We consider games with two antagonistic players—Éloïse (modelling a program) and Abélard (modelling a Byzantine environment)—and a third, unpredictable and uncontrollable player, which we call Nature. Motivated by the fact that the usual probabilistic semantics very quickly leads to undecidability when considering either infinite game graphs or imperfect-information, we propose two alternative semantics that lead to decidability where the probabilistic one fails: one based on counting and one based on topology.

中文翻译：

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与自然博弈的策略有多好？

我们考虑有两个敌对玩家的游戏——Éloïse（建模程序）和 Abélard（建模拜占庭环境）——以及第三个不可预测且无法控制的玩家，我们称之为 Nature。由于在考虑无限博弈图或不完美信息时，通常的概率语义很快会导致不可判定性，我们提出了两种替代语义，在概率语义失败的情况下导致可判定性：一种基于计数，一种基于拓扑。