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.     

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.     

Word-Of-Mouth Communication and Community Enforcement

We study a repeated game where a seller, who has a short-term incentive to supply low quality, is periodically matched with a randomly selected buyer. Buyers observe only the outcomes of their neighbors' games and may receive signals from them. When the buyer population is large, the seller may sell high quality even when each buyer observes her action in any given period with an arbitrarily small probability. When networking among buyers is costly, low quality is always supplied with a positive probability. For this case, we characterize an equilibrium where the seller randomizes between high and low quality.     

A choice of auction format in seller cheating: a signaling game analysis

In this paper, we examine which auction format, first-price or second-price, a seller will choose when he can profitably cheat in a second price auction by observing all bids by possible buyers and submitting a shill bid as pretending to be a buyer. We model this choice of auction format in seller cheating as a signaling game in which the buyers may regard the selection of a second price auction by the seller as a signal that he is a shill bidder. By introducing trembling-hand perfectness as a refinement of signaling equilibrium, we find two possible strictly perfect signaling equilibria. One is a separating equilibrium in which a noncheating honest seller selects a first price auction and a cheating seller does a second price auction. In another pooling equilibrium, however, both cheating and non-cheating sellers select a second price auction. The conclusion that a seller chooses a second price auction even if he cannot cheat is in contrast to the previous literature, which focused on the case of independent values. We thank an anonymous referee for useful comments that have improved the paper. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B) 15310023 and (C) 18530139.     

About market structure

I study an economy where sellers choose locations, and buyers choose which location to visit. All sellers in one location correspond to the Walrasian market while each seller in a separate location corresponds to the standard random matching model. Trades are consummated in auctions, and it turns out that the Walrasian market is not an equilibrium market structure. Rather, the sellers choose to distribute themselves in several locations endogenously creating the imperfectness of markets. I determine the number of sellers per location in equilibrium as a function of the ratio of buyers to sellers.     

Price formation in a matching market with targeted offers

We model a market where the surpluses from seller–buyer matches are heterogeneous but common knowledge. Price setting is synchronous with search: buyers simultaneously make one personalized offer each to the seller of their choice. With impatient players efficient coordination is not possible, and both temporary and permanent mismatches occur. Nonetheless, for patient players efficient matching (with monopsony wages) is an equilibrium. The setting is inspired by a labor market for highly skilled workers, such as the academic job market, but it can be easily adapted to, for example, the housing market or Internet advertising auctions.     

Pricing and signaling with frictions

We study a market where each seller chooses the quality and price of goods and the number of selling sites. Observing sellers? choices of prices and sites, but not quality, buyers choose which site to visit. A seller?s choices of prices can direct buyers? search and signal quality. A unique equilibrium exists and is separating. When the quality differential is large, the equilibrium implements the efficient allocation with public information. Otherwise, the quality of goods and/or the number of sites created is inefficient, due to a conflict between the search-directing and signaling roles of prices.     

Trading networks with price-setting agents

In a wide range of markets, individual buyers and sellers trade through intermediaries, who determine prices via strategic considerations. Typically, not all buyers and sellers have access to the same intermediaries, and they trade at correspondingly different prices that reflect their relative amounts of power in the market. We model this phenomenon using a game in which buyers, sellers, and traders engage in trade on a graph that represents the access each buyer and seller has to the traders. We show that the resulting game always has a subgame perfect Nash equilibrium, and that all equilibria lead to an efficient allocation of goods. Finally, we analyze trader profits in terms of the graph structure — roughly, a trader can command a positive profit if and only if it has an “essential” connection in the network, thus providing a graph-theoretic basis for quantifying the amount of competition among traders.     

Bargaining and Search with Incomplete Information about Outside Options

This paper considers a model of bargaining in which the seller makes offers and the buyer can search (at a cost) for an outside option; the outside option cannot be credibly communicated, and the seller's offer is recallable by the buyer for one period. There are essentially two equilibrium regimes. For sufficiently high search cost, the game ends immediately; otherwise the search occurs in equilibrium. Compared to the case where the buyer can communicate his outside option, the seller is worse off, and the game results in search for a smaller set of values of the search cost, i.e., less equilibrium delay.C72.     

Dynamic market for lemons with endogenous quality choice by the seller

We analyze a dynamic market for lemons in which the quality of the good is endogenously determined by the seller. Potential buyers sequentially submit offers to one seller. The seller can make an investment that determines the quality of the item at the beginning of the game, which is unobservable to buyers. At the interim stage of the game, the information and payoff structures are the same as in the market for lemons. Our main result is that the possibility of trade does not create any efficiency gain if (i) the common discounting is low, and (ii) the static incentive constraints preclude the mutually agreeable ex-ante contract under which the trade happens with probability one. Our result does not depend on whether the offers by buyers are private or public.     

Seller competition by mechanism design

This paper analyzes a market game in which sellers offer trading mechanisms to buyers and buyers decide which seller to go to depending on the trading mechanisms offered. In a (subgame perfect) equilibrium of this market, sellers hold auctions with an efficient reserve price but charge an entry fee. The entry fee depends on the number of buyers and sellers, the distribution of buyer valuations, and the buyer cost of entering the market. As the size of the market increases, the entry fee decreases and converges to zero in the limit. We study how the surplus of buyers and sellers depends on the number of agents on each side of the market in this decentralized trading environment.     

Two-part tariffs set by a risk-averse monopolist

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

How private is private information? The ability to spot deception in an economic game

We provide experimental evidence on the ability to detect deceit in a buyer–seller game with asymmetric information. Sellers have private information about the value of a good and sometimes have incentives to mislead buyers. We examine if buyers can spot deception in face-to-face encounters. We vary whether buyers can interrogate the seller and the contextual richness. The buyers’ prediction accuracy is above chance, and is substantial for confident buyers. There is no evidence that the option to interrogate is important and only weak support that contextual richness matters. These results show that the information asymmetry is partly eliminated by people’s ability to spot deception.     

Auction and the informed seller problem

A seller possessing private information about the quality of a good attempts to sell it through a second-price auction with announced reserve price. The choice of a reserve price transmits information to the buyers. We characterize the equilibria with monotone beliefs of the resulting signaling game and show that they lead to a reduced probability of selling the good compared to the symmetric information situation. We compare the unique separating equilibrium of this signaling game to the equilibrium of a screening game in which an uninformed monopoly broker chooses the trading mechanism. We show that the ex ante expected probability of trade may be larger with a monopoly broker, as well as the ex ante total expected surplus.     

Strategic Certification and Provision of Quality

We study the effect of the presence of a certification intermediary in an environment where information asymmetries are particularly severe. The intermediary improves the information that buyers have about quality. This in turn increases the incentives that the seller has to provide high-quality goods. Efficiency is increased by the presence of the intermediary, but quality is underprovided in equilibrium relative to full information. The intermediary can implement the optimal policy in many ways. The amount of information revealed ranges from full disclosure to partial, noisy disclosure.     

Equilibrium reserve prices in sequential ascending auctions

We study a model where bidders have perfectly correlated valuations for two goods sold sequentially in two ascending-price auctions. The seller sets a reserve price before the beginning of each auction. Despite the lack of commitment by the seller, we characterize an equilibrium and study its properties. Strategic non-disclosure of information takes the form of non-participation in the early auction by low-valuation bidders, while high-valuation bidders bid up to their true valuations. Some buyers who would profitably buy at the reserve price refrain from participating in order to decrease the second-auction reserve price.     

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.     

Buyer behavior under the Best Offer mechanism: A theoretical model and empirical evidence from eBay Motors

We use data from eBay Best Offer listings to analyze haggling over prices in transactions with one seller and a series of potential buyers for a limited-supply product. We characterize this transaction mechanism as a sequential-move game to investigate buyer behavior. Our model suggests that a buyer's offer price increases in relations to the number of buyers who have previously made an offer on the item and the Buy-It-Now price chosen by the seller. On the other hand, the offer price decreases for items which have been listed on eBay for a longer period of time. We empirically test our theoretical predictions using data on the sales of Toyota Camry cars on eBay Motors. The empirical evidence is consistent with our model.     

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.     

Competing auctions with endogenous quantities

Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593-1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].