Admissibility in Concurrent Games∗†

In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays ‘as well as possible’, because there is no other strategy that dominates it, i.e., that wins (almost surely) against a superset of adversarial strategies. We prove that admissible strategies always exist in concurrent games, and we characterise them precisely. Then, when the objectives of the players are ω-regular, we show how to perform assume-admissible synthesis, i.e., how to compute admissible strategies that win (almost surely) under the hypothesis that the other players play admissible strategies only. 1998 ACM Subject Classification D.2.4 Software/Program Verification, F.3.1 Specifying and Verifying and Reasoning about Programs, I.2.2 Program Synthesis