Nenad Kos

Extremal incentive compatible transfers

We characterize the boundaries of the set of transfers (extremal transfers) implementing a given allocation rule without imposing any assumptions on the agentʼs type space or utility function besides quasi-linearity. Exploiting the concept of extremal transfers allows us to obtain an exact characterization of the set of implementable allocation rules (the set of transfers is non-empty) and the set of allocation rules satisfying Revenue Equivalence (the extremal transfers coincide). We then show how the extremal transfers can be put to use in mechanism design problems where Revenue Equivalence does not hold.

Information in tender offers with a large shareholder

We study tender offers for a firm which is owned by one large shareholder who holds less than half of the total shares, and many small shareholders who each hold a unit share. Each shareholder is privately informed, yet uncertain, about the raider’s ability to improve the value of the firm, whereas the raider is unin- formed. In the benchmark model of complete information, the raider is unable to make a profit. As shown in Marquez and Y?lmaz (2008), the same obtains when the raider is facing only privately informed small shareholders. We show, however, that the combination of private information on the side of shareholders and the presence of a large shareholder can facilitate profitable takeovers. More precisely, for any given information structure, the raider can make a profit if the large shareholder holds a sufficiently large stake in the company. In the unique equilibrium outcome, neither the probability of a successful takeover nor the quilibrium price offer depends on the large shareholder’s information. Therefore, the large shareholder’s information is not reflected in the price. When the equilibrium price offer is positive, the large shareholder tenders all of his shares regardless of his information. Finally, we show that the same type of equilibria arise when there are several large shareholders, as long as their total stake in the company is smaller than one-half. Keywords: takeovers, tender offers, lemons problem, large shareholder. JEL Classification Numbers: D82, G34.

Communication and efficiency in auctions

We study auctions under restricted communication. Agents have valuations distributed over an interval but can only report one of a finite number of messages. We provide necessary conditions for welfare as well as revenue maximizing auctions in the independent private values case when bidders report simultaneously. We also show that the seller who chooses how to allocate a fixed number of messages allocates them evenly over all agents.

Selling to the mean

We study optimal selling strategies of a seller who is poorly informed about the buyer’s value for the object. When the maxmin seller only knows that the mean of the distribution of the buyer’s valuations belongs to some interval then nature can keep him to payoff zero no matter how much information the seller has about the mean. However, when the seller has information about the mean and the variance, or the mean and the upper bound of the support, the seller optimally commits to a randomization over prices and obtains a strictly positive payoff. In such a case additional information about the mean and/or the variance affects his payoff.

Optimal selling mechanisms under moment conditions

We study the revenue maximization problem of a seller who is partially informed about the distribution of buyers valuations, only knowing its first N moments. The seller chooses the mechanism generating the best revenue guarantee based on the information available, that is, the optimal mechanism is chosen according to maxmin expected revenue. We show that the transfer function in the optimal mechanism is given by non-negative monotonic hull of a polynomial of degree N. This enables us to transform the sellers problem into a much simpler optimization problem over N variables. The optimal mechanism is found by choosing the coefficients of the polynomial subject to a resource constraint. We show that knowledge of the first moment does not guarantee strictly positive revenue for the seller, characterize the solution for the cases of two moments and derive some characteristics of the solution for the general case.