Acceptable costs of minimax regret equilibrium: A Solution to security games with surveillance-driven probabilistic information

Abstract

We extend the application of security games from offline patrol scheduling to online surveillance-driven resource allocation. An important characteristic of this new domain is that attackers are unable to observe or reliably predict defenders’ strategies. To this end, in this paper we introduce a new solution concept, called acceptable costs of minimax regret equilibrium, which is independent of attackers’ knowledge of defenders. Specifically, we study how a player’s decision making can be influenced by the emotion of regret and their attitude towards loss, formalized by the principle of acceptable costs of minimax regret. We then analyse properties of our solution concept and propose a linear programming formulation. Finally, we prove that our solution concept is robust with respect to small changes in a player’s degree of loss tolerance by a theoretical evaluation and demonstrate its viability for online resource allocation through an experimental evaluation.