Budget-Constrained Sequential Auctions with Incomplete Information

I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder\\'s type. Parameters permit the existence of multiple equilibrium symmetric bidding functions that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say α, is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good α is higher when good α is sold first.sequential auctions, budget constraints, efficiency, revenue, price, sequence.

Budget Constrained Auctions with Heterogeneous Items

In this paper, we present the first approximation algorithms for the problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders can have arbitrary demand and budget constraints. Our mechanisms are surprisingly simple: We show that a sequential all-pay mechanism is a 4 approximation to the revenue of the optimal ex-interim truthful mechanism with discrete correlated type space for each bidder. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal ex-post truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sub-logarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles. We believe this approach will be useful in other Bayesian mechanism design contexts.Comment: Final version accepted to STOC '10. Incorporates significant reviewer comment

Budget-Constrained Sequential Auctions with Incomplete Information

I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder's type. Multiple equilibrium symmetric bidding functions may exist that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say α, is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good α are higher when good α is sold first.sequential auctions, budget constraints, efficiency, revenue, price, sequence

Analysis of multi-attribute multi-unit procurement auctions and capacity-constrained sequential auctions

This dissertation examines an iterative multi-attribute auction for multi-unit procurement in the first part. A multi-unit allocation problem that allows order split among suppliers is formulated to improve the market efficiency. Suppliers are allowed to provide discriminative prices over units based on their marginal costs. A mechanism called Iterative Multiple-attribute Multiple-unit Reverse Auction (IMMRA) is proposed based on the assumption of the modified myopic best-response strategies. Numerical experiment results show that the IMMRA achieves market efficiency in most instances. The inefficiency occurs occasionally on the special cases when cost structures are significantly different among suppliers. Numerical results also show that the IMMRA results in lower buyer payments than the Vickrey-Clarke-Grove (VCG) payments in most cases. In the second part, two sequential auctions with the Vickrey-Clarke-Grove (VCG) mechanism are proposed for two buyers to purchase multiple units of an identical item. The invited suppliers are assumed to have capacity constraints of providing the required demands. Three research problems are raised for the analysis of the sequential auctions: the suppliers\u27 expected payoff functions, the suppliers\u27 bidding strategies in the first auction, and the buyers\u27 procurement costs. Because of the intrinsic complexity of the problems, we limit our study to a duopoly market environment with two suppliers. Both suppliers’ dominant bidding strategies are theoretically derived. With numerical experiments, suppliers’ expected profits and buyers’ expected procurement costs are empirically analyzed

Analysis of multi-attribute multi-unit procurement auctions and capacity-constrained sequential auctions

This dissertation examines an iterative multi-attribute auction for multi-unit procurement in the first part. A multi-unit allocation problem that allows order split among suppliers is formulated to improve the market efficiency. Suppliers are allowed to provide discriminative prices over units based on their marginal costs. A mechanism called Iterative Multiple-attribute Multiple-unit Reverse Auction (IMMRA) is proposed based on the assumption of the modified myopic best-response strategies. Numerical experiment results show that the IMMRA achieves market efficiency in most instances. The inefficiency occurs occasionally on the special cases when cost structures are significantly different among suppliers. Numerical results also show that the IMMRA results in lower buyer payments than the Vickrey-Clarke-Grove (VCG) payments in most cases. In the second part, two sequential auctions with the Vickrey-Clarke-Grove (VCG) mechanism are proposed for two buyers to purchase multiple units of an identical item. The invited suppliers are assumed to have capacity constraints of providing the required demands. Three research problems are raised for the analysis of the sequential auctions: the suppliers\u27 expected payoff functions, the suppliers\u27 bidding strategies in the first auction, and the buyers\u27 procurement costs. Because of the intrinsic complexity of the problems, we limit our study to a duopoly market environment with two suppliers. Both suppliers’ dominant bidding strategies are theoretically derived. With numerical experiments, suppliers’ expected profits and buyers’ expected procurement costs are empirically analyzed

A Blotto Game with Incomplete Information

We consider a Blotto Game with Incomplete Information. A pure-strategy symmetric monotonic Bayesian equilibrium is found and its properties are discussed. Key words: Blotto Game, Imperfect Information. Journal of Economic Literature Classification: C72, D72.

Putting auction theory to work : the simultaneous ascending auction

The"simultaneous ascending auction"was first introduced in 1994 to sell licenses to use bands of radio spectrum in the United States. Much of the attention devoted to the auction came from its role in reducing federal regulation of the radio spectrum and allowing market values, rather than administrative fiat, to determine who would use the spectrum resource. Several parts of economic theory proved helpful in designing the rules for simultaneous ascending auction and in thinking about how the design might be improved and adapted for new applications. After briefly reviewing the major rules of the auction in section 2, the author turns in section 3 to an analysis based on tatonnement theory, which regards the auction as a mechanism for discovering an efficient allocation and its supporting prices. The analysis reveals a fundamental difference between situations in which the licenses are mutual substitutes and others in which the same licenses are sometimes substitutes and sometimes complements. Section 4 is a selective account of some applications of game theory to evaluating the simultaneous ascending auction design for spectrum sales. Results like those reported in section 3 have led to renewed interest in auctions in which bids for license packages are permitted. In section 5, the author uses game theory to analyze the biases in a leading proposal for dynamic combinatorial bidding. Section 6 briefly answers two additional questions that economists often ask about auction design: If trading of licenses after the auction is allowed, why does the auction form matter at all for promoting efficient license assignments? Holding fixed the quantity of licenses to be sold, how sharp is the conflict between the objectives of assigning licenses efficiently and obtaining maximum revenue? Section 7 concludes.Economic Theory&Research,International Terrorism&Counterterrorism,Markets and Market Access,Environmental Economics&Policies,Labor Policies,Markets and Market Access,Access to Markets,Economic Theory&Research,Environmental Economics&Policies,International Terrorism&Counterterrorism