The Impact of Discounting on an Auction with a Buyout Option: a Theoretical Analysis Motivated by eBay’s Buy-It-Now Feature

An auction with a buyout option occurring over continuous time with rules similar to eBays buy it now option is analyzed. When auction participants make no distinction as to when a transaction occurs, the seller optimally chooses a buyout option price so high that bidders never exercise the option. However, time impatience on either side of the transaction can motivate the seller to offer an option price low enough so that the option is exercised with positive probability. Further, allowing a time impatient seller to offer such an option results in an ex ante Pareto improvement when bidders do not discount future transactions.     

The impact of bargaining on markets with price takers: Too many bargainers spoil the broth

In this paper we study how bargainers impact on markets in which firms set a list price to sell to those consumers who take prices as given. The list price acts as an outside option for the bargainers, so the higher the list price, the more the firms can extract from bargainers. We find that an increase in the proportion of consumers seeking to bargain can lower consumer surplus overall, even though new bargainers receive a lower price. The reason is that the list price for those who do not bargain and the bargained prices for those who were already bargaining rise: sellers have a greater incentive to make the bargainers’ outside option less attractive, reducing the incentive to compete for price takers. Competition Authority exhortations to bargain can therefore be misplaced. We also consider the implications for optimal seller bargaining.     

Consumer search markets with costly revisits

This paper characterizes equilibrium outcomes in consumer search markets taking the cost of going back to stores already searched explicitly into account. We show that the optimal sequential search rule under costly revisits is very different from the traditional reservation price rule in that it is non-stationary and not independent of previously sampled prices. We explore the implications of costly revisits on market equilibrium in two celebrated search models. In the Wolinsky model, some consumers search beyond the first firm. In this class of models, costly revisits do make a substantive difference and their impact can be of the same order of magnitude as the initial search cost. In the Stahl oligopoly search model where consumers do not search beyond the first firm, there remains a unique symmetric equilibrium that has firms use pricing strategies that are identical to the perfect recall case.     

Repeated Bargaining with Persistent Private Information

The paper analyses repeated contract negotiations involving the same buyer and seller where the contracts are linked because the buyer has persistent (but not full y permanent) private information. The size of the surplus being divided is specified as a two-state Markov chain with transitions that are synchronized with contract negotiation dates. Equilibrium involves information cycles triggered by the success or failure of aggressive demands made by the seller. Because there is persistence in the Markov chain generating the surplus, a successful demand induces the seller to make another aggressive demand in the next negotiation, since the buyer's acceptance reveals that the current surplus is large. Rejection of an aggressive demand, on the other hand, leads the seller to be pessimistic about the size of the surplus in the next contract, so the seller makes a "soft" offer that is sure to be accepted. Then, after several such offers have been accepted, the seller is optimistic enough to again make an aggressive demand, creating an information cycle. An interesting feature of this cycle is that the soft price is not constant, but declines as the cycle continues, so as to offset the buyer's option value of re-starting the cycle when the current state is bad. An explicit mapping is given for the relationship between the basic parameters and the equilibrium prices and quantities; in particular, there is a closed-form solution for the threshold belief that makes the seller indifferent between hard and soft offers.     

An experimental study of auctions with a buy price under private and common values

eBayʼs Buy It Now format allows a seller to list an auction with a “buy price” at which a bidder may purchase the item immediately and end the auction. When bidders are risk averse, then theoretically a buy price can raise seller revenue when values are private (but not when values are common). We report the results of laboratory experiments designed to determine whether in practice a buy price is advantageous to the seller. We find that a suitably chosen buy price yields a substantial increase in seller revenue when values are private, and a small (but statistically insignificant) increase in revenue when values are common. In both cases a buy price reduces the variance of seller revenue. A behavioral model which incorporates the winnerʼs curse and the overweighting by bidders of their own signal explains the common value auction data better than the rational model.     

Sequential selling mechanisms

Summary In this paper we attempt to formalize the idea that a mechanism that involves multilateral communication between buyers and sellers may be dominated by one that involves simple bilateral communication. To do this we consider the well known problem in which a seller tries to sell a single unit of output to a group ofN buyers who have independently distributed private valuations. Our arguments hinge on two considerations. First, buyers communicate their willingness to negotiate with the seller sequentially, and second, buyers have the option of purchasing the good from some alternative supplier. It is shown that the seller cannot improve upon a procedure in which she offers the good to each buyer in turn at a fixed price. The seller reverts to multilateral communication if possible, only when no buyer is willing to pay the fixed price. In reasonable environments buyers will be too impatient to wait for the outcome of a multilateral negotiation and all communications will be bilateral.In many problems in mechanism design, informed traders have no alternative to participation in the mechanism that is offered by its designer. The best mechanism from the designer's point of view is then the one that is most efficient at extracting informational rents, that is, a simple auction. In a competitive environment it is likely to be costly for buyers to participate in an auction or any other multilateral selling scheme in which the seller must process information from many different buyers because alternative trading opportunities will be disappearing during the time that the seller is collecting this information. Buyers might be willing to participate in an auction, but only if they could be guaranteed that the competition that they face will not eliminate too much of their surplus.At the other extreme to the auction is a simple fixed price selling scheme 1. The seller simply waits until he meets a buyer whose valuation is high enough, given the opportunities that exist in the rest of the market, for him to be willing to pay this price. The seller extracts the minimum of the buyer's informational rents since the price that a buyer pays is independent of his valuation. Yet the seller might like this scheme if adding a second bidder to the process makes it very difficult for him to find a buyer with a valuation high enough to want to participate.In the presence of opportunity costs, the seller faces a trade-off between his ability to extract buyers informational rents and his ability to find buyers who are willing to participate in any competitive process. In practice this trade-off will impose structure on the method that is used to determine a price. In markets where there are auctions, limits are put on buyer participation. In tobacco auctions bids are submitted at a distinct point in time from buyers who are present at that time. In real estate auctions time limits are put on the amount of time the seller will wait before making a decision. These restrictions on participation are presumably endogenously selected by the seller (possibly in competition with other mechanism designers) with this trade-off in mind.On the other hand, markets in which objects appear to trade at a fixed price are rarely so simple. A baker with a fixed supply of fresh bagels is unlikely to collect bids from buyers and award the bagels to the high bidder at the end of the day. Buyers are unlikely to be willing to participate in such a scheme since they can buy fresh bagels from a competitor down the street. Yet despite the fact that bagels sell at a fixed price throughout the day, most bakers are more than willing to let it be known that they will discount price at the end of the day on any bagels that they have not yet sold. Selling used cars presents a similar problem. Each potential buyer for the used car is likely to have inspected a number of alternatives, and is likely to know the prices at which these alternative can be obtained. A seller who suggests that buyers submit a bid, then wait until the seller is sure that no higher offer will be submitted is asking buyers to forgo these alternative opportunities with no gain to themselves. To avoid the rigidity of the pure fixed price scheme most used cars are sold for a fixed price or best offer. These examples suggest that the best selling mechanism may involve a complex interplay between participation and surplus extraction considerations.The purpose of this paper is to provide a simple formalism within which the factors that determine the best contract can be evaluated. We consider the best known environment from the point of view of auction design in which there are a large number of buyers with independent private valuations for a unit of an indivisible commodity that is being sold by a single supplier who acts as the mechanism designer. We modify this standard problem in two critical ways. First, we assume that the seller meets the potential buyers sequentially rather than all at once. Secondly we assume that buyers have a valuable alternative that yields them a sure surplus. This creates a simple bidding cost that is effectively the expected loss in surplus (created by the disappearance of outside alternatives) that the buyer faces during the time that he spends negotiating with the seller.These simple assumptions allow us to calculate the impact of competition and communication costs using completely standard arguments from the mechanism design literature. We are able to show that with these assumptions the seller's expected surplus will be highest if the object is sold according to the following modified fixed price scheme: the seller contacts each of the potential buyers in turn and either offers to negotiate or announces that he no longer wishes to trade. If he offers to negotiate and the buyer agrees, the buyer immediately has the option of trading for sure with the seller at a fixed price set ex ante. If the buyer does not wish to pay this fixed price, he may submit an alternative bid. The seller will then continue to contact new buyers, returning to trade with the buyer only if no buyer wishes to pay the fixed price and no higher bid is submitted.It will be clear that in our environment, both the simple fixed price scheme and the simple auction are feasible. The simple auction prevails when the fixed price is set equal to the maximum possible valuation, while the simple fixed price scheme occurs when the fixed price is set so that buyers are willing to participate if and only if they are willing to pay the fixed price. Our results will show that a simple auction in never optimal for the seller. The seller can always strictly improve his payoff by moving to a scheme in which there is some strictly positive probability that trade will occur at the fixed price. On the other hand, there are reasonable circumstances in which the seller cannot achieve a higher payoff than the one she gets by selling at a fixed price. It is shown that for any positive participation cost, there is a large, but finite, number of potential buyers so that the seller cannot achieve a higher payoff than what she gets by selling at a fixed price. Two simple, but important continuity results are also illustrated. As the cost of participation in the mechanism increases (decreases), the probability with which the seller's unit of output is sold at a fixed price goes to one (zero) in the best modified fixed price mechanism for the seller.Our paper is not the first to generate such a modified fixed price scheme. Both McAfee and McMillan (1988) and Riley and Zeckhauser (1983) come up with similar schemes for the case in which the seller must bear a fixed cost for each new buyer that she contacts. There are two essential differences between our model and theirs. First, as the cost is interpreted as the opportunity cost of participation in the mechanism, it is reasonable to imagine that the seller advertises the mechanism ex ante. Another way of putting this is that the seller pays a fixed rather than a variable cost to communicate the mechanism to buyers. This makes it possible to assume that the mechanism is common knowledge to the seller and all the buyers at the beginning of the communication process. For this reason we can make our case using completely standard arguments. Secondly, the mechanism in the opportunity cost case plays a different allocative role than it does in the case when the seller bears a cost. The mechanism must decide whether buyers should communicate with the seller or pursue their alternative activities, as well as who should trade and at what price. It is this allocative role that makes bilateral communication superior to multilateral communication in a competitive environment. These differences allow us to show, for example, that a simple fixed price scheme is undominated for the seller when the number of buyers is finite. As shown by McAfee and McMillan, this is only possible when the number of potential buyers is infinite when the seller bears the cost of communication.Remarkably, the existence of opportunity costs to buyer participation is not, by itself, sufficient to explain why sellers might prefer bilateral communications mechanisms. Samuelson (1983) and McAfee and McMillan (1987) show that when buyers must pay a fixed cost to submit a bid, which is equivalent to giving up a valuable alternative, a seller cannot expect to earn more than she does in a second price auction (though Samuelson shows that the reserve price may depend on the number of potential buyers). One of the contributions of this paper is to show that the assumption that buyers make their participation decisions simultaneously is critical to this result. Simultaneous entry decisions means that whether or not any particular buyer is assigned to the alternative activity is independent of any other buyer's valuation. With sequential communication the seller is able to relax this constraint. It is precisely the enlargement of the class of feasible mechanism that breaks down the optimality of the simple auction.The second author acknowledges the support of the Social Sciences and Humanities Research Council of Canada and the CRDE at the Université de Montreal.     

DYNAMIC PRICE COMPETITION WITH CAPACITY CONSTRAINTS AND A STRATEGIC BUYER

We analyze a simple dynamic durable good model. Two incumbent sellers and potential entrants choose their capacities at the start of the game. We solve for equilibrium capacity choices and the (necessarily mixed) pricing strategies. In equilibrium, the buyer splits the order with positive probability to preserve competition, making it possible that a high and low price seller both have sales. Sellers command a rent above the value of unmet demand by the other seller. A buyer benefits from either a commitment not to make future purchases or by hiring an agent to always buy from the lowest priced seller.     

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.     

Auctions with a buy price: The case of reference-dependent preferences

In an auction with a buy price, the seller provides bidders with an option to end the auction early by accepting a transaction at a posted price. This paper develops a model of an auction with a buy price in which bidders use the auction's reserve price and buy price to formulate a reference price. The model both explains why a revenue-maximizing seller would want to augment her auction with a buy price and demonstrates that the seller sets a higher reserve price when she can affect the bidders' reference price through the auction's reserve price and buy price than when she can affect the bidders' reference price through the auction's reserve price only. The comparative statics properties of bidding behavior are in sharp contrast to equilibrium behavior in other models where the existence and size of the auction's buy price have no effect on bidding behavior.     

Sunk costs and fairness in incomplete information bargaining

We study a bilateral trading relationship in which one agent, the seller, can make a nonrecoverable investment in order to generate potential gains from trade. Afterwards, the seller makes a price offer that the buyer can either accept or reject. If agents are fairminded, sellers who are known by the buyer to have high investment costs are predicted to charge higher prices. If the investment cost is private information, low-cost sellers should price more aggressively and high-cost sellers less aggressively than under complete information, giving rise to disagreement and/or underinvestment. Our experiment support these predictions.     

节假日对消费者购买决策的影响——来自非季节性商品的微观证据

区别于研究我国假日经济的已有文献,采用零售扫描数据对消费者购买行为的假日效应进行微观实证研究,主要考察节假日对非季节性商品购买决策的影响。选取具有代表意义的非季节性商品的购买记录进行统计分析,发现其需求在节假日期间并没有明显增加;进一步通过异方差probit模型分析消费者的购买决策,结果表明节假日显著影响了消费者对价格的敏感度,但不同商品价格敏感度的变化方向并不一致。厂商制定节假日促销策略时应对不同的非季节性商品加以区分。     

The multiple unit auction with variable supply

Summary. The theory of multiple unit auctions traditionally assumes that the offered quantity is fixed. I argue that this assumption is not appropriate for many applications because the seller may be able and willing to adjust the supply as a function of the bidding. In this paper I address this shortcoming by analyzing a multi-unit auction game between a monopolistic seller who can produce arbitrary quantities at constant unit cost, and oligopolistic bidders. I establish the existence of a subgame-perfect equilibrium for price discriminating and for uniform price auctions. I also show that bidders have an incentive to misreport their true demand in both auction formats, but they do that in different ways and for different reasons. Furthermore, both auction formats are inefficient, but there is no unambiguous ordering among them. Finally, the more competitive the bidders are, the more likely the seller is to prefer uniform pricing over price discrimination, yet increased competition among bidders may or may not enhance efficiency. Received: June 18, 1998; revised version: January 13, 1999     

Pension Fund Herding and the Influence of Management Style

In this article, we study the herding phenomenon in Spanish equity pension funds with European investment locations from 2002 to 2012, considering whether the development of different investment strategies by the managers results in herding. In addition, we analyze the performance-herding relationship, observing whether pension fund performance decreases or increases when pension funds herd. Using the herding measure of Lakonishok et al. [1992], we do not find strong imitation behavior, although herding in the market and book-to-market styles are higher. Those pension funds that do not herd or that follow distinctive strategies do not present significant differences in performance with respect to herding funds.     

Sustainable reputations with rating systems

In a product choice game played between a long lived seller and an infinite sequence of buyers, we assume that buyers cannot observe past signals. To facilitate the analysis of applications such as online auctions (e.g. eBay), online shopping search engines (e.g. BizRate.com) and consumer reports, we assume that a central mechanism observes all past signals, and makes public announcements every period. The set of announcements and the mapping from observed signals to the set of announcements is called a rating system. We show that, absent reputation effects, information censoring cannot improve attainable payoffs. However, if there is an initial probability that the seller is a commitment type that plays a particular strategy every period, then there exists a finite rating system and an equilibrium of the resulting game such that, the expected present discounted payoff of the seller is almost his Stackelberg payoff after every history. This is in contrast to Cripps, Mailath and Samuelson (2004) [5], where it is shown that reputation effects do not last forever in such games if buyers can observe all past signals. We also construct finite rating systems that increase payoffs of almost all buyers, while decreasing the seller?s payoff.     

How do selling mechanisms affect profits,surplus, capacity and prices with unknown demand?

I analyze a model in which a seller wishes to sell multiple homogeneous goods to a large group of buyers with unknown demand. The seller may either sell objects via a posted‐price mechanism, a discriminatory‐price auction, a uniform‐price auction, their open‐bid analogs, or a revelation mechanism in which the seller first asks all potential buyers to report their valuations and then sets a reserve price. I show that the revelation mechanism leads to the greatest profits, the auction mechanisms result in identical expected profits and the posted‐price mechanism results in the smallest profits. However, the more profitable mechanisms impose stronger informational requirements that may make these mechanisms infeasible in practice, and the posted‐price mechanism also results in the greatest total surplus. I also find the seller chooses a lower capacity and reserve price in an auction than in the posted‐price mechanism.     

消费者谈判能力与厂商标价策略-模型及基于实验经济学的检验

本文建立的理论模型研究了消费者谈判能力、谈判成本和对商品的偏好程度等几方面对厂商最优标价决策的影响。当消费者谈判能力较弱时,厂商可能策略性地不对商品标价,以获取更大利润,利润大小与消费者的谈判能力呈倒U形关系;而当消费者谈判能力较强时,厂商会选择对商品进行标价以最大化利润;但若消费者谈判能力很弱,消费者很可能因无利可图而放弃购买,这时厂商就会选择标价销售。通过对模型进行模拟实验,模型的结果得到了进一步验证。本文同时证明,在一定条件下,厂商选择策略性不标价可能不是社会最优的,因此需要通过政府强制标价来实现市场有效性。     

An experimental comparison of two search models

Summary. We report an experiment designed to investigate markets with consumer search costs. In markets where buyers are matched with one seller at a time, sellers are predicted to sell at prices equal to buyers' valuations. However, we find sellers post prices that offer a more equal division of the surplus, and these prices tend to be accepted, while prices closer to the equilibrium prediction are rejected. At the other extreme, sellers are predicted to sell at a price equal to marginal cost when buyers are matched with two sellers at a time. Here, we find prices are closer to, but still significantly different from, the equilibrium prediction. Thus, our results support theoretical comparative static, but not point, predictions.     

Privately-Negotiated Input Prices

We examine settings where input prices are negotiated by industry suppliers, rather than dictated by regulators. We find that the input buyer may agree to pay a high price for an input because the high price serves to reduce the intensity of retail price competition with the input seller. Full exploitation of retail customers can result. However, retail price regulation, competition among buyers, and product heterogeneity all can limit the extraction of consumer surplus. We also identify conditions under which input price negotiations will fail to produce a mutually agreeable input price.We thank Dennis Weisman and two anonymous referees for very helpful commentsJEL classification: L43, L51, L22     

Compatibility,interoperability, and market power in upgrade markets

We examine the market power of a seller who repeatedly offers upgraded versions of a product. In the case of pure monopoly, the seller also controls compatibility across versions. In the case of an entrant who offers an upgrade, the incumbent seller also controls subsequent interoperability across versions. We argue that control of compatibility and interoperability does not allow an incumbent seller to charge a price premium relative to when such control is absent and, consequently, neither is a necessary source of market power.     

A common value auction model with endogenous entry and information acquisition

Summary Much of the auction literature assumes both a fixed number of bidders and a fixed information setting. This sidesteps the important and often costly decisions a potential bidder must make prior to an auction: Should I enter and, if I do, what level of resources should I expend evaluating the good prior to bidding? We answer these questions for a stylized information model of a common value auction. The expected selling price is shown to be the expected value of the good minus the expected aggregate entry and information costs of the bidders. Thus, the seller indirectly pays for these costs to the bidders. There are auctions where the seller seemingly restricts the bidders' information expenditures. While this restriction does influence the entry decision, we demonstrate that the overall effect can be to improve the selling price. Finally, the probability of entry and the chosen accuracy of the information are never more in the second-price auction than in the first-price auction, and the seller prefers the second-price auction.We are grateful for the comments and suggestions of seminar participants at the University of British Columbia, Dartmouth College, the University of Wisconsin, Yale University, and the International Conference on Game Theory and Economics at SUNY Stony Brook.