Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2402.11209

When Simple is Near Optimal in Security Games

Devansh Jalota·Michael Ostrovsky·Marco Pavone
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.GTcs.CCecon.THmath.OC

Keep this discovery

BibTeXRIS

Devansh Jalota, Michael Ostrovsky, Marco Pavone. 2024-02-17. When Simple is Near Optimal in Security Games. https://arxiv.org/abs/2402.11209

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

MMS Allocation for Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores to $n$ agents with subadditive cost functions arriving online in an arbitrary order. Upon an agent's arrival, we are informed of her cost function and must irrevocably assign her a set of chores. We focus on the Maximin Share (MMS) fairness notion and aim to compute an allocation in which all items are assigned, and no agent incurs a cost more than $\alpha$ times her MMS. Without any prior information about the instance (other than $n$ and $m$), we design an algorithm with a competitive ratio of $O(\min\{n, k\log^{1+\epsilon}k, \log m\})$ for any constant $\epsilon > 0$, where $k$ denotes the number of cost function types. Our bound matches the best known offline approximation guarantees for MMS under subadditive costs and is nearly optimal with respect to all three parameters: we show that even for binary additive cost functions, no online algorithm can achieve a competitive ratio of $o(\min\{n, k\log k, \log m\})$. We then consider the setting in which the $k$ cost function types are known in advance (though the realized types of arriving agents are not). For additive cost functions, we provide an algorithm with a competitive ratio of $O(\min\{\log k, \log(kn)/\log\log(kn)\})$, and show that constant-competitive algorithms do not exist for general $k$, even for the binary additive setting. For binary additive functions when $k \le n$, we propose a $3$-competitive algorithm and establish a lower bound of $2$.

cs.GT↗
arXiv2026

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT↗
arXiv2026

Existence of the Core in Approval-Based Committee Elections

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

cs.GT↗