On the Complexity of Equilibria Problems in Angel-Daemon Games

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 Σp2-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.