Bundling decisions for selling multiple objects

Summary. Auctioneers often face the decision of whether to bundle two or more different objects before selling them. Under a Vickrey auction (or any other revenue equivalent auction form) there is a unique critical number for each pair of objects such that when the number of bidders is fewer than that critical number the seller strictly prefers a bundled sale and when there are more bidders the seller prefers unbundled sales. This property holds even when the valuations for the objects are correlated for a given bidder. The results have been proved using a mathematical technique of quantiles that can be extremely useful for similar analysis. Received: November 5, 1996; revised version: January 21, 1998     

Technology selling and innovation with bargaining

We examine when the price of technology is found through bargaining between the seller and the buyer and explore its effect on the innovation incentive. Selling the technology is preferred to licensing for the innovating firm. The possibility of selling increases the incentive for innovation compared to licensing for a range of high‐cost innovation, but reduces the incentive for a range of low‐cost innovation.     

Are we selling out our patients?

In an open letter that follows, a former proponent of managed care describes how his group has let marketplace forces and greed jeopardize patients. The letter is addressed to the group's MSO physician shareholders, who've proposed selling the organization and its managed-care contracts--in effect, the group practice itself--to a capital partner. To preserve patients' privacy, names and identifying details have been changed. The author has been granted anonymity.     

Learning buyers' valuation distribution in posted-price selling

Summary. For his proof of the existence of a general competitive equilibrium Abraham Wald assumed a strictly pseudomonotone inverse market demand function or, equivalently, that market demand satisfies the Weak Axiom of Revealed Preference. It is well known that more recent existence theorems do not need this assumption. In order to clarify its role in Wald's proof, the question of existence of an equilibrium for a modified version of the Walras-Cassel model is reduced to the solvability of a related variational inequality problem. In general, the existence of a solution to such a problem can only be proved by advanced mathematical methods. We provide an elementary induction proof which demonstrates the essence of Abraham Wald's famous contribution. Received: July 22, 1997; revised version: December 11, 1997     

Sequential Screening

We study price discrimination where consumers know at the time of contracting only the distribution of their valuations but subsequently learn their actual valuations. Consumers are sequentially screened, as in a menu of refund contracts. Initial valuation uncertainty can differ in terms of first-order stochastic dominance or mean-preserving-spread. In both cases, optimal mechanisms depend on informativeness of consumers' initial knowledge about their valuations, not on uncertainty that affects all consumers. It can be optimal to "subsidize" consumers with smaller valuation uncertainty through low refund to reduce the rent to those who face greater uncertainty and purchase more "flexible" contracts.     

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.     

Sequential regulatory oversight

We examine a setting where a different regulatory commission controls the activities of a firm in each of two periods. Each commission is concerned primarily with the welfare of contemporary consumers. We examine the efficacy of three different regulatory charters in resolving the intertemporal conflicts that arise between commissions. These charters specify the extent to which the second-period commission is bound to promises made by its predecessor.     

Sequential procurement auctions

Two auctions are held in sequence with the possibility of learning between the second and the first. The buyer optimally chooses to discriminate against the winner of the first auction in the second. The optimal mechanism has a discontinuity in the winner's second bid; this strictly dominates a sequence of independent sealed bid auctions.     

Sequential two-prize contests

We study a two-stage all-pay auction with two identical prizes. In each stage, the players compete for one prize. Each player may win either one or two prizes. We analyze the unique subgame-perfect equilibrium of our model with two players where each player??s marginal values for the prizes are decreasing, constant, or increasing. We also analyze an equilibrium of the model with more than two players where each player??s marginal values for the prizes are nonincreasing.     

Buying and selling behavior in stochastic environments with backstop markets

The author acknowledges a research grant from the research program Private Forestry and helpful comments from two anonymous referees, Mats Bergman, and Runar Brännlund, Department of Economics, University of Umeå.     

Bundling as an optimal selling mechanism for a multiple-good monopolist

Multiple objects may be sold by posting a schedule consisting of one price for each possible bundle and permitting the buyer to select the price-bundle pair of his choice. We identify conditions that must be satisfied by any price schedule that maximizes revenue within the class of all such schedules. We then provide conditions under which a price schedule maximizes expected revenue within the class of all incentive compatible and individually rational mechanisms in the n-object case. We use these results to characterize environments, mainly distributions of valuations, where bundling is the optimal mechanism in the two and three good cases.     

Sequential decisions with tests

We consider a principal-agent problem where the principal wishes to be endorsed by a sequence of agents, but cannot truthfully reveal type. In the standard “herding” model, the agents learn from each other's decisions, which can lead to cascades on a given decision when later agents' private information is swamped. We augment the standard model to allow the principal to subject herself to a test designed to provide public information about her type. She must decide how tough a test to attempt from a continuum of test types, which involves trading off the higher probability of passing an easier test against the greater impact from passing a tougher test. We find that the principal will always choose to be tested, and will prefer a tough test to a neutral or easy one.     

Sequential voting with abstention

Dekel and Piccione [2000. Sequential voting procedures in symmetric binary elections. J. Polit. Economy 108, 34–55] have proven that information cascades do not necessarily affect the properties of information aggregation in sequential elections: under standard conditions, any symmetric equilibrium of a simultaneous voting mechanism is also an equilibrium of the correspondent sequential mechanism. We show that when voters can abstain, these results are sensitive to the introduction of an arbitrarily small cost of voting: the set of equilibria in the two mechanisms are generally disjoint; and the informative properties of the equilibrium sets can be ranked. If an appropriate q-rule is chosen, when the cost of voting is small the unique symmetric equilibrium of the simultaneous voting mechanism dominates all equilibria of the sequential mechanism.     

Sequential Procurement With Subcontracting

Two symmetric sellers are approached sequentially by fragmented buyers. Each buyer conducts a second-price auction and purchases from the seller who offers the lower price. Winning an auction affects bidding for future contracts because the sellers have nonconstant marginal costs. We assume that the sellers are completely informed, and we study the unique equilibrium that survives iterated elimination of weakly dominated strategies. If subcontracting between the sellers is impossible, the final allocation of contracts is generally inefficient. If postauction subcontracting is possible, the sellers can be worse off, ex ante , than when subcontracting is impossible.     

Sequential bargaining and competition

Summary This paper studies a sequential bargaining model of a decentralised market. A main objective is to explore the conditions under which the unique subgame perfect equilibrium outcome of the market game approximates the Walrasian outcome of the market. The three main messages that emerge from our results are as follows. First, contrary to conventional wisdom, frictionless markets need not be Walrasian. Second, the relative magnitudes of frictions can have a profound impact on the market outcome even in the limit as the absolute magnitudes of the frictions become negligible. And third, the relative magnitudes of certain types of frictions may have to be significantly large in order for markets to be Walrasian, reflecting that certain types of frictions are needed in the market in order to induce the Walrasian outcome.This paper is based on a chapter of my Ph.D. thesis. I would like to thank Ken Binmore, David Canning, Partha Dasgupta and Frank Hahn for their helpful comments. I owe special thanks to Ariel Rubinstein for his comments, remarks and encouragement. The comments and suggestions of an anonymous referee have significantly improved the exposition at several places.