We study a multi-unit auction with multiple bidders, each of whom has a private valuation and a budget. The truthful mechanisms of such an auction are characterized, in the sense that, under standard assumptions, we prove that it is impossible to design a non-trivial truthful auction which allocates all units, while we provide the design of an asymptotically revenue-maximizing truthful mechanism which may allocate only some of the units. Our asymptotic parameter is a budget dominance parameter which measures the size of the budget of a single agent relative to the maximum revenue. We discuss the relevance of these results for the design of Internet ad auctions.

We consider an environment where potential ex-ante symmetric buyers of an indivisible good have liquidity constraints, in that they cannot pay more than their ‘budget’ regardless of their valuation. A buyer’s valuation for the good as well as her budget are her private information. We derive the symmetric constrained-efficient and revenue maximizing auctions for this setting. In general, the optimal auction requires ‘pooling’ both at the top and in the middle despite the maintained assumption of a monotone hazard rate. Further, the auctioneer will never find it desirable to subsidize bidders with low budgets.

In many countries throughout the world, regulators are struggling to determine whether and how to introduce competition into regulated industries. This essay examines the complexities involved in the liberalization process. While stressing the importance of case-specific analyses, this essay distinguishes liberalization policies that generally are procompetitive from corresponding anticompetitive liberalization policies.

This dissertation studies mechanism design for various combinatorial problems in the presence of strategic agents. A mechanism is an algorithm for allocating a resource among a group of participants, each of which has a privately-known value for any particular allocation. A mechanism is truthful if it is in each participant’s best interest to reveal his private information truthfully regardless of the strategies of the other participants. First, we explore a competitive auction framework for truthful mechanism design in the setting of multi-unit auctions, or auctions which sell multiple identical copies of a good. In this framework, the goal is to design a truthful auction whose revenue approximates that of an omniscient auction for any set of bids. We focus on two natural settings — the limited demand setting where bidders desire at most a fixed number of copies and the limited budget setting where bidders can spend at most a fixed amount of money. In the limit demand setting, all prior auctions employed the use of randomization in the computation of the allocation and prices. Randomization

We study security-bid auctions in which bidders compete for an asset by bidding with securities whose payments are contingent on the asset’s realized value. In formal security-bid auctions, the seller restricts the security design to an ordered set and uses a standard auction format (e.g., first- or second-price). In informal settings, bidders offer arbitrary securities and the seller chooses the most attractive bid, based on his beliefs, ex post. We characterize equilibrium and show that steeper securities yield higher revenues, that auction formats can be ranked based on the security design, and that informal auctions lead to the lowest possible revenues.

In this paper, we consider the problem of designing incentive compatible auctions for multiple (homogeneous) units of a good, when bidders have private valuations and private budget constraints. When only the valuations are private and the budgets are public, Dobzinski et al [8] show that the adaptive clinching auction is the unique incentive-compatible auction achieving Pareto-optimality. They further show that this auction is not truthful with private budgets, so that there is no deterministic Pareto-optimal auction with private budgets. Our main contribution is to show the following Budget Monotonicity property of this auction: When there is only one infinitely divisible good, a bidder cannot improve her utility by reporting a budget smaller than the truth. This implies that the adaptive clinching auction is incentive

This paper focuses on implementation issues in environments where it may be costly for the players to send certain messages. We suggest an approach allowing to characterize the set of implementable outcomes, and then apply it to derive optimal mechanisms in a number of environments. The key elements of our approach are the absence of any restrictions on the communication structure in a mechanism and the ability of the principal to screen the agents not only on the basis of their preferences over the outcomes, but also on the basis of their communication abilities.

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version of the problem the seller only knows that demand will be in a neighborhood of a given model distribution. We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. While the classic monopoly policy and the maximin criterion yield a single deter-ministic price, minimax regret always prescribes a random pricing policy, or equivalently, a multi-item menu policy. The resulting optimal pricing policy under either criterion is robust to the model uncertainty. Finally we derive distinct implications of how a monopolist responds to an increase in ambiguity under each criterion.

We study the problem of maximizing revenue for auctions with multiple units of a good where bidders have hard budget constraints, first considered in [2]. The revenue obtained by an auction is compared with the optimal omniscient auction had the auctioneer known the private information of all the bidders, as in competitive analysis [7]. We show that the revenue of the optimal omniscient auction that sells items at many di#erent prices is within a factor of 2 of the optimal omniscient auction that sells all the items at a single price, implying that our results will carry over to multiple price auctions. We give the first auction for this problem, to the best of our knowledge, that is known to obtain a constant fraction of the optimal revenue when the bidder dominance (the ratio between the maximum contribution of a single bidder in the optimal solution and the revenue of that optimal solution) is large (as high as 2 ). Our auction is also shown to remain truthful if canceled upon not meeting certain criteria. On the negative side, we show that no auction can achieve a guarantee of 2-# the revenue of the optimal omniscient multi-price auction. Finally, if the bidder dominance is known in advance and is less than 5.828 , we give an auction mechanism that raises a large constant fraction of the optimal revenue when the bidder dominance is large and is asymptotically close to the optimal omniscient auction as the bidder dominance decreases. We discuss the relevance of these results for related applications.

Activity rules have emerged in recent years as an important aspect of practical auction design. The role of an activity rule in an iterative auction is to suppress strategic behavior by bidders and promote simple, continual, meaningful bidding and thus, price discovery. These rules find application in the design of iterative combinatorial auctions for real world scenarios, for example in spectrum auctions, in airline landing slot auctions, and in procurement auctions. We introduce the notion of strong activity rules, which allow simple, consistent bidding strategies while precluding all behaviors that cannot be rationalized in this way. We design such a rule for auctions with budget-constrained bidders, i.e., bidders with valuations for resources that are greater than their ability to pay. Such bidders are of practical importance in many market environments, and hindered from bidding in a simple and consistent way by the commonly used revealed-preference activity rule, which is too strong in such an environment. We consider issues of complexity, and provide two useful forms of information feedback to guide bidders in meeting strong activity rules. As a special case, we derive a strong activity rule for non budget-constrained bidders. The ultimate choice of activity rule must depend, in part, on beliefs about the types of bidders likely to participate in an auction event because one cannot have a rule that is simultaneously strong for both