We consider games with two antagonistic players --- \'Elo\"ise (modelling a program) and Ab\'elard (modelling a byzantine environment) --- and a third, unpredictable and uncontrollable player, that 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 leads 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？

我们考虑有两个对抗玩家的游戏 --- \'Elo\"ise（对程序建模）和 Ab\'elard（对拜占庭环境建模）---以及第三个不可预测和无法控制的玩家，我们称之为自然。动机由于在考虑无限博弈图或不完美信息时，通常的概率语义会很快导致不可判定性，我们提出了两种替代语义，可导致概率性失败的可判定性：一种基于计数，另一种基于拓扑。