Non-neutral information costs with match-value uncertainty

This paper investigates a model featuring a monopolist seller and a buyer with an uncertain valuation for the seller’s product. The seller chooses an information system which allows the buyer to receive a private signal, potentially correlated with her valuation. No restrictions are imposed on the conditional distributions of the signal; the cost of the information system is proportional to its precision, measured by the mutual information between the distributions of the buyer’s valuation and the signal. In equilibrium, the information system trades off the information cost against the losses deriving from a probability of trade that is either “too high,” or “too low”—depending on the relative weight of the expected losses resulting from errors of the two types—and sends “non-neutral” signals, typically. Thus, in general, the probability of a correct signal depends on the buyer’s actual valuation, and the probability of trade differs from the probability of a valuation exceeding the cost of production. The expected total surplus generated by the exchange is maximized, in equilibrium.     

Optimal Information Disclosure in Auctions and the Handicap Auction

We analyse a situation where a monopolist is selling an indivisible good to risk-neutral buyers who only have an estimate of their private valuations. The seller can release, without observing, certain additional signals that affect the buyers' valuations. Our main result is that in the expected revenue-maximizing mechanism, the seller makes available all the information that she can, and her expected revenue is the same as it would be if she could observe the part of the information that is "new" to the buyers. We also show that this mechanism can be implemented by what we call a handicap auction in interesting applications. In the first round of this auction, each buyer picks a price premium from a menu offered by the seller (a smaller premium costs more). Then the seller releases the additional signals. In the second round, the buyers bid in a second-price auction where the winner pays the sum of his premium and the second highest non-negative bid. In the case of a single buyer, this mechanism simplifies to a menu of European call options.     

Price-setting power vs. private information: An experimental evaluation of their impact on holdup

This paper investigates the extent of the holdup problem in a buyer–seller relationship in which the seller has private information about his alternative opportunities. Theory predicts that, compared to a situation in which outside options are publicly observed, the seller obtains an informational rent whereas the buyer bears an informational loss. As a result the seller is predicted to invest more while the buyer is expected to invest less. In contrast to this, private information has no impact on the investment levels observed in the experiment. But actual investments do increase with the price-setting power of the investor. These findings are roughly consistent with a model in which agents are inequality-averse. Overall the results question some recent theoretical suggestions that private information rents might substitute for price-setting power in mitigating holdup.     

Exit options in incomplete contracts with asymmetric information

This paper analyzes bilateral contracting in an environment with contractual incompleteness and asymmetric information. One party (the seller) makes an unverifiable quality choice and the other party (the buyer) has private information about its valuation. A simple deterministic exit option contract, which allows the buyer to refuse trade, achieves the first-best in the benchmark cases where either quality is verifiable or the buyer?s valuation is public information. But, when unverifiable and asymmetric information are combined, deterministic contracts are necessarily inefficient. The first-best can be achieved, however, through simple message games with stochastic terms of trade as off-equilibrium outcomes.     

Optimal selling strategies when buyers may have hard information

Consider a revenue-maximizing seller who can sell an object to one of n potential buyers. Each buyer either has hard information about his valuation (i.e., evidence that cannot be forged) or is ignorant. The optimal mechanism is characterized. It turns out that more ignorance can increase the expected total surplus. Even when the buyers are ex ante symmetric, the object may be sold to a buyer who does not have the largest willingness-to-pay. Nevertheless, an additional buyer increases the expected total surplus in the symmetric case, whereas more competition can be harmful if there are ex ante asymmetries.     

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.     

On the Interplay of Hidden Action and Hidden Information in Simple Bilateral Trading Problems

A buyer and a seller can exchange one unit of an indivisible good. While producing the good, the seller can exert unobservable effort (hidden action). Then the buyer realizes whether his or her valuation is high or low, which stochastically depends upon the seller's effort level (hidden information). The parties are risk neutral—they can rule out renegotiation and write complete contracts. It is shown that the first best cannot be achieved whenever the ex post efficient trade decision is trivial. The second-best contract is characterized and an application of the model to the choice of risky projects is briefly discussed. Journal of Economic Literature Classification Numbers: C72, C78, D23, D82.     

Asymmetric information in bilateral trade and in markets: An inversion result

I consider bilateral trade between a seller and a buyer with private valuations. The seller makes a take-it-or-leave-it price offer. If the seller observes the buyer?s valuation (symmetric information), bilateral trade is trivially efficient. If the seller cannot observe the valuation (asymmetric information), bilateral trade is inefficient. This bilateral trading game is embedded into a large matching market. In the steady-state equilibrium of the market game, the relation between the informational regime and efficiency is inverted: With small frictions efficiency obtains if information is asymmetric. If information is symmetric, however, the trading outcome can be very inefficient—even if frictions vanish.     

Do sellers offer menus of contracts to separate buyer types? An experimental test of adverse selection theory

In the basic adverse selection model, a seller makes a contract offer to a privately informed buyer. A fundamental hypothesis of incentive theory is that the seller may want to offer a menu of contracts to separate the buyer types. In the good state of nature, total surplus is not different from the symmetric information benchmark, while in the bad state, private information may be welfare-reducing. We have conducted a laboratory experiment with 954 participants to test these hypotheses. While the results largely corroborate the theoretical predictions, we also find that private information may be welfare-enhancing in the good state.     

学习能力影响下供应链企业间知识交易的最优合约配置!

在知识买方——供应链中的供应商的学习能力为其私人信息的情况下,知识卖方——制造商通过设计将知识交易量与原材料产品折扣价格相结合的合约菜单来甄别供应商的学习能力类型。在此基础上,建立信息不对称情形下的知识交易模型,通过模型求解得出最优的合约配置,并结合信息对称情形下的基准情形对合约菜单的相关性质进行了分析。最后利用数值算例对上述相关性质进行了说明。     

Bargaining with a possibly committed seller

We consider negotiations with an open time horizon where a buyer has private information about his valuation and does not know whether the seller is committed to the advertised price. This setting combines two common specifications made in the non-cooperative bargaining literature: one side is privately informed about its valuation, which is drawn from a continuum, and the other side is possibly committed to a fixed offer. We analyze the game both in discrete and in continuous time and show convergence of the two settings, which extends results from Abreu and Gul [2000. Bargaining and reputation. Econometrica 68, 85–117]. One interesting result is that as time proceeds, the non-committed seller becomes less likely to concede in a given period, i.e., it appears as if he becomes more “stubborn.” We further show that a seller may prefer to negotiate with a “worse” buyer as this enhances the value of his possible commitment.     

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.     

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.     

The value of information in a principal-agent model with moral hazard: The ex post contracting case

In a principal-agent model with moral hazard, a signal about the principal?s technology — the stochastic mapping from the agent?s action to the outcome — is observed before the contract is offered. The signal is either uninformative (null information), informative and observed only by the principal (private information), or also observed by the agent (public information). We show that, from an ex ante standpoint (before the signal is observed): (i) the agent prefers private to both null and public information; (ii) the principal sometimes prefers null to both private and public information; and (iii) when the principal prefers public to null information, she prefers public to private information, whereas the agent prefers private to public information. In this last situation, we also show that (iv) for any separating equilibrium with private information, there exists a contract with public information that both strictly prefer.     

Strategic delay and endogenous offers in bargaining games with private information

This paperendogenously determines the order of offers and the duration of delay in reaching agreement between buyers and sellers in a continuous-time bargaining game in which a seller wishes to vend an object of known cost to a buyer, to whom the value of the good is private information, and in which each player can choose to strategically delay a response to a previous offer or to interrupt the delay of his rival. Both buyers and sellers are shown to prefer to move first in a model of bargaining in which: (1) either player can make the first offer; (2) after the minimum time has elapsed from the previous offer, either player can make an offer; and (3) players can choose to strategically delay and refrain from making an offer after the previous offer. When the buyer moves first, the equilibrium response for the seller is to accept the offer immediately. When the seller moves first the equilibrium is characterized by the seller making all but the last offer, with minimal feasible delay between successive offers. Observable endogenous delay in reaching an agreement in such equilibria approaches zero as the minimal feasible delay between offers approaches zero. This indicates that in noncooperative bargaining models with private information, where players can strategically delay their offers, endogenizing the order in which players make offers removes the ability of informational asymmetries to generate equilibria exhibiting endogenous delay in reaching an agreement.     

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.     

Selling an asset to a competitor

A seller decides whether to allocate an item among two potential buyers. The seller and buyer 1 interact ex post in such a way that each of them suffers a negative externality if the other possesses the item. We show that the optimal allocation rule favors buyer 2, who does not interact ex post with the seller, and in particular bidder 1 may not obtain the good even if his valuation is highest. The auction is therefore subject to resale. When resale is possible, the seller must distort the original auction. We show that the mechanism depends crucially on the way resale is organized ex post. The seller may decide to always allocate the good to the agent with the highest valuation when rents are fully extracted by an intermediary on the resale market. However, she may resort to a stochastic mechanism when the winner of the primary auction has full bargaining power in the resale stage.     

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).     

A note on repeated-offers bargaining with one-sided incomplete information

Summary This note analyzes a modified version of the standard repeated-offers bargaining game with one-sided incomplete information studied in Fudenberg, Levine and Tirole (1985), Gul, Sonnenschein and Wilson (1986) and Ausubel and Deneckere (1989). The modification, which is introduced in the extensive form, is that the (uninformed) seller can choose to withdraw her offer immediately after the (informed) buyer accepts it. This modification is important because it removes the (implicit) commitment assumption built into the standard model that the seller is committed not to withdraw her price offer. A main result obtained is, that whether or not there is a gap between the seller's valuation and the lowest possible buyer's valuation, any seller payoff between zero and the static monopoly profit can be supported by sequential equilibria. Thus, even in the gap case there exist equilibria that completely reverse the Coase conjecture.I thank Ian Jewitt and an anonymous referee for their helpful advice and comments.     

Intertemporal self-selection with multiple buyers

Summary We consider a monopolist selling durable goods to consumers with unit demands but different preferences for quality. The seller can offer items of different quality at the same time to induce buyers to self-select, as in Mussa-Rosen (1978), but is not artificially constrained to offer only one such menu. Instead the seller can offer without precommitment asequence of menus over time. In the two-buyer case where the seller has complete information about each buyer's marginal valuation for quality, the seller's profits exceed what can be obtained from a single menu and sometimes approximate the profits of a perfectly discriminating monopolist. In companion papers (Bagnoli et al., 1990, 1992), we show that these conclusions continue to hold (1) in the infinite-horizon case with any finite number of buyers and (2) in two-period examples where the seller has incomplete information about buyer preferences.