Compositional game theory — Neil Ghani, Jules Hedges, Viktor Winschel & Philipp Zahn (2016). arXiv:1603.04641 (v3, PDF).
Introduces open games: games with a play function, a coplay function returning utilities to the past, and a best-response relation relative to a context. Open games compose sequentially and in parallel, forming a symmetric monoidal category whose string diagrams describe games built from parts, with Nash equilibria characterised compositionally.
Sources: the paper, arXiv:1603.04641v3, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definition 3: open game
- Definitions 4–8: decisions, selection functions, functions, counits
- Definitions 9–10: sequential and parallel composition
- Theorem 1: open games form a symmetric monoidal category