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.     

Income distribution, efficiency and rationing

This paper studies the impacts of income distribution on the efficiency of trade mechanism and rationing of agents who are priced out of trade in a dynamic search model with two-sided asymmetric information. Buyers and sellers have asymmetric information about valuations and incomes respectively. In such a frictional environment, the effects of several variants of changes in income distribution on efficiency of trading mechanism and the population of rationed buyers and sellers are elaborated.     

Optimal collective contract without peer information or peer monitoring

If entrepreneurs have private information about factors influencing the outcome of an investment, individual lending is inefficient. The literature typically offers solutions based on the assumption of full peer information to solve adverse selection problems and peer monitoring to solve moral hazard problems. In contrast, I show that it is possible to construct a simple budget-balanced mechanism that implements the efficient outcome even if each borrower knows only own type and effort, and has neither privileged knowledge about others nor monitoring ability. The mechanism satisfies participation incentives for all types, and is immune to the Rothschild–Stiglitz cream skimming problem despite using transfers from better types to worse types. The presence of some local information implies that the mechanism cannot be successfully used by formal lenders. Thus a local credit institution can emerge as an optimal response to the informational environment even without peer information or monitoring. Finally, I investigate the role of monitoring in this setting and show how costly monitoring can increase the scope of the mechanism.     

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.     

Price discrimination via information provision

We study price discrimination where different prices are offered as a bundle with different levels of information about a product. The seller’s price discrimination induces high valuation buyers to purchase a good without information and low valuation buyers to purchase with information. Our analysis highlights several interesting results about price discrimination: (i) the seller’s choice of information provision is the combination of full information and no information, (ii) products can be cheaper without information provision than with information provision, (iii) as a result of price discrimination, prices can be more dispersed as buyers’ valuations become largely similar, and (iv) the high valuation buyers purchase a damaged good and may earn negative surplus. Furthermore, we investigate under which circumstances price discrimination is more profitable than uniform pricing. We show that a decline in transportation costs which facilitate price discrimination can be welfare reducing.     

Nonlinear incentive provision in Walrasian markets: a Cournot convergence approach

The paper studies insurance with moral hazard in a system of contingent-claims markets. Insurance buyers are modelled as Cournot monopolists or oligopolists. The other agents condition their expectations on market prices, as in models of rational-expectations equilibrium with asymmetric information. Thereby they correctly anticipate accident probabilities corresponding to effort incentives induced by insurance buyers’ net trades. When there are many agents to share the insurance buyers’ risks, Cournot equilibrium outcomes are close to being second-best. In contrast, if insurance buyers are price takers, equilibria fail to exist or are bounded away from being second-best.     

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.     

WHO SEARCHES?*

We consider a directed search model with buyers and sellers and determine whether buyers look for sellers or vice versa. The buyers and sellers can choose to search or wait; what they do in equilibrium depends on the relative size of the two populations and the price formation mechanism. We study bargaining and auctions and find that when one population is much larger than the other the former searches and the latter waits. Under auction with roughly equal populations some buyers and sellers search and some wait. Our results challenge the practice of postulating who searches and who waits.     

Trading mechanism selection with directed search when buyers are risk averse

We endogenize the trading mechanism selection in a model of directed search with risk averse buyers and show that the unique symmetric equilibrium entails all sellers using fixed price trading. Mechanisms that prescribe the sale price as a function of the realized demand (auctions, bargaining, discount pricing, etc.) expose buyers to the “price risk”, the uncertainty of not knowing how much to pay in advance. Fixed price trading eliminates the price risk, which is why risk averse customers accept paying more to shop at such stores.     

The role of optimal threats in auction design

This paper studies revenue-maximizing auctions when buyers' outside options depend on their private information and are endogenously chosen by the seller. We show that the revenue-maximizing assignment of the object can depend crucially on the outside options that the seller can choose as threats. Depending on the shape of outside options, sometimes an optimal mechanism allocates the object in an ex-post efficient way, and, other times, buyers obtain the object more often than is efficient.     

The rate of convergence to perfect competition of matching and bargaining mechanisms

We study the steady state of a market with incoming cohorts of buyers and sellers who are matched pairwise and bargain under private information. A friction parameter is τ, the length of the time period until the next meeting. We provide a necessary and sufficient condition for the convergence of mechanism outcomes to perfect competition at the linear rate in τ, which is shown to be the fastest possible among all bargaining mechanisms. The condition requires that buyers and sellers always retain some bargaining power. The bargaining mechanisms that satisfy this condition are called nonvanishing bargaining power (NBP) mechanisms. Simple random proposer take-it-or-leave-it protocols are NBP, while k-double auctions (k-DA) are not. We find that k-DAs have equilibria that converge to perfect competition at a linear rate, converge at a slower rate or even do not converge at all.     

Remain silent and ye shall suffer: seller exploitation of reticent buyers in an experimental reputation system

By providing incentives for sellers to act in a trustworthy manner, reputation mechanisms can mitigate moral-hazard problems when particular buyers and sellers interact infrequently. However, these mechanisms rely on buyers sharing their private information about sellers, and thus may suffer from too little feedback when provision is costly. We experimentally compare a standard feedback mechanism to one in which sellers can inspect a buyer’s feedback-provision history, thus providing incentives to share private information even when costly. We find fairly high trust and trustworthiness in all markets, with buyers providing costly feedback, especially negative, sufficient to induce trustworthiness. However, feedback-provision histories did not improve outcomes, and at least weakly decreased trustworthiness with experienced participants, as this information enabled sellers to discriminate and ship less frequently to buyers lacking a reputation for information sharing.     

Ascending price Vickrey auctions for general valuations

Ascending price auctions involving a single price path and buyers paying their final bid price cannot achieve the Vickrey-Clarke-Groves (VCG) outcome in the combinatorial auctions setting. Using a notion called universal competitive equilibrium prices, shown to be necessary and sufficient to achieve the VCG outcome using ascending price auctions, we define a class of ascending price auctions in which buyers bid on a single price path. Truthful bidding by buyers is an ex post Nash equilibrium in such auctions. By giving discounts to buyers from the final price, the VCG outcome is achieved for general valuations.     

Optimal mechanism design with resale via bargaining

In this paper, we examine the optimal mechanism design of selling an indivisible object to one regular buyer and one publicly known buyer, where inter-buyer resale cannot be prohibited. The resale market is modeled as a stochastic ultimatum bargaining game between the two buyers. We fully characterize an optimal mechanism under general conditions. Surprisingly, in this optimal mechanism, the seller never allocates the object to the regular buyer regardless of his bargaining power in the resale market. The seller sells only to the publicly known buyer, and reveals no additional information to the resale market. The possibility of resale causes the seller to sometimes hold back the object, which under our setup is never optimal if resale is prohibited. We find that the seller?s revenue is increasing in the publicly known buyer?s bargaining power in the resale market. When the publicly known buyer has full bargaining power, Myerson?s optimal revenue is achieved; when the publicly known buyer has no bargaining power, a conditionally efficient mechanism prevails.     

Dynamic sorting in durable goods markets with buyer heterogeneity

In a competitive dynamic durable good market where sellers have private information about quality, I identify certain inefficiencies that arise due to heterogeneity in buyers' valuations. Even if the market induces dynamic sorting among sellers and all goods are eventually traded, inefficiency can arise because high valuation buyers buy early when low‐quality goods are sold, while high‐quality goods are allocated to low valuation buyers that buy later. This misallocation adds to the inefficiency caused by delay in trading. Under certain circumstances, high‐quality goods may never be traded as in a static market.     

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].     

Estimation of hedonic price functions with incomplete information

Existence of persistent price dispersion suggests that some buyers find lower prices through search and information acquisition, while some sellers charge higher prices by gathering information on potential buyers. If buyers are not fully informed of the lowest price available in the market they end up paying a price higher than if they had full information. Similarly, if sellers are not fully informed about the highest price they could charge, they too suffer by receiving a price lower than had they had full information. This paper develops a hedonic price model that incorporates the effects of incomplete information on both sides of the market and obtains estimates of the discrepancies between market prices and buyers’ maximum willingness to pay and sellers’ minimum willingness to accept. Correlates of such price discrepancies are also explored. We apply the technique to a data set constructed from the American Housing Survey, and find that incomplete information has had a significant impact on housing prices.     

Comment on “Correlated information, mechanism design and informational rents” [J. Econ. Theory 123 (2) (2005) 210–217]

We amend an error in [S. Parreiras, Correlated information, mechanism design and informational rents, J. Econ. Theory 123 (2005) 210–217]. Consequently, it is in general not possible to reinterpret a mechanism design model that violates the spanning condition of Crémer and McLean [J. Crémer, R. McLean, Full extraction of the surplus in bayesian, dominant strategy auctions, Econometrica 56 (1988) 1247–1258] as one in which agents hold private information about the informativeness of their signals about other agents? types. Instead, such an interpretation is warranted only when the weights used to span an agent?s set of beliefs stand in a singular relation with the prior type distribution that is known as an alternative characterization of Blackwell dominance.     

Disapproval aversion or inflated inequity acceptance? The impact of expressing emotions in ultimatum bargaining

Past experimental research has shown that when rating systems are available, buyers are more generous in accepting unfair offers in ultimatum bargaining. However, it also suggests that, under these conditions, sellers behave more fairly to avoid receiving negative feedback. This paper experimentally investigates which effect is stronger with the use of a rating system: buyers’ inflated inequity acceptance or sellers’ disapproval aversion. We explore this question by varying the information condition on the buyers’ side. Our experiment shows that in a setup where the size of the pie is common knowledge for both buyers and sellers, when a rating system is present, the sellers exhibit disapproval aversion but the buyers do not display greater acceptance of inequity. By contrast, when only sellers are aware of the size of the pie, sellers behave aggressively to exploit buyers and their behavior does not change in the presence of a rating system; however, buyers display greater acceptance of inequity when a rating system is present. We discuss how these results can be explained by a theoretical model that includes sellers’ social disapproval aversion and buyers’ disappointment aversion in addition to the players’ inequality aversion.     

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).