When Simple is Near Optimal in Security Games

Abstract: Fraud is ubiquitous across applications and involve users bypassing the rule of law, often with the strategic aim of obtaining some benefit that would otherwise be unattainable within the bounds of lawful conduct. However, user fraud can be detrimental. To mitigate the harms of user fraud, we study the problem of policing fraud as a security game between an administrator and users. In this game, an administrator deploys $R$ security resources (e.g., police officers) across $L$ locations and levies fines against users engaging in fraud at those locations. For this security game, we study both payoff and revenue maximization administrator objectives. In both settings, we show that computing the optimal administrator strategy is NP-hard and develop natural greedy algorithm variants for the respective settings that achieve at least half the payoff or revenue as the payoff-maximizing or revenue-maximizing solutions, respectively. We also establish a resource augmentation guarantee that our proposed greedy algorithms with one extra resource, i.e., $R+1$ resources, achieve at least the same payoff (revenue) as the payoff-maximizing (revenue-maximizing) outcome with $R$ resources. Moreover, in the setting when user types are homogeneous, we develop a near-linear time algorithm for the revenue maximization problem and a polynomial time approximation scheme for the payoff maximization problem. Next, we present numerical experiments based on a case study of parking enforcement at Stanford University's campus, highlighting the efficacy of our algorithms in increasing parking permit earnings at the university by over \$300,000 annually. Finally, we study several model extensions, including incorporating contracts to bridge the gap between the payoff and revenue-maximizing outcomes and generalizing our model to incorporate additional constraints beyond a resource budget constraint.