Energy Mean-Payoff Games

Authors Véronique Bruyère, Quentin Hautem, Mickael Randour, Jean-François Raskin

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Véronique Bruyère
  • Université de Mons (UMONS), Belgium
Quentin Hautem
  • Université de Mons (UMONS), Belgium
Mickael Randour
  • Université de Mons (F.R.S.-FNRS & UMONS), Belgium
Jean-François Raskin
  • Université libre de Bruxelles (ULB), Belgium

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Véronique Bruyère, Quentin Hautem, Mickael Randour, and Jean-François Raskin. Energy Mean-Payoff Games. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


In this paper, we study one-player and two-player energy mean-payoff games. Energy mean-payoff games are games of infinite duration played on a finite graph with edges labeled by 2-dimensional weight vectors. The objective of the first player (the protagonist) is to satisfy an energy objective on the first dimension and a mean-payoff objective on the second dimension. We show that optimal strategies for the first player may require infinite memory while optimal strategies for the second player (the antagonist) do not require memory. In the one-player case (where only the first player has choices), the problem of deciding who is the winner can be solved in polynomial time while for the two-player case we show co-NP membership and we give effective constructions for the infinite-memory optimal strategies of the protagonist.

Subject Classification

ACM Subject Classification
  • Software and its engineering → Formal methods
  • Theory of computation → Logic and verification
  • Theory of computation → Solution concepts in game theory
  • two-player zero-sum games played on graphs
  • energy and mean-payoff objectives
  • complexity study and construction of optimal strategies


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