Revenue Comparisons for Auctions When Bidders Have Arbitrary Types

This paper develops a methodology for characterizing expected revenue from auctions in which bidders' types come from an arbitrary distribution. In particular, types may be multidimensional, and there may be mass points in the distribution. One application extends existing revenue equivalence results. Another application shows that first-price auctions yield higher expected revenue than second-price auctions when bidders are risk averse and/or face financial constraints. This revenue ranking also extends to risk-averse bidders with general forms of non-expected utility preferences.

Strategic Judgment Proofing

A liquidity-constrained entrepreneur needs to raise capital to finance a business activity that may cause injuries to third parties --- the tort victims. Taking the level of borrowing as fixed, the entrepreneur finances the activity with senior (secured) debt in order to shield assets from the tort victims in bankruptcy. Interestingly, senior debt serves the interests of society more broadly: it creates better incentives for the entrepreneur to take precautions than either junior debt or outside equity. Unfortunately, the entrepreneur will raise a socially excessive amount of senior debt, reducing his incentives for care and generating wasteful spending. Giving tort victims priority over senior debtholders in bankruptcy prevents over-leveraging but leads to suboptimal incentives. Lender liability exacerbates the incentive problem even further. A Limited Seniority Rule, where the firm may issue senior debt up to an exogenous limit after which any further borrowing is treated as junior to the tort claim, dominates these alternatives. Shareholder liability, mandatory liability insurance and punitive damages are also discussed.

Exploiting Plaintiffs Through Settlement: Divide and Conquer

This paper considers settlement negotiations between a single defendant and $N$ plaintiffs when there are fixed costs of litigation. When making simultaneous take-it-or-leave-it offers to the plaintiffs, the defendant adopts a divide and conquer strategy. Plaintiffs settle their claims for less than they are jointly worth. The problem is worse when $N$ is larger, the offers are sequential, and the plaintiffs make offers instead. Although divide and conquer strategies dilute the defendant's incentives, they increase the settlement rate and reduce litigation spending. Plaintiffs can raise their joint payoff through transfer payments, voting rules, and covenants not to accept discriminatory offers.

The Hold-up Problem

Hold-up arises when part of the return on an agent’s relationship-specific investments is ex post expropriable by his trading partner. The hold-up problem has played an important role as a foundation of modern contract and organization theory, as the associated inefficiencies have justified many prominent organizational and contractual practices. We formally describe the main inefficiency hypothesis and sketch out the remedies suggested, as well as the more recent re-examination of the relevance of these theories.

A Dynamic Theory of Holdup

The holdup problem arises when parties negotiate to divide the surplus generated by their ex ante noncontractable investments. We study this problem in a model which, unlike the stylized static model, allows the parties to continue to invest until they agree on the terms of trade. These possible investment dynamics overturn the conventional wisdom dramatically. First, the holdup problem need not entail underinvestment-type inefficiencies when the parties are sufficiently patient. Second, inefficiencies can arise unambiguously, but the reason for their occurrence differs from the one recognized by the static model. This latter finding sheds new light on the design of contracts and organizations.Investment, Bargaining with an endogenous pie, contribution games.

Opinion as Incentives

We study a model where a decision maker (DM) must select an adviser to advise her about an unknown state of the world. There is a pool of available advisers who all have the same underlying preferences as the DM; they differ, however, in their prior beliefs about the state, which we interpret as differences of opinion. We derive atradeoff faced by the DM: an adviser with a greater difference of opinion has greater incentives to acquire information, but reveals less of any information she acquires, via strategic disclosure. Nevertheless, it is optimal to choose an adviser with at least some difference of opinion. The analysis reveals two novel incentives for an agent to acquire information: a ``persuasion'' motive and a motive to ``avoid prejudice.'' Delegation is costly for the DM because it eliminates both of these incentives. We also study the relationship between difference of opinion and difference of preference.

Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms

The random priority (random serial dictatorship) mechanism is a common method for assigning objects to individuals. The mechanism is easy to implement and strategy-proof. However this mechanism is inefficient, as the agents may be made all better off by another mechanism that increases their chances of obtaining more preferred objects. Such an inefficiency is eliminated by the recent mechanism called probabilistic serial, but this mechanism is not strategy-proof. Thus, which mechanism to employ in practical applications has been an open question. This paper shows that these mechanisms become equivalent when the market becomes large. More specifically, given a set of object types, the random assignments in these mechanisms converge to each other as the number of copies of each object type approaches infinity. Thus, the inefficiency of the random priority mechanism becomes small in large markets. Our result gives some rationale for the common use of the random priority mechanism in practical problems such as student placement in public schools.Random assignment, Random priority, Probabilistic serial, Ordinal efficiency, Asymptotic equivalence

Decoupling Liability: Optimal Incentives for Care and Litigation

A "decoupled" liability system is one in which the award to the plaintiff differs from the payment by the defendant. The optimal system of decoupling makes the defendant's payment as high as possible. Such a policy allows the award to the plaintiff to be lowered, thereby reducing the plaintiff's incentive to sue -- and hence litigation costs -- without sacrificing the defendant's incentive to exercise care. The optimal award to the plaintiff may be less than or greater than the optimal payment by the defendant. The possibility of an out-of-court settlement does not qualitatively affect these results. If the settlement can be monitored, it may be desirable to decouple it as well.