Repairing multi-player games

Shaull Almagor, Guy Avni, Orna Kupferman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Synthesis is the automated construction of systems from their specifications. Modern systems often consist of interacting components, each having its own objective. The interaction among the components is modeled by a multi-player game. Strategies of the components induce a trace in the game, and the objective of each component is to force the game into a trace that satisfies its specification. This is modeled by augmenting the game with ω-regular winning conditions. Unlike traditional synthesis games, which are zero-sum, here the objectives of the components do not necessarily contradict each other. Accordingly, typical questions about these games concern their stability - whether the players reach an equilibrium, and their social welfare - maximizing the set of (possibly weighted) specifications that are satisfied. We introduce and study repair of multi-player games. Given a game, we study the possibility of modifying the objectives of the players in order to obtain stability or to improve the social welfare. Specifically, we solve the problem of modifying the winning conditions in a given concurrent multi-player game in a way that guarantees the existence of a Nash equilibrium. Each modification has a value, reflecting both the cost of strengthening or weakening the underlying specifications, as well as the benefit of satisfying specifications in the obtained equilibrium. We seek optimal modifications, and we study the problem for various ω-regular objectives and various cost and benefit functions. We analyze the complexity of the problem in the general setting as well as in one with a fixed number of players. We also study two additional types of repair, namely redirection of transitions and control of a subset of the players.

Original languageEnglish
Title of host publication26th International Conference on Concurrency Theory, CONCUR 2015
EditorsLuca Aceto, David de Frutos Escrig
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages15
ISBN (Electronic)9783939897910
StatePublished - 1 Aug 2015
Externally publishedYes
Event26th International Conference on Concurrency Theory, CONCUR 2015 - Madrid, Spain
Duration: 1 Sep 20154 Sep 2015

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference26th International Conference on Concurrency Theory, CONCUR 2015

Bibliographical note

Publisher Copyright:
© Shaull Almagor, Guy Avni, and Orna Kupferman; licensed under Creative Commons License CC-BY.


  • Concurrent games
  • Nash equilibrium
  • Repair

ASJC Scopus subject areas

  • Software


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