Competition among mechanism designers in a common value environment

A competitive economy is studied in which sellers offer alternative direct mechanisms to buyers who have private information about their own private use value for the commodity being traded. In addition the commodity has a common value to all buyers, perhaps represented by the future resale value of the commodity. A competitive equilibrium in mechanisms is described. In every such equilibrium it is shown that sellers must offer mechanisms that are allocationally equivalent to English ascending price auctions. The reservation prices that sellers set are shown to be below their ex post cost of trading the commodity. Received: 24 April 1998 / Accepted: 8 March 1999     

Sequential bargaining with common values

We study the alternating-offers bargaining problem of assigning an indivisible and commonly valued object to one of two players who jointly own this object. The players are asymmetrically informed about the object’s value and have veto power over any settlement. There is no depreciation during the bargaining process which involves signalling of private information. We characterise the perfect Bayesian equilibrium outcome of this game which is unique if offers are required to be strictly increasing. Equilibrium agreement is reached gradually and non-deterministically. The better informed player obtains a rent.     

Common agency with risk-averse agent

In a common agency model with a risk-averse agent and private information distortion in the equilibrium policy from the first-best is greater compared to the case of a risk-neutral agent. The principals are unable to screen completely the agent’s preferences if he is sufficiently risk-averse: there is bunching in the contract. The contribution schedules keep track of informational externality. However, when the coefficient of risk-aversion goes to zero the contributions become truthful as in the complete information case.     

The set of equilibria of first-price auctions

I specify the class of functions that are equilibria of symmetric first-price auctions. A formula to recover the distribution of valuations for any equilibrium bidding strategy is given.     

Common value auctions with independent types

In this paper I consider a common value model, with independent types, where the ex-post value of the good is influenced by the bidders' information at the auction stage. The seller cannot fully extract the surplus. In a symmetric model the optimal mechanism can be implemented through first price, second price, or English auctions; but not through a Dutch auction. Other properties of the optimal auctions are that the seller's reservation price is endogenous, and that in sealed bid auctions the price may exceed the value of the object (winner's curse).     

Optimal auction with a general distribution: Virtual valuation without densities

We characterize the optimal auction in an independent private values framework for a completely general distribution of valuations. We do this introducing a new concept: the generalized virtual valuation. To show the wider applicability of this concept we present two examples showing how to extend the classical models of Mussa and Rosen and Baron and Myerson for arbitrary distributions.     

Contractual solutions to hold-up problems with quality uncertainty and unobservable investments

Consider a seller and a buyer who write a contract. After that, the seller produces a good. She can influence the expected quality of the good by making unobservable investments. Only the seller learns the realized quality. Finally, trade can occur. It is always ex post efficient to trade. Yet, it may be impossible to achieve the first best, even though the risk-neutral parties are symmetrically informed at the contracting stage and complete contracts can be written. The second best is characterized by distortions that are reminiscent of adverse selection models (i.e., models with precontractual private information but without hidden actions).     

Mechanisms that efficiently verify the optimality of a proposed action

The best known achievement of the literature on resource-allocating mechanisms and their message spaces is the first rigorous proof of the competitive mechanism's informational efficiency. In an exchange economy withN persons andK+1 commodities (including a numeraire), that mechanism announcesK prices as well as aK-compenent trade vector for each ofN−1 persons, making a total ofNK message variables. Trial messages are successively announced and after each announcement each personprivately determines, usingprivate information, whether she finds the proposed trades acceptable at the announced prices. When a message is reached with which all are content, then the trades specified in that message take place, and they satisfy Pareto optimality and individual rationality. The literature shows that no (suitably regular) mechanism can achieve the same thing with fewer thanNK message variables. In the classic proof, all the candidate mechanisms have the privacy property, and the proof uses that property in a crucial way. ‘Non-private’ mechanisms are, however, well-defined. We present a proof that forN>K,NK remains a lower bound even when we permit ‘non-private’ mechanisms. Our new proof does not use privacy at all. But in a non-private mechanism, minimality of the number of message variables can hardly be defended as the hallmark of informational efficiency, since a non-private mechanism requires some persons to know something about the private information of othersin addition to the information contained in the messages. The new proof of the lower boundNK invites a new interpretation of the competitive mechanism's informational efficiency. We provide a new concept of efficiency which the competitive mechanism exhibits and which does rest on privacy even whenN>K. To do so, we first define a class ofprojection mechanisms, wherein some of the message variables are proposed values of the action to be taken, and the rest are auxiliary variables. The competitive mechanism has the projection property, with a trade vector as its action and prices as the auxiliary variables. A projection mechanism proposes an action; for each proposal, the agents then use the auxiliary variables, together with their private information, to verify that the proposed action meets the mechanism's goal (Pareto optimality and individual rationality for the competitive mechanism) if, indeed, it does meet that goal. For a given goal, we seek projection mechanisms for which theverification effort (suitably measured) is not greater than that of any other projection mechanism that achieves the goal. We show the competitive mechanism to be verification-minimal within the class of private projection mechanisms that achieve Pareto optimality and individual rationality; that proofdoes use the privacy of the candidate mechanisms. We also show, under certain conditions, that a verification-minimal projection mechanism achieving a given goal has smallest ‘total communication effort’ (which is locally equivalent to the classic ‘message-space size’) among all private mechanisms that achieve the goal, whether or not they have the projection property.     

Selection into and across credit contracts: Theory and field research

Lenders may choose to encourage borrower side contracting using group, or co-signed, loans or discourage it using individual loans, so as to make relative performance comparisons. In this context wealth of the agents relative to outsiders, and wealth inequality among potential joint liability partners, are important factors determining the choice among loan contracts. In a related model of whether to borrow, higher covariance of returns mitigates an adverse selection effect. We test these models using relatively rich data gathered in field research in Thailand. The prevalence of joint liability contracts relative to individual contracts exhibits a U-shaped relationship with the wealth of the borrowing household and increases with the wealth dispersion. The likelihood of joint-liability borrowing increases the lower is the probability of project success, a direct affirmation of adverse selection. Higher correlation across projects makes joint liability borrowing more likely relative to all other alternatives. Strikingly, most of the results disappear if we do not condition the sample according to the dictates of the models, with selection into and across credit contracts.     

Efficient trading with nonlinear utility

In an environment in which agents have nonlinear utility and sufficiently asymmetric initial endowments, we show that efficient trading is achievable. This result is in contrast with Myerson and Satterthwaite (1983), which shows efficient trading is not possible if agents have linear utility and asymmetric initial endowments. Our result is also different from Cramton et al. (1987), in which they maintain the linear utility assumption as in Myerson and Satterthwaite but assume that traders’ initial endowments are relatively symmetric.     

On the positive correlation property in competitive insurance markets

Most competitive models of insurance markets under asymmetric information predict a positive relationship between coverage and the accident probability. This paper derives the conditions under which this prediction holds true in a general setting involving multiple loss levels and fixed administrative costs. If there is one loss level, this prediction holds necessarily true only if all equilibrium contracts offer strictly positive coverage. With multiple loss levels, the positive relationship between coverage and the accident probability may not hold true even if all contracts offer strictly positive coverage and administrative costs are zero. These results have important implications for empirical testing.     

Implementation of multi-agent incentive contracts with the principal's renegotiation offer

The purpose of this paper is to explore a mechanism for supporting desired equilibrium actions in a one-principal, multi-agent model when the principal makes a renegotiation offer. We show that there exists a mechanism in which the principal's most preferred mixed strategy is always supported. Received: 30 May 1997 / Accepted: 10 October 1998     

Multiproject team assignments

We consider expected profit maximizing mechanisms for a principal who has to allocate a group of agents among a number of projects, assuming that the principal has incomplete information about each agent's ability type, and the agents follow the Bayes-Nash or the dominant strategy equilibrium behavior. We find that while expected profit maximizing mechanisms are similar to the optimal auction (Myerson, 1981), the incentive compatibility constraints are much more restrictive. Interestingly, these constraints are satisfied if each agent's characteristics change in a consistent manner not only with types, but also from project to project. Received: 30 April 1997 / Accepted: 22 December 1998     

On the generalized principal-agent problem: Decomposition and existence results

This paper addresses the class of generalized agency problems: situations in which adverse selection and moral hazard are jointly present. We present a decomposition of the principal's optimization problem under the first-order approach that sheds light on the interactions between the two types of private information, and also significantly improves tractability. We use the decomposition to (1) provide examples of closed form solutions of the optimal contract, and (2) analyze the existence of optimal contracts. We also show that the first-order approach is valid in generalized agency problems if the production technology satisfies the linear distribution function condition (LDFC) in actions and types. For more general production technologies the Mirrlees-Rogerson sufficient conditions need to be extended to include restrictions on the form of the optimal contract. Received: 11 August 1997 / 26 September 1999     

Categorization and correlation in a random-matching game

We consider a random-matching model in which every agent has a categorization (partition) of his potential opponents. In equilibrium, the strategy of each player i is a best response to the distribution of strategies of his opponents (when they face i) in each category of his categorization. We provide equivalence theorems between distributions generated by equilibrium profiles and correlated equilibria of the underlying game.     

Optimal tax auditing when some individuals need not file

In a situation in which people who are required to fill in a tax-return coexist with tax-return-exempt people, we prove that the optimal audit policy leads to different tax compliance behavior, depending on the difficulty of detecting an evader who does not fill in a tax return, passing himself of as a non-taxpayer.