Synthesis with rational environments

Orna Kupferman, Giuseppe Perelli*, Moshe Y. Vardi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


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. We call such problem strong rational synthesis. In the strong rational synthesis 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 strong rational synthesis is 2ExpTime-complete, thus it is not more complex than traditional synthesis or 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 objective 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. Finally, we enrich the setting to one that allows coalitions of agents that constitute the system or the environment.

Original languageAmerican English
Pages (from-to)3-20
Number of pages18
JournalAnnals of Mathematics and Artificial Intelligence
Issue number1
StatePublished - 1 Sep 2016

Bibliographical note

Funding Information:
Work partially done when the author was a Ph.D. student at the Università degli Studi di Napoli Federico II and while visiting Rice University. Research partially supported by the ERC Advanced Grant RACE (291528) at Oxford.

Funding Information:
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement 278410, by the Israel Science Foundation (grant 1229/10), and by the US-Israel Binational Science Foundation (grant 2010431).

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.


  • Formal methods
  • Logics for games
  • Multi-agent systems
  • Synthesis


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