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     

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     

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     

Project evaluation and organizational form

In situations of imperfect testing and communication, as suggested by Sah and Stiglitz (AER, 1986), organizational forms can be identified with different rules of aggregating evaluations of individual screening units. In this paper, we discuss the relative merits of polyarchical organizations versus hierarchical organizations in evaluating cost-reducing R&D projects when individual units' decision thresholds are fully endogenous. Contrary to the results of Sah and Stiglitz, we find that the relative merit of an organizational form depends on the curvature of the screening functions of the individual evaluation units. We find that for certain parameters organizations would want to implement asymmetric decision rules across screening units. This allows us to derive sufficient conditions for a polyarchy to dominate a hierarchy. We also find conditions for which the cost curves associated with the two organizational forms cross each other. In this case the optimal organizational form will depend on product market conditions and on the “lumpiness” of cost-reducing R&D.     

Sprumont's characterization of the uniform rule when all single-peaked preferences are admissible

Sprumont (1991) has established that the only allocation rule for the division problem that is strategy-proof, efficient, and anonymous is the uniform rule when the domain is the set of all possible profiles of continuous single-peaked preferences. Sprumont's characterization of the uniform rule is shown to hold on any larger domain of single-peaked preferences. Received: 15 December 1998 / Accepted: 12 April 1999     

On efficient trading mechanisms between one seller and n buyers

Myerson and Satterthwaite (1983) prove that if one seller and one buyer have independent private valuations for an indivisible object then no individually rational and incentive compatible trading mechanism can guarantee ex post efficiency when gains from trade are uncertain. Makowski and Mezzetti (1993) show that this is not the case when there are at least two buyers. In the latter context, if the highest possible seller's valuation is not too large, we provide an ex post efficient mechanism in which the mechanism designer and the agents are not required to know the probability distribution for the seller's valuation. Received: February 18, 1998 / Accepted: September 10, 1999     

Implementation of optimal contracts under adverse selection

This paper studies a 2-agent, 2-type principal-multiagent model of adverse selection under the assumption that the agents each have complete information. We construct a mechanism implementing the first-best contracts in Nash equilibrium that: satisfies a condition related to individual rationality, is renegotiation-proof, has a small-sized message space, achieves unique implementation and satisfies undomination of Nash equilibrium strategies. Moreover, we prove that other requirements which relate to individual rationality (different from the one satisfied by our mechanism) are not compatible with implementation of the first-best contracts. Received: 27 July 1998 / Accepted: 26 May 2000     

Full pooling in multi-period contracting with adverse selection and noncommitment

This paper analyses multi-period regulation or procurement policies under asymmetric information between the regulator and regulated firms. As well known in the literature, some degree of separation is always optimal under any form of commitment. In contrast, we show that full pooling is optimal under noncommitment when the discount factor is sufficiently high. We also discuss the meaning of full pooling under double randomization. Finally, we provide a graphical analysis of the second-best policy in terms of the regulator's commitment capacity. Received: 4 December 1996 / 7 October 1999     

Regulation in a political economy: explaining limited commitment and the ratchet effect

Abstract. This paper shows that in a political economy with repeated elections governments that possess full commitment behave as if their commitment is limited. Two different endogenous versions of the ratchet effect obtain: If contracts of previous governments tie newly elected governments, governments are unable to resist renegotiation. If previous contracts do not bind new governments and taxation has a crowding–out effect, a ratchet effect occurs that is similar, but not identical to the standard ratchet effect that is due to intertemporal non–commitment. Social welfare may be higher in the latter case, when the governing party is allowed to use bonds. Received: March 14, 2000     

Who else is bidding? The Pareto optimality of disclosing bidder identities

This paper examines whether the seller of an object should reveal the identities of the participating bidders before bids become due. It is shown that when bidders experience identity dependent externalities and auction participation is exogenous, then for a large class of standard auction mechanisms, a policy of revelation serves to realize a higher surplus because it improves the accuracy of each bidder's estimate of her ex-post willingness-to-pay, and therefore changes the auction allocation in a more ex-post efficient manner. Furthermore, it is shown that the policy of revelation increases both the expected seller revenues as well as ex-ante expected bidder payoffs. Received: 4 February 2000 / Accepted: 15 November 2000 An earlier version of this paper had the title 'Disclosure of Bidder Identities'. I thank an anonymous referee and an Associate Editor for suggestions that improved the paper. I also acknowledge comments made by participants of the Auctions session during the North American Winter Meetings of the Econometric Society 2001 held in New Orleans. I remain solely responsible for any errors.     

Multiprincipals multiagents incentive design

This paper studies a simple setting in which the contractual arrangements which determine the incentives for agents are not designed by a single central planner, but are themselves the outcome of a game among multiple noncooperatively acting principals. The notion of an Epsilon Contracting Equilibrium is introduced to predict the outcome of the contract-design game among principals. Symmetric pure strategy Epsilon Contracting Equlibria may not exist in perfectly symmetric environments. In a symmetric Epsilon Contracting Equilibrium in mixed strategies coordination failure may lead to a suboptimal institutional network in which the agents “cheat” their principals. Received: 14 June 1995 / Accepted: 09 August 1999     

The not-so-secret-agent: Professional monitors,hierarchies and implementation

Abstract. It is well-known that, when agents in an organization possess private information that is unverifiable by an outside party, games where agents simply announce their information can have multiple equilibria that may impede the successful implementation of the organization's objectives. We show that the introduction of a professional monitor (e.g. auditor, regulator, supervisor) can help to destroy the “bad' equilibria when agents have private information but have incomplete info rmation about others' information. Received: 21 May 1998 / Accepted: 26 May 2000     

Achieving the first best in sequencing problems

Abstract. In a sequencing problem with linear time cost, Suijs (1996) proved that it is possible to achieve first best. By first best we mean that one can find mechanisms that satisfy efficiency of decision, dominant strategy incentive compatibility and budget balancedness. In this paper we show that among a more general and natural class of sequencing problems, sequencing problems with linear cost is the only class for which first best can be achieved. Received: 2 December 1999/Accepted: 9 May 2001     

Lattice structure of knowledge and agreeing to disagree

This paper is a contribution to the study of the underlying mathematical structure of common-knowledge, which gives the well-known result of Aumann about the impossibility of ‘agreeing to disagree’. We present the Bayesian subjective probability model with player's belief: i.e. a triple (? %plane1D;4AF;, μ), in which i is a player. ? is a lattice in the field of sets of a state space Ω, %plane1D;4AF;, is a correspondence assigning to each state ω a filter %plane1D;4AF;(ω) in ?, and μ is a common-prior. For this model, we impose none of the important restrictions on the information structure in the Aumann-Bacharach model: axiom of knowledge K₁. axiom of transparency K₂ and axiom of wisdom K₃. We can extend both the disagreement theorem of Aumann and the agreement theorem of Geanacoplos and Polemarchakis under the assumption that each ? is an Artinian lattice.     

A characterization of the existenceof optimal dominant strategy mechanisms

This paper provides two theorems which characterize the domains of valuation functions for which there exist Pareto efficient and truth dominant strategy mechanisms (balanced Groves mechanisms). Theorem 1 characterizes the existence of balanced Groves mechanisms for a general class of valuation functions. Theorem 2 provides new balance-permitting domains of valuation functions by reducing the problem of solving partial differential equations to the problem of solving a polynomial function. It shows that a balanced Groves mechanism exists if and only if each valuation function in the family under consideration can be obtained by solving a polynomial function with order less than , where n is the number of individuals. Received: 5 January 1997 / Accepted: 25 May 1999     

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.     

On the profitability of collusion in location games

In this note we take a first step towards the analysis of collusion in markets with spatial competition, focusing on the case of pure location choices. We find that collusion can only be profitable if a coalition contains more than half of all players. This result holds for location games played in k-dimensional Euclidean space as long as consumers are distributed via atomless density functions. For competition on the unit interval, unit circle, and unit square we also derive sufficient conditions for collusion to be profitable. The results have immediate implications for mergers in spatial markets.     

A profit-center game with incomplete information

Profit centers in a firm in multidivisional form agree in the ex ante stage upon a plan about their joint production and profit imputation. The plan is executed in the subsequent two periods of the interim stage: the setup period and the manufacturing period. In the setup period, each center has its private information, but a part of its information is revealed to the other centers through its action. Based on the information endogenously pooled this way, the centers take another round of actions in the manufacturing period. A core plan is defined as a Bayesian incentive-compatible plan of the grand coalition of profit centers, upon which no coalition can improve using its Bayesian incentive-compatible plan. A core plan is called full-information revealing if each center fully reveals its private information in the setup period. Three existence theorems for a full-information revealing core plan are established. The first two theorems impose alternative conditions on returns to scale: (1) the neoclassical convex technology, and (2) increasing returns to scale. In case (2), a stronger condition than Scarf's distributiveness is imposed on the total production set. The third theorem is based on a specific supplier-customer relationship among the divisions. Received: 13 October 1997 / Accepted: 26 July 1999     

RJVs in product innovation and cartel stability

Abstract. We characterise the interplay between firms' decision in product development undertaken through a research joint venture (RJV), and the nature of their ensuing market behaviour. Participant firms in an RJV face a trade-off between saving the costs of product innovation by developing similar products to one another, e.g., by sharing most of the basic components of their products, and investing higher initial efforts in product innovation in order to develop more distinct products. We prove that the more the firms' products are distinct and thus less substitutable, the easier their collusion is to sustain in the marketing supergame, either in prices (Bertrand) or in quantities (Cournot). This gives rise to a non-monotone dependence of firms' product portfolio upon their intertemporal preferences. Received: 1 October 1998 / Accepted: 14 December 2002 We thank the seminar audience at Centre for Industrial Economics, University of Copenhagen, where all three authors were affiliated at the time we presented the first draft of this paper, and also the two anonymous referees for Review of Economic Design for their detailed comments. The usual disclaimer applies.