Designing the Game to Play: Optimizing Payoff Structure in Security Games

Effective game-theoretic modeling of defender-attacker behavior is becoming increasingly important. In many domains, the defender functions not only as a player but also the designer of the game's payoff structure. We study Stackelberg Security Games where the defender, in addition to allocating defensive resources to protect targets from the attacker, can strategically manipulate the attacker's payoff under budget constraints in weighted L^p-norm form regarding the amount of change. Focusing on problems with weighted L^1-norm form constraint, we present (i) a mixed integer linear program-based algorithm with approximation guarantee; (ii) a branch-and-bound based algorithm with improved efficiency achieved by effective pruning; (iii) a polynomial time approximation scheme for a special but practical class of problems. In addition, we show that problems under budget constraints in L^0-norm form and weighted L^\infty-norm form can be solved in polynomial time. We provide an extensive experimental evaluation of our proposed algorithms

Imitative Follower Deception in Stackelberg Games

Information uncertainty is one of the major challenges facing applications of game theory. In the context of Stackelberg games, various approaches have been proposed to deal with the leader's incomplete knowledge about the follower's payoffs, typically by gathering information from the leader's interaction with the follower. Unfortunately, these approaches rely crucially on the assumption that the follower will not strategically exploit this information asymmetry, i.e., the follower behaves truthfully during the interaction according to their actual payoffs. As we show in this paper, the follower may have strong incentives to deceitfully imitate the behavior of a different follower type and, in doing this, benefit significantly from inducing the leader into choosing a highly suboptimal strategy. This raises a fundamental question: how to design a leader strategy in the presence of a deceitful follower? To answer this question, we put forward a basic model of Stackelberg games with (imitative) follower deception and show that the leader is indeed able to reduce the loss due to follower deception with carefully designed policies. We then provide a systematic study of the problem of computing the optimal leader policy and draw a relatively complete picture of the complexity landscape; essentially matching positive and negative complexity results are provided for natural variants of the model. Our intractability results are in sharp contrast to the situation with no deception, where the leader's optimal strategy can be computed in polynomial time, and thus illustrate the intrinsic difficulty of handling follower deception. Through simulations we also examine the benefit of considering follower deception in randomly generated games

A Polynomial Time Algorithm for Spatio-Temporal Security Games

An ever-important issue is protecting infrastructure and other valuable targets from a range of threats from vandalism to theft to piracy to terrorism. The "defender" can rarely afford the needed resources for a 100% protection. Thus, the key question is, how to provide the best protection using the limited available resources. We study a practically important class of security games that is played out in space and time, with targets and "patrols" moving on a real line. A central open question here is whether the Nash equilibrium (i.e., the minimax strategy of the defender) can be computed in polynomial time. We resolve this question in the affirmative. Our algorithm runs in time polynomial in the input size, and only polylogarithmic in the number of possible patrol locations (M). Further, we provide a continuous extension in which patrol locations can take arbitrary real values. Prior work obtained polynomial-time algorithms only under a substantial assumption, e.g., a constant number of rounds. Further, all these algorithms have running times polynomial in M, which can be very large