一句话：提出开放博弈，以对称幺半范畴与弦图给出博弈论的可组合基础，并保持纳什均衡。
本文提出“开放博弈”（open games），旨在为经济博弈论建立可组合的基础。标准博弈论工具难以处理大规模经济模型，而可组合方法有望把博弈论与理论计算机科学的方法结合，应用于此类模型。开放博弈表示相对于任意环境进行的博弈，其核心新概念是“共效用”（coutility），即开放博弈产生并返回给环境的效用。开放博弈构成对称幺半范畴的态射，因此既可通过范畴组合形成序贯行动博弈，也可通过幺半乘积形成同时行动博弈。它们还能用弦图表示，直观而形式化地展示信息流。作者证明，多种博弈可被忠实表示为开放博弈，即保持相同的纳什均衡与偏离均衡的最优反应。
We introduce open games as a compositional foundation of economic game theory. A compositional approach potentially allows methods of game theory and theoretical computer science to be applied to large-scale economic models for which standard economic tools are not practical. An open game represents a game played relative to an arbitrary environment and to this end we introduce the concept of coutility, which is the utility generated by an open game and returned to its environment. Open games are the morphisms of a symmetric monoidal category and can therefore be composed by categorical composition into sequential move games and by monoidal products into simultaneous move games. Open games can be represented by string diagrams which provide an intuitive but formal visualisation of the information flows. We show that a variety of games can be faithfully represented as open games in the sense of having the same Nash equilibria and off-equilibrium best responses.