Using the extraproximal method for computing the shortest-path mixed Lyapunov equilibrium in Stackelberg security games

•A Stackelberg security game is represented for shortest-path mixed Lyapunov equilibrium.•The extraproximal method is employed to compute the mixed stationary strategies.•We transform the Stackelberg game into a Lyapunov game.•In the game the Stackelberg and Nash equilibria coincide with the Lyapunov equilibrium.

In this paper we present a game theory model based on the extraproximal approach for computing the shortest-path Lyapunov equilibrium in Stackelberg security games. The extraproximal method is employed to compute the mixed stationary strategies: attackers operate on partial knowledge of the defender's strategies for fixed targets. We transform the Stackelberg game into a potential (Lyapunov) game replacing the ergodic behavior of the system by a shortest-path trajectory implemented by a Lyapunov-like function. In the resulting potential security game the Stackelberg and Nash equilibria coincide with the Lyapunov equilibrium. Validity of the proposed method is demonstrated both theoretically and experimentally.