Abstract
A separable network game is a multiplayer finite strategic game in which each player interacts only with adjacent players in a simple undirected graph. The utility of each player results from the aggregation of utilities in the corresponding two-player games. In our contribution, we extend this model to infinite games whose strategy sets are compact subsets of the Euclidean space. We show that Nash equilibria of a zero-sum continuous network game can be characterized as optimal solutions to a specific infinite-dimensional linear optimization problem. In particular, when the utility functions are multivariate polynomials, this optimization formulation enables us to approximate the equilibria using a hierarchy of semidefinite relaxations. We present a security game over a complete bipartite graph in which the nodes are attackers and defenders, who compete for control over given targets.
This material is based upon work supported by, or in part by, the Army Research Laboratory and the Army Research Office under grant number W911NF-20-1-0197. The authors acknowledge the support by the project Research Center for Informatics (CZ.02.1.01/0.0/0.0/16_019/0000765).
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Kroupa, T., Vannucci, S., Votroubek, T. (2021). Separable Network Games with Compact Strategy Sets. In: Bošanský, B., Gonzalez, C., Rass, S., Sinha, A. (eds) Decision and Game Theory for Security. GameSec 2021. Lecture Notes in Computer Science(), vol 13061. Springer, Cham. https://doi.org/10.1007/978-3-030-90370-1_3
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