  Fraudulent or illegal activities are 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 is detrimental, as it may compromise
safety or impose disproportionate negative externalities on particular
population groups.
  To mitigate the potential harms of user fraud, we study the problem of
policing such 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 welfare 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
welfare or revenue as the welfare-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 welfare (revenue) as the welfare-maximizing
(revenue-maximizing) outcome with $R$ resources.
  Finally, since the welfare and revenue-maximizing solutions can differ
significantly, we present a framework inspired by contract theory, wherein a
revenue-maximizing administrator is compensated through contracts for the
welfare it contributes. Beyond extending our theoretical results in the welfare
and revenue maximization settings to studying equilibrium strategies in the
contract game, we also present numerical experiments highlighting the efficacy
of contracts in bridging the gap between the revenue and welfare-maximizing
administrator outcomes.
