Concurrent Games with Ordered Objectives

We consider concurrent games played on graphs, in which each player has several qualitative (e.g. reachability or B¨uchi) objectives, and a preorder on these objectives (for instance the counting order, where the aim is to maximise the number of objectives that are fulfilled). We study two fundamental problems in that setting: (1) the value problem, which aims at deciding the existence of a strategy that ensures a given payoff; (2) the Nash equilibrium problem, where we want to decide the existence of a Nash equilibrium (possibly with a condition on the payoffs). We characterise the exact complexities of these problems for several relevant preorders, and several kinds of objectives.

• Type: Journal
• Year: 2012
• Where: FOSSACS
• Authors: Patricia Bouyer, Romain Brenguier, Nicolas Markey, Michael Ummels
• Keywords: FOSSACS 2012, Fundamental Problems, Nash Equilibrium, Payo, Software Engineering