  This paper specifies an extensive form as a 5-ary relation (that is, as a set
of quintuples) which satisfies eight abstract axioms. Each quintuple is
understood to list a player, a situation (a concept which generalizes an
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 "pentaform". A "pentaform game" is then defined to be a pentaform
together with utility functions. The paper's main result is to construct an
intuitive bijection between pentaform games and $\mathbf{Gm}$ games (Streufert
2021, arXiv:2105.11398), which are centrally located in the literature, and
which encompass all finite-horizon or infinite-horizon discrete games. In this
sense, pentaform games equivalently formulate almost all extensive-form games.
Secondary results concern disaggregating pentaforms by subsets, constructing
pentaforms by unions, and initial applications to Selten subgames and
perfect-recall (an extensive application to dynamic programming is in Streufert
2023, arXiv:2302.03855).

Theoretical Economics;Computer Science and Game Theory;Logic in Computer Science;Optimization and Control