Bayesian open games

TL;DR

This paper extends the framework of compositional game theory to incorporate stochastic environments, stochastic choices, and incomplete information, making it more applicable to complex economic models.

Contribution

It generalizes the categorical model of open games to handle stochasticity and incomplete information, enhancing its expressiveness for economic applications.

Findings

Introduces a generalized categorical framework for open games with stochastic elements.

Enables modeling of incomplete information within the compositional game theory.

Provides a more flexible and expressive tool for economic game modeling.

Abstract

This paper generalises the treatment of compositional game theory as introduced by Ghani et al. in 2018, where games are modelled as morphisms of a symmetric monoidal category. From an economic modelling perspective, the notion of a game in the work by Ghani et al. is not expressive enough for many applications. This includes stochastic environments, stochastic choices by players, as well as incomplete information regarding the game being played. The current paper addresses these three issues all at once.