  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.
