Team-maxmin equilibrium: efficiency bounds and algorithms

TL;DR

This paper explores the efficiency bounds of the Team-maxmin equilibrium, a solution concept for teams in strategic games, and evaluates algorithms for computing or approximating it, with implications for security applications.

Contribution

It introduces the first comprehensive analysis of the efficiency bounds of the Team-maxmin equilibrium and evaluates algorithms for finding or approximating it.

Findings

Bounds on inefficiency relative to Nash and Maxmin equilibria.

Algorithms with theoretical guarantees for computing the equilibrium.

Performance evaluation on standard game instances.

Abstract

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.