2023/09/27 by Fernando Tohmé, Tohmé, Fernando, Ignacio Viglizzo +1
Computer Science · Decision Sciences · #18A35 #91A35 #Advanced Algebra and Logic #Category Theory (math.CT) #Constraint Satisfaction and Optimization #FOS: Mathematics #Game Theory and Applications
paper · pdf · doi:10.48550/arxiv.2309.15981
openalex publication_date 2023/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Strategic games admit a multi-graph representation, in which two kinds of relations, accessibility, and preferences, are used to describe how the players compare the possible outcomes. A category of games with a fixed set of players GamI is built from this representation, and a more general category Gam is defined with games having different sets of players, both being complete and cocomplete. The notion of Nash equilibrium can be generalized in this context. We then introduce two subcategories of Gam, NE and GamNE in which the morphisms are equilibria-preserving. We illustrate the expressivity and usefulness of this framework with some examples.