Computational Aspects of Uncertainty Profiles and 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 performance of the execution of a web orchestration on a moderate faulty or under stress environment. Angel-daemon games are a natural example of zero-sum games whose representation is naturally succinct. We show that the problems of deciding the existence of a pure Nash equilibrium or of a dominant strategy for a given player are Σ^p_2 -complete. Furthermore, computing the value of an angel-daemon game is EXP-complete. Thus, our results match the already known classification of the corresponding problems for the generic families of succinctly represented games with exponential number of actions.