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.     

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.     

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.     

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.     

Efficient mechanisms for bilateral trading

We consider bargaining problems between one buyer and one seller for a single object. The seller's valuation and the buyer's valuation for the object are assumed to be independent random variables, and each individual's valuation is unknown to the other. We characterize the set of allocation mechanisms that are Bayesian incentive compatible and individually rational, and show the general impossibility of ex post efficient mechanisms without outside subsidies. For a wide class of problems we show how to compute mechanisms that maximize expected total gains from trade, and mechanisms that can maximize a broker's expected profit.     

The Dynamic Vickrey Auction

We study the efficient allocation of a single object over a finite time horizon. Buyers arrive randomly over time, are long-lived, and have independent private values. The valuation of a buyer may depend on the time of the allocation in an arbitrary way. We construct an incentive compatible mechanism in which (A) there is a single financial transaction (with the buyer), (B) ex-post participation constraints are fulfilled, (C) there is no positive transfer to any agent and (D) payments are determined online. We exploit that under the efficient allocation rule, there is a unique potential winning period for each buyer. This reduces the multidimensional type to one dimension and the payment of the winner can be defined as the lowest valuation for the potential winning period, with which the buyer would have won the object. In a static model, this payment rule coincides with the payment rule of the Vickrey Auction.     

A Stackelberg Game Model of Trade in Renewable Resources with Competitive Sellers*

We model international trade in renewable resources between a single buyer and competitive sellers as a Stackelberg differential game. The buyer uses unit and ad valorem tariffs to indirectly encourage conservation of the renewable resource under study. First, we show that the efficacy of these trade policy instruments in promoting conservation depends fundamentally on whether harvesting costs are stock dependent or independent. When harvesting costs are stock independent, the optimal open‐loop tariffs are dynamically consistent. In contrast, when harvesting costs are stock dependent, the optimal open‐loop tariffs are dynamically inconsistent. Secondly, we point out that whether the terminal value of the resource stock is higher with the stock independent or the stock dependent cost function cannot be resolved unambiguously. Thirdly, we show that it does not make sense for the buyer to use both tariffs simultaneously. Finally, we discuss the implications of these and other findings for renewable resource conservation in general.     

The inefficiency of price quantity bargaining

In bargaining between a buyer and several sellers on prices and quantities, strategic inefficiencies arise. By reallocating quantities between agreements, the buyer can increase its share of the surplus. With two symmetric sellers producing substitutes, the quantity in the first agreement will be higher than the efficient quantity, and the quantity in the last lower, thus implying that sellers are strategically discriminated. When asymmetries are not too large and sellers produce substitutes, the buyer first agrees with the seller with the lowest marginal cost and only the most efficient order of agreement is an equilibrium outcome. When goods are complements, both equilibrium quantities are lower than the efficient levels.     

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.     

Monopolistic screening and uninformed buyers

In the standard monopolistic screening problem, buyers obtain information rent as a result of possessing private information; if a contract can be offered before the buyer knows his valuation, the seller can extract the full (expected) surplus. I consider a situation where the buyer may or may not have private information about his valuation at the time the contract is offered. Is the seller (strictly) better off as compared to the standard situation? The answer depends crucially on the specific model. In the 2-types model, unless the probability (that the buyer is uninformed) reaches a critical threshold, the seller is unable to benefit from the buyer's ignorance. In the continuum-types model, on the other hand, optimal expected profit is strictly higher than in the standard model whenever this probability is positive.     

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.     

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.     

Price signaling and the strategic benefits of price rigidities

We analyze trade between a perfectly informed price setting party (seller) and an imperfectly informed price taker (buyer). Differently from most of the literature, we focus on the case in which, under full information, it would be inefficient to trade goods of sufficiently poor quality. We show that the unique equilibrium surviving D1 is characterized by market breakdown, although trade would be mutually beneficial in some state of nature. This occurs independently of the precision of the information available to the buyer. The model thus implies that signaling through prices may exacerbate the effect of adverse selection rather than mitigate it. Under D1, the seller would always benefit from committing to prices that do not reveal her information. We develop this intuition by analyzing the strategic advantages of price rigidities. We show that price rigidities help restore trade and could even enhance effectiveness of prices as signals of quality.     

Taxes and the Efficiency-Rent Extraction Trade-off

This paper presents an adverse selection model in which progressive taxation enhances productive efficiency by encouraging a principal (buyer) to be less aggressive in contracting with an agent (seller). Wary of padded cost budgets, the buyer employs a hurdle‐rate procurement policy. With a low cost hurdle, the buyer keeps greater profits when transactions are undertaken but trade occurs less often. While the hurdle is unaffected by a flat tax, a progressive tax tilts the buyer's preference: the buyer's benefit from a lower hurdle becomes less pronounced, since the marginal increase in his profits is muted in after‐tax terms. The result is increased trade and the possibility of Pareto improvements.     

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.     

BETTER LATER THAN NEVER? AN EXPERIMENT ON BARGAINING UNDER ADVERSE SELECTION

A central result in the literature on bargaining with asymmetric information is that the uninformed party (buyer) can screen the informed party (seller) over time. Screening eliminates trade failures that are otherwise common in the presence of adverse selection, but the downside of the bargaining institution is the cost associated with repeated offers and time frictions. This article reports an experimental test of these predictions. We find that rates of trade are substantially higher in the bargaining institution than in control treatments in which we remove the possibility to make repeated offers (take‐it‐or‐leave‐it offer) or the time frictions. However, we also observe a persistent overdelay before agreements are reached, that is, bargaining takes longer than theoretically predicted. This lowers efficiency below its predicted level and below the level observed in the take‐it‐or‐leave‐it offer institution. We identify possible channels for overdelay in the form of fairness preferences and loss aversion, concluding that there are important behavioral deviations from the standard model that are detrimental to the efficiency of bargaining under incomplete information.     

Dynamic bilateral bargaining under private information with a sequence of potential buyers

A seller owning a single, indivisible asset faces the random arrival of privately informed buyers, with whom he can bargain sequentially. Our key result is that despite the arrival of alternative buyers the Coase conjecture continues to hold under stationary strategies if the distribution of buyer valuations has convex support: Negotiations end almost immediately and the asset is sold almost at the minimum of the seller's own reservation value and the lowest possible valuation of a buyer. We also show existence of multiple stationary equilibria, though, in the special case where the support of buyers' valuations exhibits a sufficiently large “interior gap”. Taken together, our findings thus also point to a potential pitfall when analyzing only two-type distributions in more applied work.     

Sequential bargaining,external effects of agreement,and public intervention

In some bargaining situations, agreement has implications for agents beyond the parties involved, and if so, delays in reaching an agreement or failing to reach an agreement, when this would be profitable, may imply significant welfare losses. The question raised in this paper is whether the intervention of a government, who has a positive valuation of agreement and therefore offers a subsidy, will reduce such delays and inabilities to reach agreement? Based on a perfect Bayesian equilibrium in a sequential bargaining game with intervention, we show that in equilibrium intervention always reduces the ex ante equilibrium inefficiency and conditionally reduces expected delays in trade. However, for intervention in the form of a subsidy to take place, the aggregate of the seller’s reservation price and the externalities must be (almost) as high as the buyer’s upper valuation limit.     

Asymmetric Nash equilibrium in emission rights auctions

This paper studies the problems of emission rights auctions, and presents a uniform price auction mechanism based on three assumptions, i.e., all buyers are asymmetric, every buyer submits a nonincreasing continuous demand function, and every buyer's valuation to per unit of the emission rights is common value information. It focuses on solving the asymmetric Nash equilibrium for this auction mechanism. It concludes that there exist multiple Nash equilibria in our auction mechanism, but the arbitrary low equilibrium prices cannot emerge. We also give several suggestions on how to induce the auction to a desired ideal equilibrium state in mechanism design of emission rights auctions.     

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.