Translating Extensive Form Games to Open Games with Agency

TL;DR

This paper extends open games to encompass extensive form games with perfect and imperfect information by introducing notions of agency and choice operators, enhancing their compositionality and expressiveness.

Contribution

It introduces a formal way to incorporate player agency and choice operators into open games, addressing key limitations and improving their compositional structure.

Findings

Open games can now model extensive form games with perfect and imperfect information.

The new choice operators unify previous open game operators, streamlining the calculus.

Enhanced compositionality and expressiveness of open games demonstrated.

Abstract

We show open games cover extensive form games with both perfect and imperfect information. Doing so forces us to address two current weaknesses in open games: the lack of a notion of player and their agency within open games, and the lack of choice operators. Using the former we construct the latter, and these choice operators subsume previous proposed operators for open games, thereby making progress towards a core, canonical and ergonomic calculus of game operators. Collectively these innovations increase the level of compositionality of open games, and demonstrate their expressiveness.