Abstract
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.
Work partially supported by FET pro-active Integrated Project 15964 (AEOLUS) and by Spanish projects TIN2005-09198-C02-02 (ASCE), MEC-TIN2005-25859-E and TIN2007-66523 (FORMALISM). The first author was also partially supported by the FP6 Network of Excellence CoreGRID funded by the European Commission (Contract IST-2002-004265).
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Gabarro, J., García, A., Serna, M. (2008). On the Complexity of Equilibria Problems in Angel-Daemon Games . In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_4
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