econ.THOct 13, 2026

Falsification-proof non-market allocation mechanisms

Authors: Eduardo Perez-Richet, Vasiliki Skreta

Organizations: Sciences Po, CEPR · UT Austin, UCL, CEPR

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Abstract

Relying on manipulable characteristics to target the allocation of resources is fraught with difficulties. Naively optimal rules lead to falsification and allocative inefficiency. Optimizing the rule for allocative efficiency while accounting for falsification typically induces falsification, at a heavy cost to the agents. Moreover, falsification generates negative externalities. We characterize optimal falsification-proof rules under a broad range of falsification technologies. We also provide an honesty condition under which they solve the unconstrained problem of a planner who maximizes a weighted sum of allocative surplus and agents' welfare.

Figures & tables

Figure 1: Cumulative surplus, matching pairs and growth interval.
Figure 2: Default setups, Euclidean costs with ( UID ): Cd(x)=log⁡(1+x)log⁡(1+d)\mathcal{C}^{d}(x)=\frac{\log(1+x)}{\log(1+d)} resulting in an S-shape, gaming ability γ=log⁡(1+d)\gamma=\log(1+d) with d=1,3,5,6d=1,3,5,6 . Binding regime if d≤4d\leq 4 , slack regime with probability gap Γ>0\Gamma>0 otherwise. Under low-score priority, Γ\Gamma is withheld from agents and corresponds to the gap between the d=5,6d=5,6 curves and 1 at s‾\overline{s} . Under high-score priority, Γ\Gamma is allocated to agents and corresponds to the gap between the d=5,6d=5,6 curves and 0 at s‾\underline{s} .
Figure 3: Low-score priority default setup, cost Cd(x)=log⁡(1+x)log⁡(1+d)\mathcal{C}^{d}(x)=\frac{\log(1+x)}{\log(1+d)} , gaming ability γ=log⁡(1+d)\gamma=\log(1+d) .
Figure 4: Payoff trajectories. Low-score priority default setup, cost Cd(x)=log⁡(1+x)log⁡(1+d)\mathcal{C}^{d}(x)=\frac{\log(1+x)}{\log(1+d)} , gaming ability γ=log⁡(1+d):0→∞\gamma=\log(1+d):0\to\infty . The gray zone depicts the set of attainable allocative payoffs (without accounting for falsification costs).
Figure 5: Welfare impact of honesty. Low-score priority default setup, d:0→6d:0\to 6 .
Figure 6: Group 1’s lower gaming ability hurts a low quota group ( ϕ2=0.2\phi_{2}=0.2 ). Cost Cγi(x)=(1/γi)x/(1+x)\mathcal{C}^{\gamma_{i}}(x)=(1/\gamma_{i})x/(1+x) , score distribution U(−1,1)U(-1,1) , ϕ2=0.2\phi_{2}=0.2 , γ2=0.8\gamma_{2}=0.8 , ρˉ=0.2\bar{\rho}=0.2 , μ1=μ2=0.5\mu_{1}=\mu_{2}=0.5
Figure 7: Group 1’s lower gaming ability leaves a high quota group unaffected
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