We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category, which can be used to compose probabilistic games in parallel and sequentially. We also consider morphisms between games, and show that intuitive constructions give rise to functors and adjunctions between pure and probabilistic open games.

中文翻译：

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混合策略的组合博弈论：使用分配律的概率开放博弈

我们扩展了组合博弈论的开放博弈框架，以包含混合策略，充分利用离散概率分布单子。我们表明，由此产生的博弈形成了一个对称的幺半群类别，可用于并行和顺序地组合概率博弈。我们还考虑了博弈之间的态射，并表明直观构造会产生纯开放博弈和概率开放博弈之间的函子和附属。