Catch Me If You Can: Combatting Fraud in Artificial Currency Based Government Benefits Programs

TL;DR

This paper tackles misreporting fraud in artificial currency–based government benefits by introducing an audit mechanism that elicits a signaling game between an administrator and users. The authors show that, in the budget-unconstrained setting, signaling game equilibria exist and can be computed efficiently via a linear program, with explicit bounds on misreporting probability and excess payments that improve as the audit cost lowers or the fine rises. They extend the analysis to budget-constrained settings, identifying budget thresholds that guarantee equilibrium existence and showing how coalitions influence outcomes; they also prove that, under many parameter regimes, the total cost of auditing is no larger than the cost of no-audit scenarios, indicating practical viability. A Washington, D.C. transit benefits case study demonstrates substantial reductions in total costs relative to no-audit strategies, supporting the mechanism’s real-world relevance and scalability to other benefits programs. The work further explores extensions to cryptographic safeguards against black-market fraud and discusses broader implications for fraud mitigation in resource-allocation systems.

Abstract

Artificial currencies have grown in popularity in many real-world resource allocation settings, gaining traction in government benefits programs like food assistance and transit benefits programs. However, such programs are susceptible to misreporting fraud, wherein users can misreport their private attributes to gain access to more artificial currency (credits) than they are entitled to. To address the problem of misreporting fraud in artificial currency based benefits programs, we introduce an audit mechanism that induces a two-stage game between an administrator and users. In our proposed mechanism, the administrator running the benefits program can audit users at some cost and levy fines against them for misreporting their information. For this audit game, we study the natural solution concept of a signaling game equilibrium and investigate conditions on the administrator budget to establish the existence of equilibria. The computation of equilibria can be done via linear programming in our problem setting through an appropriate design of the audit rules. Our analysis also provides upper bounds that hold in any signaling game equilibrium on the expected excess payments made by the administrator and the probability that users misreport their information. We further show that the decrease in misreporting fraud corresponding to our audit mechanism far outweighs the administrator spending to run it by establishing that its total costs are lower than that of the status quo with no audits. Finally, to highlight the practical viability of our audit mechanism in mitigating misreporting fraud, we present a case study based on the Washington D.C. federal transit benefits program. In this case study, the proposed audit mechanism achieves several orders of magnitude improvement in total cost compared to a no-audit strategy for some parameter ranges.

Figures (4)

• Figure 1: Comparison of the total costs of the no audit mechanism to our audit mechanism with a coalition size $l=1$ and $l=150$ for a fine $k = 300$ and for audit costs $c = 25$ (left), $c = 75$ (center), and $c = 125$ (right) as $q_{\min}$ varies. Each plot also depicts the $\$83,333$ of monthly fraud in Washington D.C.'s FTBP.
• Figure 2: Comparison of the total costs of the no audit mechanism to our audit mechanism with a coalition size $l=1$ and $l=150$ for a cost $c = 75$ and for audit fines $k = 100$ (left), $k = 300$ (center), and $k = 500$ (right) as $q_{\min}$ varies. Each plot also depicts the $\$83,333$ of monthly fraud in Washington D.C.'s FTBP.
• Figure 3: User utility $\mathcal{U}^R$ in a two type setting $\mathcal{S} = \left\{ L,H \right\}$ with $f(H) - f(L) = \Delta f \geq 0$. The plot is made assuming that (a) users of type $H$ will always signal truthfully, since this is a dominant strategy and (b) the administrator is always playing a best response according to \ref{['eqn:p2_best_resp']}. Under these assumptions, the user strategy is entirely determined by the misreporting probability $\boldsymbol{\pi}(s = H | m = L)$. We analyze the plot by looking at three different regimes: regime 1 is $[0, \frac{\bm{q}_H}{\bm{q}_L} \frac{c}{\Delta f + k - c})$, regime 2 is $(\frac{\bm{q}_H}{\bm{q}_L} \frac{c}{\Delta f + k - c}, 1]$ and regime 3 is when $\boldsymbol{\pi}(s = H | m = L) = \frac{\bm{q}_H}{\bm{q}_L} \frac{c}{\Delta f + k - c}$. Regime 1 corresponds to the case where $\boldsymbol{\sigma}(H) = 0$ is the administrator's unique best response. In the absence of an audit, $\mathcal{U}^R$ is an increasing function of the misreporting probability. Regime 2 corresponds to the case where $\boldsymbol{\sigma}(H) = 1$ is the administrator's unique best response. In this regime, $\mathcal{U}^R$ is decreasing, since a higher misreporting probability increases the probability of getting caught and paying the fine. In regime 3 the administrator is indifferent between auditing and not auditing, and hence any $\boldsymbol{\sigma}(H) \in [0,1]$ is a best response. In terms of the user utility, $\mathcal{U}^R$ interpolates from the blue point to the red point along the dashed line as $\boldsymbol{\sigma}(H)$ varies from $0$ to $1$. Importantly, this figure shows that $\mathcal{U}^R$ has a maximum if and only if $\boldsymbol{\sigma}(H)$ is chosen to be $0$ in regime 3. As a consequence, this says that the game has an equilibrium if and only if the administrator plays $\boldsymbol{\sigma}(H) = 0$ in regime 3. Fortunately, despite equilibria not existing when $\boldsymbol{\sigma}(H) > 0$ in regime 3, we still have $\epsilon$-equilibria for any $\epsilon \geq 0$ by choosing $\boldsymbol{\pi}(s = H | m = L) \in [\frac{\bm{q}_H}{\bm{q}_L} \frac{c}{\Delta f + k - c} - \frac{\epsilon}{q_L \Delta f}, \frac{\bm{q}_H}{\bm{q}_L} \frac{c}{\Delta f + k - c})$.
• Figure 4: Variation in the maximum misreporting probability of users for a range of audit fines $k$ and audit costs $c$ for three different values of $q_{\min}$.

Theorems & Definitions (29)

• Example 1: Federal Transit Benefits Program
• Example 2: Food Assistance Program
• Definition 1: Misreporting Fraud
• Definition 2: Signaling Game Equilibria
• Definition 3: Bayesian Persuasion Equilibria
• Theorem 1: Signaling Game Equilibrium Existence
• Theorem 2: Bayesian Persuasion Equilibrium Characterization
• Lemma 1
• Corollary 1: Misreporting Probability Bound
• Corollary 2: Excess Payments Bound