Optimal contract mechanisms for principal-agent problems with moral hazard and adverse selection

Summary We examine the problem of incentive compatibility and mechanism design for incomplete information principal-agent problems. Allowing for risk aversion on the part of the principal and agent, we show the existence of an optimal, incentive compatible contract selection mechanism for the principal under conditions of moral hazard and adverse selection. Since we assume that the contract set is a function space of state contingent contracts, and that the set of agent types is uncountable, the set of contract selection mechanisms becomes infinite dimensional. Hence, novel existence arguments are required. Our existence result extends those of Grossman and Hart [10] and Page [23] to an infinite dimensional setting with incomplete information.     

The ABC mechanism: an incentive compatible payoff mechanism for elicitation of outcome and probability transformations

When it comes to experiments with multiple-round decisions under risk, the current payoff mechanisms are incentive compatible with either outcome weighting theories or probability weighting theories, but not both. In this paper, I introduce a new payoff mechanism, the Accumulative Best Choice (“ABC”) mechanism that is incentive compatible for all rational risk preferences. I also identify three necessary and sufficient conditions for a payoff mechanism to be incentive compatible for all models of decision under risk with complete and transitive preferences. I show that ABC is the unique incentive compatible mechanism for rational risk preferences in a multiple-task setting. In addition, I test empirical validity of the ABC mechanism in the lab. The results from both a choice pattern experiment and a preference (structural) estimation experiment show that individual choices under the ABC mechanism are statistically not different from those observed with the one-round task experimental design. The ABC mechanism supports unbiased elicitation of both outcome and probability transformations as well as testing alternative decision models that do or do not include the independence axiom.

     

The robustness of the independent private value model in Bayesian mechanism design

Summary. In a Bayesian model of group decision-making, dependence among the agents' types has been shown to have a beneficial effect on the design of incentive compatible mechanisms that achieve the efficient choice associated with complete information. This effect is shown here to depend as much upon the use of large monetary transfers among the agents as it does upon dependence: if the transfers are bounded in magnitude, then nonexistence in the case of independence of an efficient, incentive compatible, ex ante budget-balanced and interim individually rational mechanism is robust to the introduction of a small amount of dependence among types. This robustness result supports the use of the simplifying assumption of independence in mechanism design. Received: October 28, 1996; revised version: May 28, 1997     

A characterization of efficient, bayesian incentive compatible mechanisms

Summary. A mechanism that is both efficient and incentive compatible in the Bayesian-Nash sense is shown to be payoff-equivalent to a Groves mechanism at the point in time when each agent has just acquired his private information. This equivalence result simplifies the question of whether or not an efficient, Bayesian incentive compatible mechanism can satisfy other desired objectives, for the search for an appropriate mechanism can be restricted to the family of Groves mechanisms. The method is used to extend the result of Myerson and Satterthwaite on the inefficiency of bilateral bargaining to a multilateral setting. Received: June 30, 1997; revised version: May 22, 1998     

中国分权式改革的激励难题及其政策选择——一种合约视角的分析

中国分权式改革成功的关键在于基于合约设计的经济激励机制的引人,为整个国民经济发展奠定了坚实的动力基础.同时,合约激励实施过程中产生的大量激励扭曲现象也经经济转型带来了巨大的改革成本.中国分权式改革面临的这种激励悖论成为制约当关中国经济可持续发展的激励难题.着力破解这些激励难题,需要从政府、企业和个人等不同层面构建和完善与现代市场经济体制相契合的激励兼容机制.     

Announcement or Contribution? The Relative Efficiency of Manipulated Lindahl Mechanisms

The private provision mechanism is individually incentive compatible but inefficient. The Lindahl mechanism is efficient but not incentive compatible. We analyze the outcome of the manipulated Lindahl mechanism. When the demand announcements of participants are unrestricted the Lindahl mechanism suffers from multiple equilibria. If the government removes the multiplicity by restricting the functional form of announcements the resulting Lindahl equilibrium can be made approximately efficient. Approximate efficiency is achieved by announcements that are one-dimensional regardless of the number of participants in the mechanism. This is in contrast to mechanisms that achieve exact efficiency but require announcements whose dimensionality increases at the same rate as the number of participants. The mechanism we describe benefits from simplicity at the cost of approximate efficiency. We demonstrate that mechanisms in which a linear demand function is announced are supermodular so play will converge to the Nash equilibrium for a range of learning dynamics.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Mechanism design for general screening problems with moral hazard

Summary We study the problem faced by an incomplete information monopolist seeking to design a line of contracts so as to simultaneously screen consumers by type and resolve the moral hazard problems associated with contract performance. We formulate the monopolist's problem as a mechanism design problem in which the set of consumer types is taken to be a Polish space, and the contract space an arbitrary compact metric space. Allowing for risk aversion on the part of the monopolist and consumers, and taking as the feasible set of mechanisms the collection of all measurable functions defined on the space of consumer types with values in the space of contracts, we present a new characterization of incentive compatibility in an infinite dimensional setting which allows us to reformulate the monopolist's design problem as an unconstrained optimization problem (i.e., as a problem without the incentive compatibility contraints). Using simple techniques, we then demonstrate the existence of an optimal screening mechanism for the monopolist. We thus extend the existing analysis of the incomplete information monopoly problem to an infinite dimensional setting with moral hazard, and we provide an existence result not available in the existing literature.I thank seminar participants at Indiana University, McGill University, and the University of Calgary for helpful comments. I also thank Kerry Back, Bob Becker, Praveen Kumar, Mark Johnson, Ramon Marimon, Murat Sertel, Bill Sealey, Gordon Sick, and Nicholas Yannelis for helpful comments. The comments and suggestions of an anonymous referee are especially appreciated. I am solely responsible for any errors.     

Mechanisms for a spatially distributed market

We consider the problem of a spatially distributed market with strategic agents. A single good is traded in a set of independent markets, where shipment between markets is possible but costly. The problem has previously been studied in the non-strategic case, in which it can be analyzed and solved as a min-cost-flow problem. We consider the case where buyers and sellers are strategic. Our first result gives a double characterization of the VCG prices, first as distances in a certain residue graph and second as the minimal (for buyers) and maximal (for sellers) equilibrium prices. This provides a computationally efficient, individually rational and incentive compatible welfare maximizing mechanism. This mechanism is, necessarily, not budget balanced and we also provide a budget-balanced mechanism (which is also computationally efficient, incentive compatible and individually rational) that achieves high welfare. Finally, we present results for some extensions of the model.     

Adverse selection under ignorance

Summary. We examine an adverse selection relationship in which the principal may ignore the ex ante distribution of the agent's types. The principal's behavior is described by a disutility function that covers the standard minimax regret and minimax loss criteria. We show that the incentive compatible and individually rational mechanism, which minimizes the maximal (or the minimal) principal's disutility over a set of priors, requires the efficient agents to realize the corresponding first-best actions and may demand actions lower than the first-best ones from less efficient agents. We also analyze the qualitative differences between the case in which the principal considers regrets and the case in which he considers losses. Received: 19 October 1998; revised version: 9 November 1999     

Revelation of preferences for public goods: Aggregation by Abelian operations

When the utility functions for the public and private goods are additively separable, in the two-public-alternative situation, a new class of incentive compatible mechanisms is presented, and some of its properties are explored. If there are more than two public alternatives and if the utility functions remain separable according to a generalized addition (called an abelian operation), it is also possible to construct incentive compatible mechanisms. Such mechanisms are similar to those of Groves but they do not involve maximizing a sum of utilities.     

增强城市群综合承载能力的政府合作机制研究

在明确增强城市群综合承载能力的内涵与标志的基础上,基于机制设计理论,以增强城市群综合承载能力为目标,以城市群内各地方政府为参与主体,按照"资源有效配置、信息有效利用、激励相容"三个机制设计标准进行了增强城市群综合承载能力的政府合作机制设计,并构建了政府合作增强城市群综合承载能力的理论分析模型,为以政府合作的方式增强城市群综合承载能力提供了对策建议和分析框架。     

INCENTIVE EFFICIENT PRICE SYSTEMS IN LARGE INSURANCE ECONOMIES WITH ADVERSE SELECTION

We decentralize incentive efficient allocations in large adverse selection economies by introducing a competitive market for mechanisms, that is, for menus of contracts. Facing a budget constraint, informed individuals purchase (lottery) tickets to enter mechanisms, whereas firms sell tickets and supply slots at mechanisms at given prices. Beyond optimization, market clearing, and rational expectations, an equilibrium requires that firms cannot favorably change, or cut, prices. An equilibrium exists and is incentive efficient. An equilibrium can be computed as the solution to a programming problem that selects the incentive efficient outcome preferred by the highest type within an appropriately defined set. For two‐types economies, this is the only equilibrium outcome.     

Efficient mechanisms for bilateral trading

We consider bargaining problems between one buyer and one seller for a single object. The seller's valuation and the buyer's valuation for the object are assumed to be independent random variables, and each individual's valuation is unknown to the other. We characterize the set of allocation mechanisms that are Bayesian incentive compatible and individually rational, and show the general impossibility of ex post efficient mechanisms without outside subsidies. For a wide class of problems we show how to compute mechanisms that maximize expected total gains from trade, and mechanisms that can maximize a broker's expected profit.     

Coalitional Bayesian Nash implementation in differential information economies

Summary. A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally implements it. Our main theorem proves that a social choice set is coalitionally implementable if and only if it is interim individually rational, interim efficient, coalitional B ayesian incentive compatible, and satisfies a coalitional Bayesian monotonicity condition as well as a closure condition. As an application of our main result, we show that the private core and the private Shapley value of an economy with differential information are coalitionally implementable. Received: January 12, 1998; revised version: March 30, 2000     

Efficiency versus optimality in procurement

We study procurement procedures that simultaneously determine the specification and price of a good. Suppliers can offer and produce the good in either of two possible specifications, both of which are equally good for the buyer. Production costs are interdependent and unknown at the time of bidding. Each supplier receives two signals about production cost, one per specification. Our model is a special case of the interdependent value settings with multidimensional types in Jehiel and Moldovanu (Econometrica 69:1237–1259, 2001) where an efficient and incentive compatible mechanism exists. We characterize equilibrium bidding behavior if the winning supplier is selected purely on the basis of price, regardless of the specification offered. While there is a positive chance of obtaining an inefficient specification, this procurement mechanism involves lower information rents than efficient mechanisms, suggesting that there is a trade-off between minimizing expected expenditure for the good, and ensuring that the efficient specification is chosen.     

Incentive compatibility in non-quasilinear environments

We derive several implications of incentive compatibility in general (i.e., not necessarily quasilinear) environments. Building on Kos and Messner (2013), we provide a (partial) characterization of incentive compatible mechanisms.     

机制设计理论综述

机制的新理解和激励相容概念使得机制设计框架得以确立,显示原理极大简化了分析框架。公共品经济难以有效权衡配置效率、自愿参与和激励相容。公共品提供的占优策略均衡机制,在拟线性环境和一般性经济环境下分别导致帕累托严格无效和独裁。在贝叶斯环境下,对于公共品经济和私人品经济,帕累托效率与自愿参与均难以兼容。其中,公共品不兼容性在极限角度仍成立。纳什执行及其拓展试图使在所设机制下的所有均衡结果对于社会选择目标而言都最优。放松关于信息结构和理性的假定,理论的最新发展围绕信息结构内生化、机制稳健化以及计算机制设计问题展开。