Team-versus-one games
Recently, my work focus on settings in which a team of players, for example representing a decentralised computer-controlled system, competes against an environment. Those players are limited in how they can communicate, and in particular, in settings in which randomised strategies are necessary to maximise their chances (think of rock-paper-scissors), the classical notion of Nash equilibrium does not capture the outcome they can guarantee together. This contrasts, for example, with the semantics of logics such as Randomised (or Probabilistic) Alternating Temporal Logic (RATL, PATL), in which one can express the fact that a given coalition of players can guarantee a given outcome. We defined an extension of those logics, Individually Randomised Alternating Temporal Logic (IRATL), and showed that a fragment of it, in concurrent graph games, is decidable in PSPACE. We also proposed a formalism called dicey games, to capture settings in which players may resort to sources of randomness that are shared, but only among a given subset of the team (Léonard Brice, Thomas Henzinger, Kaushik Thejaswini). We studied such games in a one-shot setting.