Introducing open games
Open games are a framework for doing game theory (in the sense of economics, not game semantics) in the familiar setting of open systems and monoidal categories. Open games are the morphisms of a category in which composition and monoidal product correspond roughly to sequential and simultaneous play. (The definitions are very non-obvious, though, with a sort of continuation passing style behind the scenes.) Forward-reasoning of agents leads to a limited sort of ‘partial' duality, and the resulting category has a curious structure which has features of a compact closed category, but doesn’t fit into any of the usual axiom systems. I will start with a theoretically cleaner setting that already exhibits these strange features (and may be of more general interest), namely the opposite fibration of Jacob’s ‘simple fibration’.
This will be an introductory talk, assuming no knowledge of game theory, and partly an opportunity for me to introduce myself to those I haven’t met yet. I will survey the work that is done (including basic expressivity and conservativity theorems relating open games to standard game theory), work that is in progress (morphisms between open games lead to a monoidal double category; iteration of games can be characterised using coalgebras of functors; adding Bayesian players), and future work (heading towards high level things such as sheaves of games).