On the Complexity of Equilibria Problems in Angel-Daemon Games

  • Joaquim Gabarro
  • Alina García
  • Maria Serna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)


We analyze the complexity of equilibria problems for a class of strategic zero-sum games, called Angel-Daemon games. Those games were introduced to asses the goodness of a web or grid orchestration on a faulty environment with bounded amount of failures [6]. It turns out that Angel-Daemon games are, at the best of our knowledge, the first natural example of zero-sum succinct games in the sense of [1],[9]. We show that deciding the existence of a pure Nash equilibrium or a dominant strategy for a given player is \(\mathsf{\Sigma}^p_2\)-complete. Furthermore, computing the value of an Angel-Daemon game is EXP-complete. Thus, matching the already known complexity results of the corresponding problems for the generic families of succinctly represented games with exponential number of actions.


Nash Equilibrium Equilibrium Problem Turing Machine Mixed Strategy Dominant Strategy 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Joaquim Gabarro
    • 1
  • Alina García
    • 1
  • Maria Serna
    • 1
  1. 1.ALBCOM Research GroupUniversitat Politècnica de CatalunyaBarcelonaSpain

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