Bankruptcy Rules for Strategic Agents

Bankruptcy rules are rules for dividing an insufficient estate among people with different claims. Existing rules assume that the claims are publicly known. When this is not the case, claimants have a strong incentive to claim more than they are due, as bankruptcy rules give larger allocations to claimants with larger claims. A remedy often used by legal systems is to make over-reporting costly by requiring evidence and imposing penalties. But this remedy also increases the legal expenses of proving true claims, which might result in under-reporting. Encouraging true reporting requires fine-tuning of the legal costs. This paper incorporates the costs of supporting both true and false claims into the bankruptcy model. Claimants incur costs for the true and false parts of their claims, with false claims costing at least as much per unit as true claims. The goal is to set cost rates that induce claimants to report their true entitlements, neither more nor less. Whether this is possible depends on the allocation rule. The proportional and constrained equal awards rules cannot guarantee truthfulness at any positive true-claim cost rate; the same holds for constrained equal losses with at least three claimants. For $N\ge2$ claimants, the rule TAL-1/N from the parameterized Talmud family induces truthfulness exactly when the true-claim cost rate is at most 1/N and the false-claim cost rate is at least 1-1/N. This rule is optimal in the sense that its truthful cost region contains that of every piecewise smooth allocation rule: it gives the legal system the maximum possible flexibility in setting the legal costs. For two claimants, TAL-1/2 (aka Contested Garment rule) uniquely attains this optimal region.