps between sets of strategy profiles are order-embedding), and the morphisms in the category of sets are relations.

Date: 2026-08
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