How Good Is a Strategy in a Game With Nature?

02/23/2020

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by   Arnaud Carayol, et al.

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We consider games with two antagonistic players —Éloïse (modelling a program) and Abélard (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.