Fair Adversaries and Randomization in Two-Player Games
Two-player games are used to model open systems. One player models the system, trying to respect some specification, while the other player models the environment. In classical model checking, the objective is to verify that the system can respect its specification, whatever the environment does.
In this article, we consider a more realistic scenario when the environment is supposed to be fair. We define a notion of fair player in two-player games. Our solution is inspired by Banach-Mazur games, and leads to a definition of a novel class of 3-player games called ABM-games. For ω-regular specifications on finite arenas, we explore the properties of ABM-games and devise an algorithm for solving them. As the main result, we show that winning in an ABM-game (i.e. winning against a fair player) is equivalent to winning with probability one against the randomized adversary.
KeywordsGames Markov decision processes fairness
- 1.Baier, C., Bertrand, N., Bouyer, P., Brihaye, T., Größer, M.: Almost-sure model checking of infinite paths in one-clock timed automata. In: LICS 2008, pp. 217–226. IEEE Computer Society, Los Alamitos (2008)Google Scholar
- 3.Bertrand, N., Genest, B., Gimbert, H.: Qualitative determinacy and decidability of stochastic games with signals. In: LICS 2009, pp. 319–328. IEEE Computer Society, Los Alamitos (2009)Google Scholar
- 4.Berwanger, D., Grädel, E., Kreutzer, S.: Once upon a time in the West. Determinacy, complexity and definability of path games. In: Vardi, M.Y., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 226–240. Springer, Heidelberg (2003)Google Scholar
- 5.Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Algorithms for omega-regular games with imperfect information. Logical Methods in Computer Science 3(3) (2007)Google Scholar
- 6.Chatterjee, K., Jurdziński, M., Henzinger, T.A.: Quantitative stochastic parity games. In: SODA 2004, pp. 114–123. ACM/SIAM (2004)Google Scholar
- 8.Emerson, E.A., Jutla, C.: Tree automata, mu-calculus and determinacy (extended abstract). In: FOCS 1991, pp. 368–377. IEEE Computer Society, Los Alamitos (1991)Google Scholar
- 10.Lichtenstein, O., Pnueli, A., Zuck, L.D.: The glory of the past. In: Parikh, R. (ed.) Logic of Programs 1985. LNCS, vol. 193, pp. 196–218. Springer, Heidelberg (1985)Google Scholar
- 14.Varacca, D., Völzer, H.: Temporal logics and model checking for fairly correct systems. In: LICS 2006, pp. 389–398. IEEE Computer Society, Los Alamitos (2006)Google Scholar