Equilibrium price and advertisement distributions

We consider an economy where many sellers sell identical goods to many buyers. Each seller has a unit supply and each buyer has a unit demand. The only possible information flow about prices is through costly advertising. We show that in equilibrium the sellers use mixed strategies in pricing which leads to price and advertisement distributions. With convex advertising costs each seller sends only one advertisement in the market. We also delineate a class of advertising costs which ensures that sellers may send multiple advertisements in equilibrium. Higher prices are advertised more than lower prices.     

Equilibrium in a market with intermediation is Walrasian

We show that a profit maximizing monopolistic intermediary may behave approximately like a Walrasian auctioneer by setting bid and ask prices nearly equal to Walrasian equilibrium prices. In our model agents choose to trade either through the intermediary or privately. Buyers (sellers) trading through the intermediary potentially trade immediately at the ask (bid) price, but sacrifice the spread as gains. A buyer or seller who trades privately shares all the gains to trade with this trading partner, but risks costly delay in finding a partner. We show that as the cost of delay vanishes, the equilibrium bid and ask prices converge to the Walrasian equilibrium prices. Received: 2 February 1996 / Accepted: 28 March 1997     

Personalized Pricing and Quality Customization

We embed the principal–agent model in a model of spatial differentiation with correlated consumer preferences to investigate the competitive implications of personalized pricing and quality allocation (PPQ), whereby duopoly firms charge different prices and offer different qualities to different consumers, based on their willingness to pay. Our model sheds light on the equilibrium product-line pricing and quality schedules offered by firms, given that none, one, or both firms implement PPQ. The adoption of PPQ has three effects in our model: it enables firms to extract higher rents from loyal customers, intensifies price competition for nonloyal customers, and eliminates cannibalization from customer self-selection. Contrary to prior literature on one-to-one marketing and price discrimination, we show that even symmetric firms can avoid the well-known Prisoner's Dilemma problem when they engage in personalized pricing and quality customization. When both firms have PPQ, consumer surplus is nonmonotonic in valuations such that some low-valuation consumers get higher surplus than high-valuation consumers. The adoption of PPQ can reduce information asymmetry, and therefore sellers offer higher-quality products after the adoption of PPQ. Overall, we find that while the simultaneous adoption of PPQ generally improves total social welfare and firm profits, it decreases total consumer surplus.     

Descending price multi-item auctions

We propose a simultaneous descending price auction mechanism to sell multiple heterogeneous items, each owned by a distinct seller, to a number of buyers. Each buyer has known private valuations on items, and wants at most one item. We show that if the sellers follow a descending price offer procedure and the buyers follow a greedy strategy for accepting the offers, the auction results in a nearly efficient allocation, and terminates close to a competitive equilibrium price vector. The descending price offer strategy of the sellers is close to a Nash equilibrium. However, we show that the buyers are better off waiting in our auction. There is a maximum limit (corresponding to the minimum competitive equilibrium price vector) till which they can wait without running into the risk of not winning any item. If the buyers wait within this limit, the prices can be brought arbitrarily close to a uniquely defined competitive equilibrium price vector.     

Random Advertising and Monopolistic Price Dispersion

We investigate the role of price advertising in a market where consumers are imperfectly informed about prices. We consider a monopolist whose demand depends on price and advertising expenditure. This demand function is derived from optimizing behavior of consumers. Uninformed consumers may pay a cost to visit the seller and obtain price information. Advertising enables the monopolist to increase the number of informed consumers. In equilibrium the uninformed consumers form rational price expectations, and the seller necessarily adopts a random pricing and advertising strategy.     

Strategic stocking for new products to signal quality information

This paper investigates the signaling role of stocking for new experience products in a two-period setting. The seller privately observes the product quality information, which cannot be resolved until the second selling period. We show that the stocking plays a pivotal role in signaling the quality information, and the equilibrium strategy depends highly on ordering cost and the consumer prior belief about the seller type. If the seller is unable to dynamically decide the retail prices, separating equilibrium arises more frequently and such a fixed pricing may result in a win-win situation for both seller and consumers.     

佣金约束条件下排污权双边叫价拍卖机制设计

通过排污权交易提高环境资源的使用效率和配置效率,实现环境资源最优配置。排污权和排污权市场理论研究是环境资源可持续利用的重要研究课题,而排污权交易模型是排污权市场理论与实践中排污权交易的核心。本文采用双边叫价拍卖交易模式,建立了排污权交易双边叫价拍卖的不完全信息博弈模型,给出了双边叫价拍卖的机制设计。该机制具有有效性和激励相容性。     

基于拍卖的垄断型产品供应链的博弈分析

论文研究了基于拍卖交易的垄断型产品供应链中卖方和买方的博弈问题,成交价格同时取决于卖方向拍卖市场的供货数量和买方向拍卖市场的竞拍数量。博弈结果显示,在垄断供应的情况下,博弈的纳什均衡将会是买卖双方都不通过拍卖渠道来进行交易,只有在非常极端的条件下可以达成供货和竞拍等量的均衡。最后,论文引入一个新卖方作为买方参与拍卖后的补货来源,得到的新均衡解能使原买卖双方的收益提高,从而说明单纯的拍卖并不总是最好的交易方式,多渠道的销售方式有时更能保障买卖双方的利益。     

Buyer brokerage: Experimental evidence

This paper offers an experimental investigation of two commission structures for buyer brokerage. One commission structure is the currently used structure in the industry where both the seller’s broker and the buyer’s broker each receive a percentage of the sales price as their compensation from the seller. In an alternative commission structure, while the seller’s broker still receives a percentage of the sales price from the seller, the buyer’s broker is compensated by the buyer and the compensation is inversely related to the sales price. We find that how the buyer’s broker gets compensated has significant implications. While both commission structures yield a similar probability of reaching an agreement, the alternative commission structure yields a lower price and a longer time to reach an agreement. Furthermore, the alternative commission structure achieves a better alignment of the interests of the buyer and the buyer’s broker without affecting the earnings of the players in the transaction. We also find that the improvement in the alignment of interests is more significant for female buyers than for male buyers. Furthermore, a higher listing price by the seller and a higher initial bid price by the buyer each lead to a significant increase in the negotiated price.     

A mechanism for package allocation problems with gross substitutes

We consider a package allocation problem in which a seller owns many indivisible objects and the rest of the agents, buyers, are interested in packages of these objects. Buyers’ valuations satisfy monotonicity and the gross substitutes condition (Kelso and Crawford, 1982). The aim of this paper is to analyze the following mechanism: simultaneously, each buyer requests to the seller a package by announcing how much he would pay for it; once buyers have played, the seller decides the final assignment of packages and the prices, as long as this assignment makes no buyer worse off than with his initial request. The subgame perfect equilibrium outcomes of the mechanism correspond to the Vickrey outcome (Vickrey, 1961) of the market.     

Neutrality of buyer and seller commissions to auction house profit

This paper presents an examination of optimal revenue management of a monopoly auction house through which a seller sells goods via a second‐price auction. The house charges commissions to both the buyer and seller. Results demonstrate that a continuum of combinations of optimal buyer and seller commission rates exists, all of which yield the same expected profit of the house. Additionally, we discuss several possible factors that lead to the prevailing custom of zero buyer commission, such as commission aversion of buyers, the house's incentive to maximize the hammer price, and seller and buyer preferences for apparently lowered commission rates.     

An equilibrium model of insider trading in continuous time

We study a Bayesian–Nash equilibrium model of insider trading in continuous time. The supply of the risky asset is assumed to be stochastic. This supply can be interpreted as noise from nonrational traders (noise traders). A rational informed investor (the insider) has private information on the growth rate of the dividend flow rewarded by the risky asset. She is risk averse and maximizes her inter-temporal utility rate over an infinite time-horizon. The market is cleared by a risk neutral market maker who sets the price of the risky asset competitively as the conditional present value of future dividends, given the information supplied by the dividend history and the cumulative order flow. Due to the presence of noise traders, the market demand does not fully reveal the insider’s private information, which slowly becomes incorporated in prices. An interesting result of the paper is that a nonstandard linear filtering procedure gives an a priori form for the equilibrium strategy to be postulated. We show the existence of a stationary linear equilibrium where the insider acts strategically by taking advantage of the camouflage provided by the noise which affects the market maker’s estimates on private information. In this equilibrium, we find that the insider’s returns on the stock are uncorrelated over long periods of time. Finally, we show that the instantaneous variance of the price under asymmetric information lies between the instantaneous variance of the price under complete and incomplete information. The converse inequalities hold true for the unconditional variance of the price.     

On the informed seller problem: optimal information disclosure

We consider a revenue-maximizing seller who, before proposing a mechanism to sell her object(s), observes a vector of signals correlated with buyers’ valuations. Each buyer knows only the signal that the seller observes about him, but not the signals she observes about other buyers. The seller first chooses how to disclose her information and then chooses a revenue-maximizing mechanism. We allow for very general disclosure policies, that can be random, public, private, or any mixture of these possibilities. Through the disclosure of information privately, the seller can create correlation in buyers’ private information, which then consist of valuations plus beliefs. For the standard independent private values model, we show that information revelation is irrelevant: irrespective of the disclosure policy an optimal mechanism for this informed seller generates expected revenue that is equal to her maximal revenue under full information disclosure. For more general allocation environments that allow also for interdependent, for common values, and for multiple items, disclosure policies may matter, and the best the seller can do is to disclose no information at all.     

International pharmaceutical supply prices: Definitions — problems — policy implications

In cases where the buyer and the seller of goods and services are companies belonging to the same group the prices charged for goods and services are called ‘international delivery prices’ or ‘international transfer prices’. The peculiarities of research-based companies are such that attempts to ascertain in practice what constitutes an ‘appropriate’ international delivery price are beset by a number of problems. Any scheme that is devised to solve the problems of international transfer prices should feature general ‘rules’ on how the various countries ought to share in central costs. As international transfer prices are a prerequisite for an efficient world economy based on the division of labour an agreement should be reached on the design and content of suitable delivery price systems for a research-intensive industry.     

Learning quality through prices and word‐of‐mouth communication

This paper studies the effect of word‐of‐mouth communication on the optimal pricing strategy for new experience goods. I consider a dynamic monopoly model with asymmetric information about product quality, in which consumers learn in equilibrium from both prices and other consumers. The main result is that word‐of‐mouth communication is essential for the existence of separating equilibria, wherein the high‐quality monopolist signals high quality through a low introductory price (lower than the monopoly price), and the low‐quality one charges the monopoly price. The intuition is simple: low prices are costly, and will only be used by firms confident enough that increased experimentation (and therefore communication among consumers) will yield good news about quality and increased future profits. Additional results are the following: for the high‐quality seller, the expected price (quantity) is increasing (decreasing) over time; whereas for the low‐quality one, the opposite is true. Moreover, signaling becomes more difficult when consumers pay less attention to their peers' reports and more attention to past prices. Finally, word‐of‐mouth communication improves consumer welfare.     

Game contingent claims in complete and incomplete markets

A game contingent claim is a contract which enables both the buyer and the seller to terminate it before maturity. For complete markets Kifer [Finance and Stochastics 4 (2000) 443–463] shows a connection to a (zero-sum) Dynkin game whose value is the unique no-arbitrage price of the claim. But, for incomplete markets one needs a more general approach. We interpret the contract as a generalized non-zero-sum stopping game. For the complete case this leads to the same results as in Kifer [Finance and Stochastics 4 (2000) 443–463]. For the general case we show the existence of an equilibrium point under the condition that both the seller and the buyer have an exponential utility function. For other utility functions such a point need not exist in the context of incomplete markets.     

Testing the Information Structure of Eastern European Markets: The Warsaw Stock Exchange

This paper investigates the content of the information set used by the agents in the Warsaw Stock Exchange - WSE. Three “candidate variables” are examined — consumers’ prices, the zloty/US$ exchange rate and the refinancing rate of the National Bank of Poland — with respect to three WSE stocks, from different sectors of the economy. The methodology employed supposes that the innovations in the price series are orthogonal to all variables within or outside the information set. Beyond the question of how to specify the agents expectations, the WSE trading rules and the high volatility period present in all monthly price series were additional problems to render it operational. Given the solutions adopted, in only three out of the nine cases tested, it was possible to reject the null that the candidate did not belong to the information set. This is a signal that macroeconomic fundamentals are still absent from the WSE. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于不完全信息动态博弈模型的报价策略研究

目前应用博弈论对价格谈判所进行的研究大多集中于讨价还价问题,而关于报价问题的研究往往依靠定性分析。因此本文建立了一个关于报价策略的三阶段不完全信息动态博弈模型,并通过求解证明：在谈判双方信息对称的条件下,无论对买方还是卖方来说,“抢先报价”都是占优策略。在买卖双方都采取“抢先报价”策略时,报价顺序博弈的结果具有不确定性。在现实中买卖双方往往会通过各种其他手段来达到抢先报价的目的。     

Adverse selection and costly information acquisition in asset markets

We develop an asset exchange model with adverse selection and costly information acquisition incentives. A seller of an asset knows the true value of the asset, while a buyer can obtain information about the asset’s quality at a cost. An equilibrium offer is pooling, but a buyer can purchase only good assets after producing the costly information about the asset’s quality. When the probability that the seller holds good assets is above the threshold value, a trade can occur with and without information acquisition, depending on the information acquisition cost, and the trade volume and social welfare are higher in equilibrium without information production than in equilibrium with information production. When the probability of facing good assets is below the threshold value, a trade occurs only after screening the quality of assets, and, hence, the market collapses if the information acquisition cost is sufficiently high. As the information acquisition cost increases, social welfare can increase or decrease depending on the probability of facing good and bad assets.     

Buyer–seller networks with demand shocks and intermediation

We present a model in which buyers and sellers use links to trade with each other. Each seller produces a good which can be one of two types. Buyers are ex ante identical but receive specification or valuation shocks after the links are formed. We show that efficient networks are stable and that severing a link in an efficient network results in a higher price for the buyer but a lower price for the seller. We also examine network intermediation when sellers (buyers) form links sequentially. When sellers form links sequentially, the first seller becomes an intermediary and shares links with other sellers; this makes all sellers better off. However, when buyers form links sequentially, buyers may or may not share links. If links are shared multiple intermediaries result.