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...

This paper specifies an extensive form as a 5-ary relation (i.e. set of quintuples) which satisfies certain abstract axioms. Each quintuple is understood to list a player, a situation (e.g. information set), a decision node, an action, and a successor node. Accordingly, the axioms are understood...

Alós-Ferrer and Ritzberger (2013) specify each node in a game tree as the set of outcomes that yet remain conceivable. In contrast, Streufert (2015a) specifies each node as the set of choices that have already been made. This symmetry suggests that the two formulations are "dual" in some sense....

Von Neumann and Morgenstern (1944) specify both nodes and choices as sets of outcomes. This outcome-set formulation is extended to the infinite horizon by the discrete extensive forms of Alós-Ferrer and Ritzberger (2013). I propose to restrict such outcome-set forms with a new assumption called...

Osborne and Rubinstein (1994) specify each node in a game tree as a sequence of actions. It is well-known that such actions can be replaced by choices (i.e. agent-specific actions) without loss of generality. I find that this sequential formulation is redundant in the sense that nodes can be...

It would be useful to have a category of extensive-form games whose isomorphisms specify equivalences between games. Since working with entire games is too large a project for a single paper, I begin here with preforms, where a "preform" is a rooted tree together with choices and information...

It would be useful to have a category of extensive-form games whose isomorphisms specify equivalences between games. Toward this goal, Streufert (2016) introduced the category of node- and-choice preforms, where a "preform" is a rooted tree together with choices and information sets. This paper...

The literature specifies extensive-form games in several styles, and eventually I hope to formally translate games across those styles. Toward that end, this paper defines NCF, the category of node-and-choice forms. The category's objects are game forms in any style, and the category's...

The current literature formally links "OR forms" (named after Osborne and Rubinstein 1994) with "KS forms" (named after Kuhn and Selten by Kline and Luckraz 2016). It also formally links "simple forms" with "AR forms" (both from Alós-Ferrer and Ritzberger 2016, with the former less prominent...

This paper develops the category NCG. Its objects are node-and-choice games, which include essentially all extensive-form games. Its morphisms allow arbitrary transformations of a game's nodes, choices, and players, as well as monotonic transformations of the utility functions of the game's...