MEETINGS AND MECHANISMS

This article shows how meeting frictions affect equilibrium trading mechanisms and allocations in an environment where identical sellers post mechanisms to compete for buyers with ex ante heterogeneous private valuations. Multiple submarkets can emerge, each consisting of all sellers posting a particular mechanism and the buyers who visit those sellers. Under mild conditions, high-valuation buyers are all located in the same submarket, and low valuation buyers can be in: (i) the same submarket, (ii) a different submarket, and (iii) a mixture of (i) and (ii). The decentralized equilibrium is efficient when sellers can post auctions with reserve prices or entry fees.     

High profit equilibria in directed search models

We consider a model of directed search where the sellers are allowed to post mechanisms with entry fees. Regardless of the number of buyers and sellers, the sellers are able to extract all the surplus of the buyers by introducing entry fees and making price schedules positively sloped in the number of buyers arriving to their shops. This is in contrast to results that are achieved for large markets under the assumption that sellers cannot influence the utility of any particular buyer (market utility assumption), in which case buyers obtain strictly positive rents. If there is a bound on the prices or on the entry fees that can be charged, then the equilibrium with full rent extraction does not exist any more, and the market utility assumption is restored for large markets.     

COMPETITIVE PRICING AND EFFICIENCY IN SEARCH EQUILIBRIUM*

We consolidate and generalize some results on price determination and efficiency in search equilibrium. Extending models by Rubinstein and Wolinsky and by Gale, heterogeneous buyers and sellers meet according to a general matching technology and prices are determined by a general bargaining condition. When the discount rate r and search costs converge to 0, we show that prices in all exchanges are the same and equal the competitive, market clearing, price. Given positive search costs, efficiency obtains iff bargaining satisfies Hosios' condition and r=0. When prices are set by third‐party market makers, however, we show that search equilibrium is necessarily efficient.     

Does risk aversion explain behavior in a lemon market?

Siegenthaler proposes an ingenious solution to the lemon market adverse selection problem. He incorporates ‘‘cheap talk’’ in which sellers send out costless and nonbinding messages informing potential buyers of the quality of their goods; these messages could be true or false. This segments the market into several submarkets. Potential buyers need to decide which submarket to enter and what price to bid for the goods. Sellers then decide whether to accept the bid or not. He experimentally tests his model and finds that the comparative static results align with his theory, although the data do not exactly fit the model. Indeed, he does not fit the model to the data. His theory assumes risk-neutral decision-makers (DMs). Two reasons why the fit is not perfect may be that the DMs are not risk neutral and not perfectly rational. In this note, we report the results of fitting an asymmetric risk averse quantal response equilibrium (QRE) extension of his model to his data, and we find that the extension fits well. We show that the results are consistent with the market evidence and shed light on future research on lemon markets.     

Surplus Extraction and Competition

A competitive economy is studied in which sellers offer alternative direct mechanisms to buyers who have correlated private information about their valuations. In contrast to the monopoly case where sellers charge entry fees and extract all buyers' surplus, it is shown that in the unique symmetric equilibrium with competition, sellers hold second price auctions with reserve prices set equal to their cost. Most important, it is a best reply for sellers not to charge entry fees of the kind normally used to extract surplus, even though it is feasible for them to do so.     

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).     

Convergence to perfect competition of a dynamic matching and bargaining market with two-sided incomplete information and exogenous exit rate

Consider a decentralized, dynamic market with an infinite horizon and incomplete information in which buyers and sellers' values for the traded good are private and independently drawn. Time is discrete, each period has length δ, and each unit of time a large number of new buyers and sellers enter the market. Within a period each buyer is matched with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, the seller and winning buyer exit with their realized utility. Traders who fail to trade either continue in the market to be rematched or exit at an exogenous rate. We show that in all steady state, perfect Bayesian equilibria, as δ approaches zero, equilibrium prices converge to the Walrasian price and realized allocations converge to the competitive allocation.     

A search model of centralized and decentralized trade

This paper presents a search model of centralized and decentralized trade. In a centralized market, trades are intermediated by market makers at publicly posted bid–ask prices. In a decentralized market, traders search counterparties. Prices are negotiated and transactions are conducted in private meetings among traders. Traders can choose which market to enter. The determinants of bid–ask spreads and liquidity are analyzed. The welfare consequence of the market fragmentation is also analyzed. It is shown that compared to the competitive market-making, monopolistic market-making may improve social welfare.     

FOR‐PROFIT SEARCH PLATFORMS

We consider optimal pricing by a profit‐maximizing platform running a dynamic search and matching market. Buyers and sellers enter in cohorts over time, meet, and bargain under private information. The optimal centralized mechanism, which involves posting a bid–ask spread, can be decentralized through participation fees charged by the intermediary to both sides. The sum of buyers' and sellers' fees equals the sum of inverse hazard rates of the marginal types, and their ratio equals the ratio of buyers' and sellers' bargaining weights. We also show that a monopolistic intermediary in a search market may be welfare enhancing.     

Comparative statics in a simple class of strategic market games

This paper investigates the effects of entry in two-sided markets where buyers and sellers act strategically. Applying new tools from supermodular optimization/games, sufficient conditions for different comparative statics results are obtained. While normality of one good is sufficient for the equilibrium price to be increasing in the number of buyers, normality of both goods is required for equilibrium bids and sellers' equilibrium utilities to be increasing in the number of buyers. When the economy is replicated, normality of both goods and gross substitutes guarantee that the equilibrium of the strategic market game converges monotonically (in quantities) to the competitive equilibrium. Simple counter-examples are provided to settle other potential conjectures of interest.     

Equilibrium in Auction and Bargaining Markets When Agents Can Wait and Search

The paper studies two market structures and two modes of trade. The agents, buyers and sellers, can choose whether to stay or search. The meetings take place randomly, and trades are consummated by auction or by bargaining. There are altogether four possible markets but in equilibrium at most two markets are active simultaneously. There is almost always a unique evolutionary stable equilibrium which consists of an auction market when the numbers of buyers and sellers differ greatly, and two simultaneous auction markets when the numbers are relatively close.     

Advertising,consumer search costs and prices in a professional service market

Since stigler's (1961) seminal article on the economics of information it has been argued that producer advertising is a substitute for consumer search. This view of advertising has been implicit in recent liberalization of restrictions on advertising by professionals (e.g. lawyers, doctors, accountants, etc.). Using th e model of the price discriminating professional developed by Masson and Wu (1974) the impact of solicitor advertising on the level of conveyancing fees charged by a sample of Scottish Solicitors is estimated. The analysis distinguishes between different forms of advertising. The advertising-of-information theory cannot be rejected for some forms of advertising in one (property value) submarket but it can be in the other (higher property value) submarket. The evidence here rejects (i) the view that all advertising is a substitude for consumer search and (ii) the view that actions to reduce search costs (such as advertising) necessarily reduce price discrimination.     

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.     

Insurance market games: Scale effects and public policy

We propose a game-theoretic model to study various effects of scale in an insurance market. After reviewing a simple static model of insurer solvency (in which all customers have inelastic demand), we present a one-period game in which both the buyers and sellers of insurance make strategic bids to determine market price and quantity. For the case in which both buyers and sellers are characterized by constant absolute risk aversion, we show that a unique market equilibrium exists under certain conditions. For the special case of risk-neutral insurers, we then consider how both the price and quantity of insurance, as well as other quantities of interest to public-policy decision makers, are affected by the number of insurance firms, the number of customers, and the total amount of capital provided by investors.     

Platform intermediation in a market for differentiated products

We study a two-sided market where a platform attracts firms selling differentiated products and buyers interested in those products. In the subgame perfect equilibrium of the game, the platform fully internalises the network externalities present in the market and firms and consumers all participate in the platform with probability one. The monopolist intermediary extracts all the economic rents generated in the market, except when firms and consumers can trade outside the platform, in which case consumers obtain a rent that corresponds to the utility they would get if they did trade outside the platform. The market allocation is constraint-efficient in the sense that the monopoly platform does not introduce distortions over and above those arising from the market power of the differentiated product sellers. An increase in the number of retailers increases the amount of variety in the platform but at the same time increases competition. As a result, the platform lowers the firm fees and raises the consumer charges. In contrast, an increase in the extent of product differentiation raises the value of the platform for the consumers but weakens competition. In this case, the platform raises both the charge to the consumers and the fee for the firms.     

A note on Peters and Severinov, “Competition among sellers who offer auctions instead of prices”

We consider a market in which sellers compete for buyers by advertising reserve prices for second-price auctions. Applying the limit equilibrium concept developed in Peters and Severinov (1997) [1], we show that the competitive matching equilibrium is characterized by a reserve price of zero. This corrects a result in Peters and Severinov (1997) [1].     

Bertrand price competition with differentiated commodities

This develops a general equilibrium, differentiated commodity version of Bertrand price competition. We study two, related market games in which buyers as well as sellers announce both quantities and prices. In the first game, buyers' strategies are artificially restricted. The Nash allocations of this game will be nearly competitive, provided that the commodities supplied by sellers are sufficiently similar. In the second game, the restriction on buyers' strategies is relaxed and a stronger solution criterion, called local perfection, is invoked. The locally perfect equilibria of the unrestricted game coincide the Nash equilibria of the restricted game.     

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.     

STRATEGIC ADVERTISING AND DIRECTED SEARCH

Imperfect observability and costly informative advertising are introduced into a standard directed search framework. Capacity‐constrained sellers send costly advertisements to direct buyers' uncoordinated search by specifying their location and terms of trade. We show that the equilibrium advertising intensity is nonmonotonic in the buyer–seller ratio. In addition, we also find that price posting dominates auctions since both mechanisms yield the same expected revenue, but the latter results in higher advertising expense. Finally, we find a positive comovement between market transparency and price for low market tightness when the measure of informed buyers is endogenous.     

Sequential auctions with randomly arriving buyers

We analyze a dynamic market in which buyers compete in a sequence of private-value auctions for differentiated goods. New buyers and new objects may arrive at random times. Since objects are imperfect substitutes, buyers? values are not persistent. Instead, each buyer?s private value for a new object is a new independent draw from the same distribution.We consider the use of second-price auctions for selling these objects, and show that there exists a unique symmetric Markov equilibrium in this market. In equilibrium, buyers shade their bids down by their continuation value, which is the (endogenous) option value of participating in future auctions. We characterize this option value and show that it depends not only on the number of buyers currently present on the market and the distribution of their values, but also on anticipated market dynamics.