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.     

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.     

Equilibrium Partner Switching in a Bargaining Model With Asymmetric Information

We study a model in which the seller of an indivisible object faces two potential buyers and makes an offer to either of them in each period. We find that the seller's ability to extract surplus from them depends crucially on the value of the cost of switching from one buyer to the next. If the seller is pessimistic about the buyers' valuations and there is a switching cost, however small, then the market is a natural bilateral monopoly; the second buyer is never called on. If the switching cost is zero, or if the seller is optimistic, then switching, and possibly recall of the original buyer, may occur.     

An optimal auction with correlated values and risk aversion

We consider an auction setting where the buyers are risk averse with correlated private valuations (CARA preferences, binary types), and characterize the optimal mechanism for a risk-neutral seller. We show that the optimal auction extracts all buyer surplus whenever the correlation is sufficiently strong (greater than 1/3 in absolute value), no matter how risk averse the buyers are. In contrast, we note that a sufficiently risk-averse seller would not use a full rent extracting mechanism for any positive correlation of the valuations even if the buyers were risk neutral.     

A solution to the hold-up problem involving gradual investment

We consider a setting in which the buyer's ability to hold up a seller's investment is so severe that there is no investment in equilibrium of the static game typically analyzed. We show that there exists an equilibrium of a related dynamic game generating positive investment. The seller makes a sequence of gradually smaller investments, each repaid by the buyer under the threat of losing further seller investment. As modeled frictions converge to zero, the equilibrium outcome converges to the first best. We draw connections between our work and the growing literature on gradualism in public good contribution games and bargaining games.     

Buyer and/or seller power? An application to the Brazilian milk market

Despite its importance, the co-existence of buyer and seller power has been largely neglected in the empirical literature. In this article, we develop a stochastic frontier model to measure channel market power as deviations from a perfectly competitive frontier and decompose it into buyer and seller power. We provide an empirical illustration using milk data from five Brazilian states and find that channel market power ranges between 4% and 12% of the wholesale price, but that 75% of the market power is accounted for by retail buyer power. The methodology proposed can provide a rapid assessment of the degree of market power in other markets and a method for separating out buyer and seller power in the market channel.     

The power of randomness in Bayesian optimal mechanism design

We investigate the power of randomness in the context of a fundamental Bayesian optimal mechanism design problem—a single seller aims to maximize expected revenue by allocating multiple kinds of resources to “unit-demand” agents with preferences drawn from a known distribution. When the agents' preferences are single-dimensional Myerson's seminal work (1981) shows that randomness offers no benefit—the optimal mechanism is always deterministic. In the multi-dimensional case, when agents' preferences are arbitrarily correlated, Briest et al. (2010) showed that the gap between the expected revenue obtained by an optimal randomized mechanism and an optimal deterministic mechanism can be unbounded even when a single agent is offered only 4 services. We show that when the agents' values involve no correlation or a specific kind of positive correlation, the benefit of randomness is only a small constant factor.     

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.     

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.     

Time-on-the-Market as a Sign of Quality

The inferences a prospective home buyer can make about the quality of a house from the amount of time it spends on the market and the seller"s optimal strategy in light of these inferences are investigated. Depending upon the information structure, the seller may have an incentive to post an inordinately high initial price (in order to "dampen" the signal transmitted to future prospective buyers) or an inordinately low initial price (in order to make an early sale and avoid consumer "herding"). It is shown that the sellers of high-quality homes do best when inspection outcomes are publicly recorded and do worst when inspection outcomes are not public and the price history is not observable. Costly inspections create more adverse selection but deter consumer herding.     

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.     

Sequentially Optimal Auctions

In auctions where a seller can post a reserve price but if the object fails to sell cannot commit never to attempt to resell it, revenue equivalence between repeated first price and second price auctions without commitment results. When the time between auctions goes to zero, seller expected revenues converge to those of a static auction with no reserve price. With many bidders, the seller equilibrium reserve price approaches the reserve price in an optimal static auction. An auction in which the simple equilibrium reserve price policy of the seller mirrors a policy commonly used by many auctioneers is computed.Journal of Economic LiteratureClassification Numbers: C78, D44, D82.     

Auctions with private uncertainty and resale opportunities

When an auction is followed by an opportunity for resale, bidder valuations are endogenously determined, reflecting anticipated profit from buying/selling in the resale market. These valuations vary with the resale market structure, can differ across auction types, and may be lower or higher than if resale were impossible. Although resale introduces a common value element to the model, revenue equivalence can hold; when it fails, this is due not to affiliation but to differences in information conveyed to the secondary market. Information linkages between markets can also lead to signaling and, in some cases, preclude separation in the auction.     

The Shill Bidding Effect versus the Linkage Principle

The analysis of second price auctions with externalities is utterly modified if the seller is unable to commit not to participate in the mechanism. For the General Symmetric Model introduced by Milgrom and Weber [P. Milgrom, R. Weber, A theory of auctions and competitive bidding, Econometrica 50 (1982) 1089-1122] we characterize the full set of separating equilibria that are symmetric among buyers and with a strategic seller being able to bid in the same way as any buyer through a so-called shill bidding activity. The revenue ranking between first and second price auctions is different from the one arising in Milgrom and Weber: the benefits from the highlighted ‘Linkage Principle’ are counterbalanced by the ‘Shill Bidding Effect.’     

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.     

Sequential bargaining in a market with one seller and two different buyers

A matching and bargaining model in a market with one seller and two buyers, differing only in their reservation price, is analyzed. No subgame perfect equilibrium exists for stationary strategies. We demonstrate the existence of inefficient equilibria in which the low buyer receives the good with large probability, even as friction becomes negligible. We investigate the relationship between the use of Nash and sequential bargaining. Nash bargaining seems applicable only when the sequential approach yields a unique stationary strategy subgame perfect equilibrium.     

A Walrasian Rubinstein and Wolinsky model

We provide a full dynamic analysis of a continuous-time variant of Rubinstein and Wolinsky (1985) matching and bargaining model with unbalanced flows of buyers and sellers. The focus is on the price limit as the frictions of search are removed. It is found that a necessary and sufficient condition for the limit price to be Walrasian at all times is the alignment of the initial buyer and seller stocks with the flows.     

Exclusive Versus Non-exclusive Dealing in Auctions with Resale

We consider a seller who can either sell exclusively through resellers, or allow potential consumers to purchase directly from him. The consumers’ willingness to pay is private information. All transactions are in the form of second-price sealed bid auctions. We show that, if the resellers can gain access to a substantially bigger portion of the market than the seller himself, the seller obtains a higher revenue by dealing exclusively through them, i.e., by committing to not sell to any consumer. The result is due to a “winner’s curse” effect: the resellers win only if the consumers that they compete against submit lower bids, i.e., if part of their customer base has low valuations. This depresses the resellers’ willingness to pay relative to what they would be willing to pay under an exclusive resale contract. Our results do not depend on the presence of transaction costs: exclusive dealing yields strictly higher revenue even when the resellers can market the item at zero cost. We would like to thank Richard Engelbrecht-Wiggans, Michael Rothkopf and seminar participants at Iowa State University, the Midwest Mathematical Economics meetings, the Milken Institute, Rutgers University, SUNY at Stony Brook Summer Workshop on Game Theory, for helpful comments and suggestions.     

Is There a Hold‐up Problem?

We report on a hold‐up experiment in which unilateral investment is followed by bilateral bargaining according to Nash’s demand game. Without communication, investment is low and coordination is poor. Unilateral communication facilitates coordination, but not perfectly. Successful coordination predominantly entails “fair” outcomes. Perhaps surprisingly, sellers (investors) do at least as well under buyer communication as under seller communication.     

Bargaining, search, and outside options

This paper studies a two-sided incomplete information bargaining model between a seller and a buyer. The buyer has an outside option, which is modeled as a sequential search process during which he can choose to return to bargaining at any time. Two cases are considered: In Regime I, both agents have symmetric information about the search parameters. We find that, in contrast to bargaining with complete information, the option to return to bargaining is not redundant in equilibrium. However, the no-delay result still holds. In Regime II, where agents have asymmetric information about the outside option, delay is possible. The solution characterizes the parameters for renegotiation and those for search with no return to the bargaining table.