THE OPTIMAL LISTING STRATEGIES IN ONLINE AUCTIONS

This article proposes a unified framework to completely characterize the seller's optimal listing strategy in the online auction as a function of her rate of time impatience. Specifically, the fixed‐price listing, the regular auction, and the buy‐it‐now (BIN) auction are each a solution of the seller's single optimization problem under different values of the rate of intertemporal discount: The perfectly patient seller adopts the regular auction, the sellers with a medium range of time impatience adopt the BIN auction, and the most impatient of sellers adopt the fixed‐price listing. Moreover, under mild conditions, the reverse price is inversely related to the value of the seller's discount factor, either within or across formats. This in turn implies that the posted price in the fixed‐price sale is greater than the reserve price of the BIN auction, followed by that of the regular auction. These predictions offer clear empirical implications.     

Mechanism design with a liquidity constrained buyer: The 2×2 case

This paper studies the implications of buyers' liquidity constraints for the optimal selling strategy. The possibility that a buyer faces a binding liquidity constraint affects the seller's strategy in a nontrivial way. Specifically, when a seller has one unit of a good to sell to a buyer with a quasilinear utility function, the `no-haggling' result indicates that textbook monopoly pricing is optimal, absent liquidity constraints. Introducing a potentially binding liquidity constraint vitiates the no-haggling result, and can make it strictly beneficial for the seller to use nonlinear pricing, to commit to a declining price sequence, or to require the buyer to post a cash bond.     

THE DETERMINANTS OF PRICE IN ONLINE AUCTIONS: MORE EVIDENCE FROM QUANTILE REGRESSION

This study explores how seller reputations affect auction prices and concludes that earlier findings may be biased due to the misspecification of seller reputation. This paper contributes to the literature by offering significant empirical evidence using Taiwanese internet auction data. Our study reveals that the influence of seller reputations on auction prices is significant, irrespective of the assumptions of linear or non‐linear relationships with price. However, failure to consider the non‐linear setting of seller reputation leads us to underestimate the impact of reputation when the seller's reputation score is low, but overestimates it when the seller's reputation becomes high. Using quantile regression, this study finds evidence of considerable differences in their impact on auction prices that are dependent on the distribution of price levels.     

Two-part tariffs set by a risk-averse monopolist

This paper revisits the classical issues of two-part tariffs by considering risk aversion of a monopolistic seller. Under demand uncertainty, equilibrium unit price declines and approaches towards marginal cost as the seller becomes more risk averse. Marginal-cost pricing prevails, irrespective of the seller’s risk attitude, if clients are homogenous. Under cost uncertainty, unit price is higher than marginal cost and monotonically increases in risk aversion. The model is then extended to accommodate buyers’ risk aversion and it is found that demand uncertainty makes unit price decline in the seller’s risk aversion again but increase in buyers’ risk aversion.     

Equilibrium opacity in ultimatum‐offer bargaining

We consider ultimatum bargaining between a seller and a buyer of an asset. They know each other's valuation of the asset. Both can defer their decisions to delegates. These delegates have opaque preferences. Seller and buyer choose the opacity of their delegate. For the seller's delegate this choice is restricted to a random reservation price drawn from the set of symmetric two‐point distributions around the seller's true reservation price. The opacity choice of the buyer's delegate is restricted to a random willingness‐to‐pay drawn from the set of symmetric two‐point distribution around the buyer's true willingness‐to‐pay. We characterize the set of pure‐strategy equilibria in their delegation choices. Multiple equilibria arise. Except for two corner solutions, both players will exploit the strategy of opacity. A large set of efficient equilibria exist. For these, opacity choices do not reduce the probability of transacting, but benefit the buyer compared with the no‐delegation equilibrium. We also study the robustness of the results with respect to the player's ability to also resort to a tougher delegate in addition to the opacity choice.     

A MARKET WITH FRICTIONS IN THE MATCHING PROCESS: AN EXPERIMENTAL STUDY*

We construct a laboratory market in which there is a friction in the matching between buyers and sellers. Sellers simultaneously post prices and then buyers simultaneously choose a seller. If more than one buyer chooses the same seller, the seller's single unit is randomly sold to one of them. Our results show a broad consistency with theoretical predictions, although price dispersion exists and is slow to decay. Prices also exceed the equilibrium level when there are only two sellers, and buyers' purchase probabilities are insufficiently responsive to price differences when there are two sellers.     

Price and information disclosure in the private art market: A signalling game

In this paper, we model private art market agents’ strategic interactions in presence of two types of asymmetric information, about artwork quality and buyer’s knowledge, assuming the seller does not know how informed is the buyer while the buyer does not know the quality of the artwork before purchase. If the seller can choose either a high or a low price and the buyer can signal his type to the seller, we identify the conditions for both equilibria with pooling buyer signalling strategy and with separating strategy, as well as conditions for equilibria where the seller fixes the price according to the actual quality and where he posts prices trying to take advantage of buyer’s limited information. Finally, we identify the condition for the emergence of a “counter-lemon” result, where low-quality artworks and uninformed collectors exit the market, suggesting that seller uncertainty does not directly benefit the buyers, but it can impact the quality traded in the market.     

Multidimensional Bargaining Under Asymmetric Information

A buyer with private information regarding marginal valuation bargains with a seller to determine price and quantity of trade. Depending on parameter values, a high‐valuation buyer wants either to reveal information to create value or to conceal it to capture value. In the first case, equilibrium trades are efficient. In the second case, the low‐valuation buyer purchases less than her efficient quantity, and there can be a one‐period delay in trade. The quantity distortion is the only inefficiency that persists when time between offers approaches zero. There exist equilibria that are independent of the seller's prior beliefs.     

Robustness to strategic uncertainty

We introduce a criterion for robustness to strategic uncertainty in games with continuum strategy sets. We model a player's uncertainty about another player's strategy as an atomless probability distribution over that player's strategy set. We call a strategy profile robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in which every player's strategy is optimal under his or her uncertainty about the others. When payoff functions are continuous we show that our criterion is a refinement of Nash equilibrium and we also give sufficient conditions for existence of a robust strategy profile. In addition, we apply the criterion to Bertrand games with convex costs, a class of games with discontinuous payoff functions and a continuum of Nash equilibria. We show that it then selects a unique Nash equilibrium, in agreement with some recent experimental findings.     

Monopoly Price Dispersion Under Demand Uncertainty

When a monopolist sets its price before its demand is known, then it may set more than one price and limit the availability of its output at lower prices. This article adds demand uncertainty and price rigidities to the standard model of monopoly pricing. When there are two states of demand and the ex post monopoly price is greater when demand is high then the monopolist's optimal ex ante pricing strategy is to set two prices and limit purchases at the lower price.     

Robust monopoly pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the pricing policies under two distinct decision criteria with multiple priors: (i) maximin utility and (ii) minimax regret. The equilibrium price under either criterion is lower then in the absence of uncertainty. The concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty.     

DIRECTED SEARCH AND THE BERTRAND PARADOX

I study a directed search model of oligopolistic competition, extended to incorporate general capacity constraints, congestion effects, and pricing based on ex post demand. In the presence of any one of these ingredients, the Bertrand paradox fails to hold. Hence, despite the emphasis that has been placed by the literature on sellers' capacity constraints as a resolution to the paradox, the existence of such constraints is only a subcase of a general class of environments where the paradox fails. Specifically, Bertrand's paradox will not arise whenever the buyers' expected utility from visiting a seller is decreasing in that seller's realized demand.     

Learning about the arrival of sales

We analyse optimal stopping when the economic environment changes because of learning. A primary application is optimal selling of an asset when demand is uncertain. The seller learns about the arrival rate of buyers. As time passes without a sale, the seller becomes more pessimistic about the arrival rate. When the arrival of buyers is not observed, the rate at which the seller revises her beliefs is affected by the price she sets. Learning leads to a higher posted price by the seller. When the seller does observe the arrival of buyers, she sets an even higher price.     

Search, common knowledge, and competition

This paper analyzes the effects of buyer search costs and seller private and common knowledge on seller competition. It shows that lack of common knowledge results in the equilibrium price continuously decreasing to the perfectly competitive one as buyer search costs for price decrease from positive for all buyers to zero for all buyers, even if each market agent's uncertainty (in the private knowledge) is small. At the same time, if the uncertainty of each seller about buyer valuations is small, the effects of a small change in the search costs or of information structure on pricing may be large (but continuous).     

Competition and confidentiality: Signaling quality in a duopoly when there is universal private information

We model non-cooperative signaling by two firms that compete over a continuum of consumers, assuming each consumer has private information about the intensity of her preferences for the firms' respective products and each firm has private information about its own product's quality. We characterize a symmetric separating equilibrium in which each firm's price reveals its respective product quality. We show that the equilibrium prices, the difference between those prices, the associated outputs, and profits are all increasing functions of the ex ante probability of high safety. If horizontal product differentiation is sufficiently great then equilibrium prices and profits are higher under incomplete information about quality than if quality were commonly known. Thus, while signaling imposes a distortionary loss on a monopolist using price to signal quality, duopolists may benefit from the distortion as it can reduce competition. Finally, average quality is lower since signaling quality redistributes demand towards low-quality firms.     

Policy Uncertainty about Australia's Carbon Price: Expert Survey Results and Implications for Investment

Australia's carbon‐pricing policy remains in doubt due to a lack of bipartisan political support. A survey of Australian‐based carbon‐pricing experts demonstrates profound policy uncertainty: 40 per cent of respondents expect the current carbon‐pricing mechanism to be repealed, but 80 per cent expect that there will be a carbon price in 2020. The forward price curve is U‐shaped and has great variance, with the 60 per cent confidence interval spanning from zero to A$25/t in 2020. Carbon policy uncertainty causes large excess costs in Australia's energy sector and may result in delay and diversion of investment.     

Pricing, learning, and strategic behavior in a single-sale model

Summary. We analyze an infinite horizon model where a seller who owns an indivisible unit of a good for sale has incomplete information about the state of the world that determines not only the demand she faces but also her own valuation for the good. Over time, she randomly meets potential buyers who may have incentives to manipulate her learning process strategically. We show that i) the seller's incentives to post a high price and to experiment are not necessarily monotonic in the information conveyed by a buyer's rejection; and ii) as the discount factors tend to one, there are equilibria where the seller always ends up selling the good at an ex-post individually rational price. Received: January 6, 1999; revised version: July 15, 2000     

不确定情形下的市场定价机制:基于心理-权力框架对新古典价格理论的审视

现实市场存在严重的不确定性,供给成本、消费效用以及质量信号等都是价格的函数,从而也就无法基于供求曲线交叉来获得均衡价格.因此,在不确定的现实市场中,人们往往需要借助一定的锚定值来预测产品和劳务的价格并促成契约和交易.同时,不同产品的价格锚定值往往依赖于基于一定规则所形成的等级序列,进而形成锦标赛制的市场定价体系,即不同产品的价格水平和不同劳务的工资水平往往依赖于其所属等级.进而,锦标赛制定价所遵循的不是生产成本原则或劳动投入原则,也不是客观功用原则或产出贡献原则,从而往往既不公平也无效率.锦标赛制定价体系之所以流行,根本原因在于市场经济中的权力结构是不对称的;尤其是,权力碎片化发展使得极少数强势者拥有了市场定价的权力,而定价原则是基于特定主权者的利益最大化和少数富人的效用最大化.正是基于锚定效应和权力分析框架的结合,我们才可以揭示出不确定市场中统一的锦标赛制定价体系及其嵌入的利益导向.显然,这将有助于我们深入审视新古典经济学价格理论,识别现实市场中的厂商定价策略,更好地解释各种市场行为和竞争形态,同时有助于我们更深刻地洞识市场机制的内在缺陷,进而为市场监管和收入分配等公共政策提供依据和方向.     

High Price Strategy and Quality Signalling

I investigate a high price strategy by a durable‐goods producer for signalling the high quality of goods. It is assumed that two types of monopolists exist: high‐quality and low‐quality. The monopolist's type is assumed to be unknown to consumers in the first period. Before the beginning of the second period, a product reputation established in the past period enables consumers to recognize the real type of the monopolist. I show that there occurs a signalling equilibrium where the high‐quality type monopolist uses a high price strategy. An interaction between the new and old products peculiar to the durable‐goods markets plays an important role in the pricing strategy.     

Risk attitudes and the stag-hunt game

A stag-hunt game (with the risky and safe actions) has two pure Nash equilibria that are Pareto-rankable. The risky action leads either to the Pareto-superior equilibrium (high payoff) or to out of equilibrium (low payoff) depending on the opponent’s action. Both players may want to obtain high payoff but uncertainty about the opponent’s action may prevent them to take such strategic risk. This paper investigates how information about the risk attitude of an opponent affects a player’s action choice in the stag-hunt game. I find that although a subject’s propensity to choose the risky action depends on her opponent’s risk attitude, it does not depend on her own risk attitude.