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.     

Prices for cash and cash for prices? Theory and evidence on convenient pricing

A transaction between a seller and a buyer incurs a payment cost. The payment cost is borne by the seller, depending on the payment instrument the buyer chooses, cash or card. Card payment is more costly than cash payment, so the seller prefers that the buyer pays cash. In this article, we study the strategy of the seller setting a convenient price, which simplifies transactions and pushes the buyer to pay cash. The theoretical analysis, which models both the seller and the buyer in a game setting, derives two propositions: (1) the seller is more likely to set a more convenient price and (2) the buyer is more likely to pay cash a more convenient price. The empirical analysis supports both propositions. Thus, sellers adopt a convenience pricing strategy – prices for cash – and this strategy pushes buyers to pay cash – cash for prices.     

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.     

Contract enforcement in sellers' markets

I present an infinitely repeated game model where a monopolist seller has a contractual obligation with several buyers in each period. If a contract is violated the buyer can collect some compensation and impose a penalty on the seller. There are an infinite number of subgame perfect equilibria in this model, but I employ the concept of e-validated equilibrium to pick out a unique equilibrium outcome for the game where the seller is able to dominate the buyers. This model is clearly applicable to supply problems of Soviet-type economies, but it can explain certain phenomena of Western economies as well.     

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).     

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.     

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.     

Legal Remedies for Breach of the Regulatory “Contract”

We present a model of the regulatory contract that focuses on the mutual investment of buyer and seller and recognizes the cost of contractual renegotiation and the importance of breach remedies when contracts are incomplete. We model renegotiation as a litigation game played before a quasi-judicial administrative court. We find that the standard contractual remedy of expectations damages cannot implement first-best levels of investment for both buyer and seller. If the seller fully recovers its sunk investment upon buyer breach, however, then first-best levels of investment by both buyer and seller can be supported provided litigation costs are small enough.     

DYNAMIC PRICE COMPETITION WITH CAPACITY CONSTRAINTS AND A STRATEGIC BUYER

We analyze a simple dynamic durable good model. Two incumbent sellers and potential entrants choose their capacities at the start of the game. We solve for equilibrium capacity choices and the (necessarily mixed) pricing strategies. In equilibrium, the buyer splits the order with positive probability to preserve competition, making it possible that a high and low price seller both have sales. Sellers command a rent above the value of unmet demand by the other seller. A buyer benefits from either a commitment not to make future purchases or by hiring an agent to always buy from the lowest priced seller.     

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.     

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.     

Bilateral bargaining, unverifiable quality, and options to return

Summary. The paper investigates an alternating-offers bargaining game between a buyer and a seller who face several trading opportunities. These items (goods or services) differ in their non-verifiable quality characteristics which gives rise to a moral hazard problem on the seller's part. For the special case of two goods, we completely characterize the set of subgame-perfect equilibria. We find that the seller always extends an option to return the good, while the buyer may suffer from this warranty. Also, qualitatively different types of equilibrium outcomes occur depending on the parameters of the model: (a) the seller may obtain a larger share of the surplus although the parties ex ante have symmetric bargaining positions, (b) the subgame-perfect equilibrium may entail inefficient trade, and (c) multiple equilibria may exist including equilibria with delay in negotiations. Finally, we analyze a situation where bargaining proceeds after the good was returned which is shown to reestablish uniqueness and efficiency of equilibrium.Received: 23 August 2001, Revised: 3 April 2003, JEL Classification Numbers: C78, L14, L15, D82. Correspondence to: Christoph LülfesmannThis paper has greatly benefitted from discussions with Avner Shaked and Timothy von Zandt. We also wish to thank Wolfgang Leininger, Zvika Neeman, Clemens Puppe, Wolfram Richter, Karl Schlag, Ilya Segal, and seminar participants in Dortmund, Bonn and Berkeley for helpful comments and discussions. Financial support by Deutsche Forschungsgemeinschaft, SFB 303 at the University of Bonn is gratefully acknowledged.     

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.     

Intertemporal pricing in markets with differential information

Summary This paper provides a theory of intertemporal pricing in a small market with differential information about the realizations of a stochastic process which determines demand. We study the sequential equilibria in stationary strategies of the stochastic game between a seller and buyer. The seller has zero cost of producing one unit of a non-durable good in all market periods. The buyer's value for the good is a random variable governed by a simple Markov process. At the beginning of each period the unit's value is determined by nature and is privately revealed to the buyer. The seller posts a single price offer each period, which the buyer either accepts or rejects. Only two types of price paths emerge in equilibrium: either prices are constant, or they have persistent cycles between a low and a high value. In both cases, however, prices are sticky in the sense that changes in price are less frequent than changes in the economy's fundamentals.We thank John Rust and Asher Wolinsky for helpful comments. We also gratefully acknowledge financial support from NSF grant SES 89-09242.     

浅析网上无形市场与传统专业市场的替代性与互补性

网上无形市场和传统专业市场的互替与互补取决于交易主体的理性选择。买卖双方会通过对网上交易的内生交易成本与两种市场交易方式的外生交易成本进行博弈比较来选择最优的流通方式,从而使不同交易制度间呈现出互替与互补状态。网上交易的内生交易成本量则由当该内生交易成本和降低其发生所造成的外生交易成本这两者的总和达到最低时的资源配置量所决定。     

Option to wait in a search model

We consider a standard search model with buyers and sellers. Upon meeting the buyers make a take-it-or-leave-it offer, but the sellers have an option not to trade immediately but wait for more agents to appear. If more buyers come, there is excess demand, and the buyers engage in auction to get the good. Analogously, if more sellers come, the sellers engage in a Bertrand-type pricing game to sell the object. The option to wait restricts the price offer of the buyer; in an equilibrium in which trades are consummated without delay there is a unique price offer for the buyer.JEL Classification: C78, D44, D831     

Strategic Buyers and Privately Observed Prices

A model of finitely repeated price competition between two sellers with differentiated goods and a large buyer is analyzed. The set of pure strategy sequential equilibria is investigated under public and private monitoring. With private monitoring, i.e., when prices are not observable to the competing sellers, all sales are made by the better seller and the set of repeated game equilibrium payoffs coincides with the stage game subgame perfect equilibrium payoffs. This is in sharp contrast to the game with perfect monitoring where the folk theorem obtains. Journal of Economic Literature Classification Numbers: C72, D43.     

Indeterminacy and directed search

The directed search approach assumes each seller posts a fixed price and, ex post, randomly allocates the good should more than one buyer desire the good. This paper assumes sellers can post prices which are contingent on ex post realized demand; e.g. an advertisement might state the Bertrand price should there be more than one buyer, which corresponds to an auction outcome. Competition in fixed prices and ex post rationing describes equilibrium behavior. There is also real market indeterminacy: a continuum of equilibria exists which are not payoff equivalent. Sellers prefer the equilibrium in auctions.     

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.     

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.