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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 to specify abstract relationships between players, situations, nodes, and actions. Such an extensive form is called a "5-form", and a "5-form game" is defined to be a 5-form together with utility functions. The paper's main result is to construct a bijection between (a) those 5-form games with information-set situations and (b) Gm games (Streufert 2021). In this sense, 5-form games equivalently formulate almost all extensive-form games. An application weakens the tree axiom in the presence of the other axioms, which leads to a convenient decomposition of 5-forms.

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