Team-maxmin equilibrium: efficiency bounds and algorithms
This addresses a gap in game theory for security scenarios where agents control non-communicating resources, but it is incremental as it builds on an unexplored concept.
The paper tackles the problem of analyzing the efficiency bounds of Team-maxmin equilibrium in strategic games, showing it is unique and exists, and evaluates algorithms for finding it with theoretical guarantees and performance tests on standard game instances.
The Team-maxmin equilibrium prescribes the optimal strategies for a team of rational players sharing the same goal and without the capability of correlating their strategies in strategic games against an adversary. This solution concept can capture situations in which an agent controls multiple resources-corresponding to the team members-that cannot communicate. It is known that such equilibrium always exists and it is unique (unless degeneracy) and these properties make it a credible solution concept to be used in real-world applications, especially in security scenarios. Nevertheless, to the best of our knowledge, the Team-maxmin equilibrium is almost completely unexplored in the literature. In this paper, we investigate bounds of (in)efficiency of the Team-maxmin equilibrium w.r.t. the Nash equilibria and w.r.t. the Maxmin equilibrium when the team members can play correlated strategies. Furthermore, we study a number of algorithms to find and/or approximate an equilibrium, discussing their theoretical guarantees and evaluating their performance by using a standard testbed of game instances.