Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly

The seller of N distinct objects is uncertain about the buyer's valuation for those objects. The seller's problem, to maximize expected revenue, consists of maximizing a linear functional over a convex set of mechanisms. A solution to the seller's problem can always be found in an extreme point of the feasible set. We identify the relevant extreme points and faces of the feasible set. We provide a simple algebraic procedure to determine whether a mechanism is an extreme point. We characterize the mechanisms that maximize revenue for some well-behaved distribution of buyer's valuations.     

A note on dynamic monopoly pricing under consumption externalities

We analyze dynamic monopoly pricing under consumption externalities, focusing on pricing under negative externalities. We also attempt to generalize models in the previous literature, which encompass both negative and positive externalities, by incorporating a consumer’s discount factor for past sales as a parameter. Analyzing our model reveals oscillation as the optimal price path in the presence of negative externalities.     

A test of monopoly price dispersion under demand uncertainty

A test of the predictions of Dana’s (2001) model of monopoly price dispersion under demand uncertainty using ticket price data from Major League Baseball shows that ticket price dispersion changes systematically with demand uncertainty, verifying the predictions of the model.     

A comparison between the core and the monopoly solutions in a mixed exchange economy

Summary. Using a mixed market model for analyzing imperfectly competitive economies, we maximize the oligopolists' Welfare Function, given individual rationality and feasibility constraints. We prove that solutions belong to the core for a large class of economies. This class includes, in particular, every monopoly having a single type of small traders. Note that all such solutions yield the large trader, utility-wise, strictly more than at any monopoly solution, where the monopolist plays strategically, and the ocean of small traders act as being as price-takers. Received: March 4, 1996; revised version July 7, 1996     

Simple contracts, renegotiation under asymmetric information, and the hold-up problem

In this article it is demonstrated that voluntary bargaining over a collective decision under asymmetric information may well lead to ex post efficiency if the default decision is non-trivial. It is argued that the default decision may be interpreted as a ‘simple’ contract that the parties have written ex ante. This result is used in order to show that simple unconditional contracts which are renegotiated may allow the hold-up problem to be solved, even if the parties’ valuations are private information.     

Selection effects in auctions for monopoly rights

We demonstrate that auctioning market licenses may result in higher market prices than assigning them via more random allocation mechanisms. When future market profit is uncertain, winning an auction is like winning a lottery ticket. If firms differ in risk attitudes, auctions select the least risk-averse firm, which, in turn, set a higher price (or a higher quantity, in case quantity is the decision variable) in the marketplace than an average firm.     

Entry deterrence and innovation in durable-goods monopoly

This paper investigates the efficiency of innovation investments in a durable-goods monopoly when a potential entrant threatens to innovate as well. We show that the durability of the good endows the monopolist with the power to discourage rival innovation since current sales alter the demand for a new generation of the good. The equilibrium is therefore determined not only by the incentive for intertemporal price discrimination in durable-goods monopoly, but also by the incumbent's concern for maintaining the technological leadership. We demonstrate that entry deterrence followed by no innovation always implies underinvestment in innovation.     

Contract renegotiation in a continuous state space

Summary. When players are unable to write complete state contingent contracts it is shown, within the context of a non-cooperative contracting-renegotiation game, that the only subgame perfect equilibrium allocations are those that correspond to the set of first-best allocations. Players are able to implement this set of allocations by signing an initial contract that is subsequently renegotiated in all states of the world. The contracting-renegotiation problem is complicated in an interesting way by assuming that the state space is continuous. The issue of the existence of an initial contract, that is subsequently renegotiated to the set of first-best allocations, must be resolved. Unlike Aghion, Dewatripont and Rey [1994], the results here do not require nor depend upon the comonotonicity of the objective functions. Received: January 27, 1995; revised version July 1, 1996     

Robust monopoly pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the pricing policies under two distinct decision criteria with multiple priors: (i) maximin utility and (ii) minimax regret. The equilibrium price under either criterion is lower then in the absence of uncertainty. The concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty.     

Mixed pricing in oligopoly with limited monopoly

We analyze price competition between two brands. Buyers consist of switchers and two segments of customers with limited brand loyalty. We identify a unique symmetric mixed-strategy price equilibrium and find that competition is most relaxed when there exists some switchers.     

Regulation and the market for checks

This paper presents an analysis of the market for checks using the monopoly problem as an approximation. The need for such an analysis arises due to the following policy proposal: from time to time, the Turkish government considers increasing the lump-sum amount that drawee banks are legally responsible to pay per bad check. The purpose of this proposal is to ease out firms' liquidity needs especially during recessions. We show that banks will tend to restrict the quantity of checks as a response to such a policy action. We report that a percentage point increase in banks' obligation per bad check could lead up to a 1.7% decline in the total supply of checks on the margin. This means that such a policy change may harm the real economy rather than providing support. We establish that the extent of the monopoly distortion depends on three main factors: (i) the elasticity of demand for checks, (ii) how fast the fraction of bad checks increases with the total supply of checks, and (iii) the degree of preference heterogeneity.     

Double moral hazard and renegotiation

We examine renegotiation in a double moral hazard model with an ex ante budget balancing constraint when both the principal and the agent are allowed to make a renegotiation offer even though the principal proposes an initial contract. Under a belief restriction, any perfect-Bayesian equilibrium leads to an allocation that is superior to the second-best allocation of the standard double moral hazard model without renegotiation. The result of this paper gives some reasons for the existence of intermediary organizations such as holding companies, law houses, consulting firms, investment banks or venture capital. The result can also provide the rationalization for a fund set up by a group of firms of the industry in which their product is legally required to be recyclable.     

Optimal selling strategies when buyers may have hard information

Consider a revenue-maximizing seller who can sell an object to one of n potential buyers. Each buyer either has hard information about his valuation (i.e., evidence that cannot be forged) or is ignorant. The optimal mechanism is characterized. It turns out that more ignorance can increase the expected total surplus. Even when the buyers are ex ante symmetric, the object may be sold to a buyer who does not have the largest willingness-to-pay. Nevertheless, an additional buyer increases the expected total surplus in the symmetric case, whereas more competition can be harmful if there are ex ante asymmetries.     

Unpriced quality

A monopolist charges the same price for differentiated products when high quality products are likely to be assigned to low valuation consumers. The argument explains the use of ‘unpriced quality’ for concert tickets, movie theaters, and elsewhere.     

Competition in bureaucracy and corruption

This paper studies the consequences of introducing competition between bureaucrats. Firms are supposed to invest into eliminating negative externalities of production, while bureaucrats administer the process by issuing licences. Some bureaucrats are corrupt, that is, they issue a licence to any firm in exchange for a bribe. The competition regime is found to create more ex ante incentives for firms to invest, while the monopoly regime is better at implementing ex post allocation, that is, distributing the licences given the firms' investment decisions. Additional results on the effect of punishments and bureaucrats' rotation are provided.     

Nash implementation and uncertain renegotiation

We study Nash implementation when the outcomes of the mechanism can be renegotiated among the agents but the planner does not know the renegotiation function that they will use. We characterize the social objectives that can be implemented in Nash equilibrium when the same mechanism must work for every admissible renegotiation function, and show the importance of allowing the planner to sometimes take away resources from the agents.     

Optimal supervision intensity, collusion, and the organization of work

Abstract.  The intensity of supervision, defined as the proportion of supervisors to bottom-rank productive workers, differs widely across organizations and nations. Analysing three monitoring systems that differ in their supervision intensity, I show that the possibility of collective shirking arrangements can impose a system-dependent limit on the range of implementable performances. This brings about a tradeoff in the choice of the monitoring system: the system that economizes on incentive costs may implement an inferior range of performances. Applications of the model generate work-disutility-, ethics- and job-characteristics-based explanations for variations in the intensity of supervision.     

Learning about the arrival of sales

We analyse optimal stopping when the economic environment changes because of learning. A primary application is optimal selling of an asset when demand is uncertain. The seller learns about the arrival rate of buyers. As time passes without a sale, the seller becomes more pessimistic about the arrival rate. When the arrival of buyers is not observed, the rate at which the seller revises her beliefs is affected by the price she sets. Learning leads to a higher posted price by the seller. When the seller does observe the arrival of buyers, she sets an even higher price.     

Optimality and renegotiation in dynamic contracting

We characterize the optimal renegotiation-proof contract in a dynamic principal–agent model in which the type of the agent may change stochastically over time. We show that, under general conditions, the optimal contract with commitment is renegotiation proof even when type realizations are serially correlated. When the renegotiation-proofness constraint is binding, it is always optimal to partially screen the types by offering a menu of choices to the agent; and the distortion induced by the renegotiation-proofness constraint is non-decreasing in the persistence of types.     

When is multidimensional screening a convex program?

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x,y) of product type y to agent type x — and on the principal?s costs c(y) — which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal?s problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal?s optimal strategy — and similarly of the strategy maximizing the expected welfare of the agents when the principal?s profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang?s necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.