How Good Is a Strategy in a Game with Nature?

Abstract

We consider games with two antagonistic players -- Éloïse (modelling a program) and Abelard (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.