License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2015.325
URN: urn:nbn:de:0030-drops-53741
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Almagor, Shaull ; Avni, Guy ; Kupferman, Orna

Repairing Multi-Player Games

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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 omega-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 omega-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.

BibTeX - Entry

  author =	{Shaull Almagor and Guy Avni and Orna Kupferman},
  title =	{{Repairing Multi-Player Games}},
  booktitle =	{26th International Conference on Concurrency Theory (CONCUR 2015)},
  pages =	{325--339},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-91-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{42},
  editor =	{Luca Aceto and David de Frutos Escrig},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-53741},
  doi =		{10.4230/LIPIcs.CONCUR.2015.325},
  annote =	{Keywords: Nash equilibrium, concurrent games, repair}

Keywords: Nash equilibrium, concurrent games, repair
Collection: 26th International Conference on Concurrency Theory (CONCUR 2015)
Issue Date: 2015
Date of publication: 26.08.2015

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