Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/261273 
Year of Publication: 
2021
Series/Report no.: 
Research Report No. 2021-2
Publisher: 
The University of Western Ontario, Department of Economics, London (Ontario)
Abstract: 
This paper introduces Gm, which is a category for extensive-form games. It also provides some applications. The category's objects are games, which are understood to be sets of nodes which have been endowed with edges, information sets, actions, players, and utility functions. Its arrows are functions from source nodes to target nodes that preserve the additional structure. For instance, a game's information-set collection is newly regarded as a topological basis for the game's decision-node set, and thus a morphism's continuity serves to preserve information sets. Given these definitions, a game monomorphism is characterized by the property of not mapping two source runs (plays) to the same target run. Further, a game isomorphism is characterized as a bijection whose restriction to decision nodes is a homeomorphism, whose induced player transformation is injective, and which strictly preserves the ordinal content of the utility functions. The category is then applied to some game-theoretic concepts beyond the definition of a game. A Selten subgame is characterized as a special kind of categorical subgame, and game isomorphisms are shown to preserve strategy sets, Nash equilibria, Selten subgames, subgame-perfect equilibria, perfect-information, and no-absentmindedness. Further, it is shown that the full sub-category for distinguished-action sequence games is essentially wide in the category of all games, and that the full subcategory of action-set games is essentially wide in the full subcategory for games with no-absentmindedness.
Subjects: 
Continuously labeled tree
Selten subgame
Nash equilibrium
subgame-perfect equilibrium
distinguished-action game
sequence game
action-setgame
JEL: 
C73
Document Type: 
Working Paper

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