Synthesis with Rational Environments

Abstract

Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. The environment often consists of agents that have objectives of their own. Thus, it makes sense to soften the universal quantification on the behavior of the environment and take the objectives of its underlying agents into an account. Fisman et al. introduced rational synthesis: the problem of synthesis in the context of rational agents. The input to the problem consists of temporal-logic formulas specifying the objectives of the system and the agents that constitute the environment, and a solution concept (e.g., Nash equilibrium). The output is a profile of strategies, for the system and the agents, such that the objective of the system is satisfied in the computation that is the outcome of the strategies, and the profile is stable according to the solution concept; that is, the agents that constitute the environment have no incentive to deviate from the strategies suggested to them. In this paper we continue to study rational synthesis. First, we suggest an alternative definition to rational synthesis, in which the agents are rational but not cooperative. In the non-cooperative setting, one cannot assume that the agents that constitute the environment take into account the strategies suggested to them. Accordingly, the output is a strategy for the system only, and the objective of the system has to be satisfied in all the compositions that are the outcome of a stable profile in which the system follows this strategy. We show that rational synthesis in this setting is 2EXPTIME-COMPLETE, thus it is not more complex than traditional synthesis or cooperative rational synthesis. Second, we study a richer specification formalism, where the objectives of the system and the agents are not Boolean but quantitative. In this setting, the goal of the system and the agents is to maximize their outcome. The quantitative setting significantly extends the scope of rational synthesis, making the game-theoretic approach much more relevant.

Synthesis with rational environments

“…In [17], we continued the study of rational synthesis and in this paper we extend those results. We present the following contributions.…”

“…In rational synthesis, introduced in [14], synthesis is defined in a way that takes into account the rationality of the agents that constitute the environment and involves an assumption that an agent cooperates with a strategy to a strategy profile in which his objective is satisfied. Here and in [17], we extend the idea and consider also strong rational synthesis, in which agents need not cooperate with suggested strategies and may prefer different strategies that are at least as beneficial for them.…”

Extended Graded Modalities in Strategy Logic

“…In order to specify such payoffs with formulas, we follow a formalization from [30] called objective LTL. We then discuss appropriate solution concepts, and show how to express these in GRADEDSL.…”

“…2 Since many natural formulas have a small number of quantifiers, and even smaller nesting depth of blocks of quantifiers, the complexity of the model-checking problem is not as bad as it seems. Several solution concepts can be expressed as SL formulas with a small number of quantifiers [9,18,26,29,30,37]. We illustrate this by expressing uniqueness of various solution concepts, including winning-strategies in two-player zero-sum games and equilibria in multi-player non zero-sum games.…”

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

“…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.…”