We improve the framework of open games with agency by showing how the players' counterfactual analysis giving rise to Nash equilibria can be described in the dynamics of the game itself (hence diegetically), getting rid of devices such as equilibrium predicates. This new approach overlaps almost completely with the way gradient-based learners are specified and trained. Indeed, we show feedback propagation in games can be seen as a form of backpropagation, with a crucial difference explaining the distinctive character of the phenomenology of non-cooperative games. We outline a functorial construction of arena of games, show players form a subsystem over it, and prove that their 'fixpoint behaviours' are Nash equilibria.

翻译：我们通过展示博弈动力学内部（即叙事性层面）如何刻画玩家产生纳什均衡的反事实分析，从而改进了带有能动性的开放博弈框架，消除了平衡谓词等额外机制。这一新方法与基于梯度学习器的规范及训练方式几乎完全重叠。事实上，我们证明博弈中的反馈传播可视为反向传播的一种形式，其关键差异解释了非合作博弈现象学的独特特征。我们勾勒了博弈竞技场的函子性构造，展示玩家在其上构成子系统，并证明其“不动点行为”即为纳什均衡。