Exchanging heterogeneous goods via sealed bid auctions and transportation systems

A primary commodity such as wheat, rice, coffee, oil, etc., is shipped fromm locations where it was grown or pumped ton manufacturers. Each manufacturer processes, packages, advertises, and distributes the commodity under a consumer product brand name. The resulting heterogeneous good is sold at a sealed bid auction, in competition with the other manufacturers of the consumer product, tok final customers. The problem to be considered in this paper is to find a way of determining prices for the goods produced and the physical exchanges between seller and buyer which satisfy flow conditions and which take into account the evaluations of the goods by both sellers and buyers. The first model for doing this is given in section 1, which combines the idea of a sealed bid auction due to Shapley, Shubik and Thompson, with a conventional transportation system. The sealed bid auction is used to determine the exchange prices, and the transportation system is used to calculate the production and transportation costs. It is suggested that the resulting model type can also be applied in a wide range of problems that arise in the marketing of goods sold under brand names (i.e., heterogeneous goods) regardless of whether they are actually exchanged at formal auctions. We show in section 6 that our model is a generalization of the transshipment model in a recent paper by Dubey and Shapley [1]. In their model they considered a number of oligopolists engaged in transshipping and trading goods. Their oligopolists set their prices in order to maximize profits, rather than having them determined by an auction process as is done in our model. In section 7, we extend the model to one in which the wholesalers are permitted to make positive profits. We show how to calculate the values of coalitions of the various players in the model.The work of the first named author was prepared as part of the activities of the Management Sciences Research Group, Carnegie Mellon University, under Contract No. N00014-85-K-0198 NR 047-048 with the Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

The emissions trading paradox

This article considers the price history of CO₂ allowances in the EU Emission Trading Scheme. Since European Emissions Trading started in 2005, the prices of allowances have varied between less than one and thirty Euro per ton of CO₂. This previously unpredicted volatility and, more notably, a significant price crash in May 2005 led to the hypothesis that electricity producers might use their market power to influence the prices of allowances. Besides market power, the combination of information asymmetry and price interdependencies (between prices of primary goods – especially electricity – and allowances) plays an important role in explaining the emissions trading paradox. The model presented will show that banking can lead to such a price crash if market participators act rationally. Furthermore, in such a scenario banking can be profitable for sellers at the cost of buyers.     

Capacity and entry issues in online exchanges

With the advent of open standards and Internet technologies, the number of sellers who can participate in online exchanges is greatly increased. We model the competition between identical sellers vying for the same business, and find that there exists a mixed-strategy equilibrium in prices. The results help us understand the dynamics between a seller’s capacity and his motivation to participate in an auction.     

Auctions with an asking price

This paper studies a sales mechanism, prevalent in housing markets, where the seller does not reveal or commit to a reserve price but instead publicly announces an asking price. We show that the seller sets an asking price such that, in equilibrium, buyers of certain types would accept it with positive probability. We also show that this sales mechanism, with an optimally chosen asking price set prior to the seller learning her value, does better than any standard auction with a reserve price equal to the seller’s reservation value. We then extend the analysis to the case where the asking price reveals information about the seller’s reservation value. We show that in this case there is a separating equilibrium with fully-revealing asking prices, which is revenue-equivalent to a standard auction with a reserve price set at the seller’s reservation value.     

The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multi-unit demands consists of a set of sellers that own a given number of indivisible units of potentially many different goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents?? utilities that are attainable at equilibrium.     

Efficiency of purchasing and selling agents in markets with quality uncertainty: The case of illicit drug transactions

Since Akerlof’s theory of lemons, economists have viewed quality uncertainty as an informational advantage for sellers. Drawing on frontier techniques, we propose in this paper a simple method for measuring inefficiency of both sellers and buyers in markets for goods with different levels of quality. We apply a non-parametric robust double-frontier framework to the case of illicit substance markets, which suffer from imperfect information about drug quality for purchasers and to a lesser extent for sellers. We use unique data on cannabis and cocaine transactions collected in France that include information about price, quantity exchanged and purity. We find that transactional inefficiency does not really benefit either dealers or purchasers. Furthermore, information influences the performance of agents during market transactions.     

Manipulation via endowments in auctions with multiple goods

We study manipulation via endowments in a market in an auction setting with multiple goods. In the market, there are buyers whose valuations are their private information, and a seller whose set of endowments is her private information. A social planner, who wants to implement a socially desirable allocation, faces the seller’s manipulation via endowments, in addition to buyers’ manipulation of misreporting their valuations. We call a mechanism immune to the seller’s manipulation via endowments destruction-proof. In general, there exists no mechanism which is destruction-proof, together with strategy-proofness of the buyers, efficiency, and participation. Nevertheless, we find a restricted domain of the buyers’ valuation profiles satisfying a new condition called per-capita goods–buyer submodularity. We show that, in this domain, there exists a mechanism which is destruction-proof, together with the above properties. The restriction is likely to be met when each winner’s valuation is close to the next-highest valuation. We also provide a relation to monopoly theory, and argue that per-capita goods–buyer submodularity is independent of the standard elasticity argument.     

Dualization Problem over the Product of Chains: Asymptotic Estimates for the Number of Solutions

A key intractable problem in logical data analysis, namely, dualization over the product of partial orders, is considered. The important special case where each order is a chain is studied. If the cardinality of each chain is equal to two, then the considered problem is to construct a reduced disjunctive normal form of a monotone Boolean function defined by a conjunctive normal form, which is equivalent to the enumeration of irreducible coverings of a Boolean matrix. The asymptotics of the typical number of irreducible coverings is known in the case where the number of rows in the Boolean matrix has a lower order of growth than the number of columns. In this paper, a similar result is obtained for dualization over the product of chains when the cardinality of each chain is higher than two. Deriving such asymptotic estimates is a technically complicated task, and they are required, in particular, for proving the existence of asymptotically optimal algorithms for the problem of monotone dualization and its generalizations.     

Vickrey–Dutch procurement auction for multiple items

We consider a setting where there is a manufacturer who wants to procure multiple items from a set of suppliers each of whom can supply one or more of these items (bundles). We design an ascending price auction for such a setting which implements the Vickrey–Clarke–Groves outcome and truthful bidding is an ex post Nash equilibrium. Our auction maintains non-linear and non-anonymous prices throughout the auction. This auction has a simple price adjustment step and is easy to implement in practice. As offshoots of this auction, we also suggest other simple auctions (in which truthful bidding is not an equilibrium by suppliers) which may be suitable where incentives to suppliers are not a big concern. Computer simulations of our auction show that it is scalable for the multi-unit case, and has better information revelation properties than its descending auction counterpart.     

Investigating buyer and seller strategies in online auctions

The annual turnover of online auctions is already in tens of billions of dollars and this amount is predicted to grow substantially over the next few years. Hence, it is important to know how buyers and sellers can influence their chances of success. Therefore, data were collected from eBay auctions for three different categories of collectible items, namely those with a published guide price, those with a rough guide price and those having no easily obtainable guide price. The options available to buyers and sellers of items were then analysed. It was found that it was hard for the seller to influence an item's achieved price significantly, apart from items with no guide price where the starting price could have an effect. Most bidders bid close to the current value and so there were insufficient data to determine the consequences of timing on the placing of high bids. For low bids, delaying a bid was found to improve significantly the chances of winning for one of the data sets.     

All-pay auctions with pre- and post-bidding options

Motivated by the emergence of online penny or pay-to-bid auctions, in this study, we analyze the operational consequences of all-pay auctions competing with fixed list price stores. In all-pay auctions, bidders place bids, and highest bidder wins. Depending on the auction format, the winner pays either the amount of their bid or that of the second-highest bid. All losing bidders forfeit their bids, regardless of the auction format. Bidders may visit the store, both before and after bidding, and buy the item at the fixed list price. In a modified version, we consider a setting where bidders can use their sunk bid as a credit towards buying the item from the auctioneer at a fixed price (different from the list price). We characterize a symmetric equilibrium in the bidding/buying strategy and derive optimal list prices for both the seller and auctioneer to maximize expected revenue. We consider two situations: (1) one firm operating both channels (i.e. fixed list price store and all-pay auction), and (2) two competing firms, each operating one of the two channels.     

Pricing and clearing combinatorial markets with singleton and swap orders

In this article we consider combinatorial markets with valuations only for singletons and pairs of buy/sell-orders for swapping two items in equal quantity. We provide an algorithm that permits polynomial time market-clearing and -pricing. The results are presented in the context of our main application: the futures opening auction problem. Futures contracts are an important tool to mitigate market risk and counterparty credit risk. In futures markets these contracts can be traded with varying expiration dates and underlyings. A common hedging strategy is to roll positions forward into the next expiration date, however this strategy comes with significant operational risk. To address this risk, exchanges started to offer so-called futures contract combinations, which allow the traders for swapping two futures contracts with different expiration dates or for swapping two futures contracts with different underlyings. In theory, the price is in both cases the difference of the two involved futures contracts. However, in particular in the opening auctions price inefficiencies often occur due to suboptimal clearing, leading to potential arbitrage opportunities. We present a minimum cost flow formulation of the futures opening auction problem that guarantees consistent prices. The core ideas are to model orders as arcs in a network, to enforce the equilibrium conditions with the help of two hierarchical objectives, and to combine these objectives into a single weighted objective while preserving the price information of dual optimal solutions. The resulting optimization problem can be solved in polynomial time and computational tests establish an empirical performance suitable for production environments.     

A procedure to compute the nucleolus of the assignment game

The assignment game introduced by Shapley and Shubik (1972)  [6] is a model for a two-sided market where there is an exchange of indivisible goods for money and buyers or sellers demand or supply exactly one unit of the goods. We give a procedure to compute the nucleolus of any assignment game, based on the distribution of equal amounts to the agents, until the game is reduced to fewer agents.     

基于价格歧视策略的多单元逆向多属性英式拍卖机制

针对现有的多单元逆向多属性拍卖机制的市场分配效率都比较低,不利于社会效益最大化和采购双方长期合作等问题,设计了高效率的基于价格歧视策略的多单元逆向多属性英式拍卖机制,利用线性混合整数规划建立了赢者确定模型,并基于新建立的拍卖机制给出了拍卖流程和投标策略,为供应商提供投标决策支持。然后通过设计数值实例和对比模拟实验收集数据,采取统计分析的方法验证了新设计的拍卖机制市场分配效率和采购方的效益都比较高。上述研究结果适用于通过逆向多属性拍卖与信息技术相结合的网上自动化多单元商品采购。     

Sequential auctions on Böhm-Bawerk's horse market

This paper studies what prices and final allocations would arise under strategic (or sophisticated) behavior of buyers when homogeneous goods are auctioned off sequentially, one at a time. It is shown, using subgame perfect equilibria, that prices (and thus final allocations) vary depending on the order of goods to be auctioned off. However, opposed to the case where buyers bid sincerely, the number of goods sold out is always unchanged and final allocations are always Pareto-optimal in any sequence of auctions.     

Equilibrium points of a class of many-person games

This paper deals with the competitive equilibrium points of a class of (n+1)-person games, the players beingn sellers and a single buyer. Each seller offers a price for his product; depending upon the prices offered, the buyer then determines the amount he wishes to buy from each seller. Two types of equilibrium points in this class of games are discussed.The authors are indebted to Professor G. Leitmann for his valuable comments on an earlier version of this paper.     

Reverse bullwhip effect in pricing

Price variability is one of the major causes of the bullwhip effect. This paper analyzes the impact of procurement price variability in the upstream of a supply chain on the downstream retail prices. Procurement prices may fluctuate over time, for example, when the supply chain players deploy auction type procurement mechanisms, or if the prices are dictated in market exchanges. A game theory framework is used here to model a serial supply chain. Sequential price game scenarios are investigated to show that there is an increase in retail price variability and an amplified reverse bullwhip effect on prices (RBP) under certain demand conditions.     

Competing trade mechanisms and monotone mechanism choice

We investigate the choice between posted prices and auctions of competing sellers with private valuations. Assuming that buyers face higher hassle costs in auctions, we show the existence of monotone pure strategy equilibria where sellers offer posted prices rather than auctions if and only if they have a sufficiently high reservation value. Posted prices sell with lower probability but yield a larger revenue in case of trade. Using an empirical strategy to compare revenues of posted prices and auctions that takes selling probabilities explicitly into account, we find our theoretical predictions supported by data from eBay auctions on ticket sales for the EURO 2008 European Football Championship.     

Ex-post price stability with convex costs

Homogeneous goods markets with convex costs, do not generally possess Bertrand-Nash equilibria in pure strategies. In order to identify ex-post stable prices in such markets, the set of outcomes feasible in Bertrand competition are analysed as a non-transferable utility coalitional game. The market-clearing price is shown to always implement a strict-core outcome. Moreover, where at least two sellers compete, the strict-core converges to only admit market-clearing outcomes. The analysis has implications for a number of prominent models of oligopoly competition. When firms engage in capacity pre-commitment, the set of ex-post stable prices converges to the corresponding Cournot prices. This result holds for arbitrary capacity choices and a general class of rationing rules. Conversely, double-marginalisation is never ex-post stable.