Separable Network Games with Compact Strategy Sets

• Published in: Decision and Game Theory for Security Vol. 13061; pp. 37 - 56
• Main Authors: Kroupa, Tomáš, Vannucci, Sara, Votroubek, Tomáš
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Continuous game; Polynomial game; Separable network game
• ISBN: 9783030903695; 3030903699
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-90370-1_3

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.