License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2021.8
URN: urn:nbn:de:0030-drops-143854
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Brice, Léonard ; Raskin, Jean-François ; van den Bogaard, Marie

Subgame-Perfect Equilibria in Mean-Payoff Games

LIPIcs-CONCUR-2021-8.pdf (0.7 MB)


In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the notion of negotiation function. We establish that the plays that are supported by SPEs are exactly those that are consistent with the least fixed point of the negotiation function. Finally, we show that the negotiation function is piecewise linear, and can be analyzed using the linear algebraic tool box. As a corollary, we prove the decidability of the SPE constrained existence problem, whose status was left open in the literature.

BibTeX - Entry

  author =	{Brice, L\'{e}onard and Raskin, Jean-Fran\c{c}ois and van den Bogaard, Marie},
  title =	{{Subgame-Perfect Equilibria in Mean-Payoff Games}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-143854},
  doi =		{10.4230/LIPIcs.CONCUR.2021.8},
  annote =	{Keywords: Games on graphs, subgame-perfect equilibria, mean-payoff objectives.}

Keywords: Games on graphs, subgame-perfect equilibria, mean-payoff objectives.
Collection: 32nd International Conference on Concurrency Theory (CONCUR 2021)
Issue Date: 2021
Date of publication: 13.08.2021

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