Non-Zero Sum Games for Reactive Synthesis

Abstract

Abstract. In this invited contribution [7], we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.

Constrained Existence Problem for Weak Subgame Perfect Equilibria with ω-Regular Boolean Objectives

“…Given (G , v 0 ) an initialized Boolean game and thresholds x, y ∈ {0, 1} |Π| , decide whether there exists a weak SPE in (G , v 0 ) with payoff p such that x ≤ p ≤ y. 3 In the next sections, we solve the constraint problem for the classical ω-regular objectives. The complexity classes that we obtain are shown in Table 1; they are detailed in Section 4.…”

“…More recently, generalization from zero-sum to non zero-sum, and from two players to n players have been considered in the literature, see e.g. [1,3,4,5,10,12,16,21,26] and the surveys [8,20]. Those extensions are motivated by two main limitations of the classical setting.…”

“…Notice that (G , v 0 ) is subgame of itself 3. The order ≤ is the componentwise order, that is, x i ≤ p i ≤ y i , for all i ∈ Π.…”

Computer Aided Synthesis: A Game-Theoretic Approach

“…In this article, we propose a comprehensive introduction to classical algorithmic solutions to the synthesis problem for two-player zero-sum games and for multi-player non zero-sum games. A complementary survey can be found in [9], and detailed expositions in the case of Boolean objectives are provided in [38,39]. We study the existence of winning strategies (in two-player zero-sum games) and equilibria (in multi-player non zero-sum games) satisfying some given constraints, in particular the complexity class of the decision problem and the memory re-quired for the related strategies.…”

Admissible Strategies in Timed Games

“…Then, it should be clear that the zero-sum approach may fail to find a winning strategy even if solutions exist when the objective of the environment is taken into account, or it may produce sub-optimal solutions because those solutions are overcautious in order to be able to face with all possible behaviors of the environment, even if they are in contradiction with the environment's objectives. Recently, several new solution concepts for synthesis of reactive systems that take the objectives of the environment into account, and so relax the fully adversarial assumption, have been introduced [10]. One approach that is particularly promising is based on the notion of admissible strategies [7,23,13,12,11].…”