Energy and Mean-Payoff Games with Imperfect Information

  • Aldric Degorre
  • Laurent Doyen
  • Raffaella Gentilini
  • Jean-François Raskin
  • Szymon Toruńczyk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6247)


We consider two-player games with imperfect information and quantitative objective. The game is played on a weighted graph with a state space partitioned into classes of indistinguishable states, giving players partial knowledge of the state. In an energy game, the weights represent resource consumption and the objective of the game is to maintain the sum of weights always nonnegative. In a mean-payoff game, the objective is to optimize the limit-average usage of the resource. We show that the problem of determining if an energy game with imperfect information with fixed initial credit has a winning strategy is decidable, while the question of the existence of some initial credit such that the game has a winning strategy is undecidable. This undecidability result carries over to mean-payoff games with imperfect information. On the positive side, using a simple restriction on the game graph (namely, that the weights are visible), we show that these problems become EXPTIME-complete.


Perfect Information Imperfect Information Winning Strategy Game Graph Quasi Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Aldric Degorre
    • 1
  • Laurent Doyen
    • 2
  • Raffaella Gentilini
    • 3
  • Jean-François Raskin
    • 1
  • Szymon Toruńczyk
    • 2
  1. 1.Université Libre de Bruxelles (ULB)Belgium
  2. 2.LSV, ENS Cachan & CNRSFrance
  3. 3.University of PerugiaItaly

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