Arbeitspapier
A category for extensive-form games
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.
- Language
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Englisch
- Bibliographic citation
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Series: Research Report ; No. 2021-2
- Classification
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Wirtschaft
Stochastic and Dynamic Games; Evolutionary Games; Repeated Games
- Subject
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Continuously labeled tree
Selten subgame
Nash equilibrium
subgame-perfect equilibrium
distinguished-action game
sequence game
action-setgame
- Event
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Geistige Schöpfung
- (who)
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Streufert, Peter Alfred
- Event
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Veröffentlichung
- (who)
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The University of Western Ontario, Department of Economics
- (where)
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London (Ontario)
- (when)
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2021
- Handle
- Last update
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10.03.2025, 11:43 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Streufert, Peter Alfred
- The University of Western Ontario, Department of Economics
Time of origin
- 2021
Other Objects (12)
The category of node-and-choice extensive-form games
The category of node-and-choice forms for extensive-form games
The category of node-and-choice preforms for extensive-form games
Normal Form Structures in Extensive Form Games
Prudent rationalizability in generalized extensive-form games
Kuhn's theorem for extensive form Ellsberg games
Kuhn's Theorem for Extensive Form Ellsberg Games
Rationality and Extensive Form Correlated Equilibria in Stochastic Games
Convergence of best response dynamics in extensive-form games
Prudent Rationalizability in Generalized Extensive-Form Games with Unawareness
Strategie equivalence and bounded rationality in extensive form games
Stochastic stability in finite extensive-form games of perfect information
The category of node-and-choice extensive-form games
The category of node-and-choice forms for extensive-form games
The category of node-and-choice preforms for extensive-form games
Normal Form Structures in Extensive Form Games
Prudent rationalizability in generalized extensive-form games
Kuhn's theorem for extensive form Ellsberg games
Kuhn's Theorem for Extensive Form Ellsberg Games
Rationality and Extensive Form Correlated Equilibria in Stochastic Games
Convergence of best response dynamics in extensive-form games
Prudent Rationalizability in Generalized Extensive-Form Games with Unawareness
Strategie equivalence and bounded rationality in extensive form games
Stochastic stability in finite extensive-form games of perfect information
The category of node-and-choice extensive-form games
The category of node-and-choice forms for extensive-form games
The category of node-and-choice preforms for extensive-form games
Normal Form Structures in Extensive Form Games
Prudent rationalizability in generalized extensive-form games
Kuhn's theorem for extensive form Ellsberg games
Kuhn's Theorem for Extensive Form Ellsberg Games
Rationality and Extensive Form Correlated Equilibria in Stochastic Games
Convergence of best response dynamics in extensive-form games
Prudent Rationalizability in Generalized Extensive-Form Games with Unawareness
Strategie equivalence and bounded rationality in extensive form games