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.     

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.     

Fooling All of the People Some of the Time: A Theory of Endogenous Sequencing in Confidential Negotiations

We analyse a bargaining game in which one party, called the buyer, has the option of choosing the sequence of negotiations with other participants, called sellers. When the sequencing of negotiations is confidential and the sellers' goods are highly complementary, efficient, non-dissipative equilibria exist in which the buyer randomizes over negotiation sequences. In these equilibria, the buyer can obtain higher pay-offs than in pure strategy equilibria or in public negotiations. The degree of sequencing uncertainty that maximizes buyer pay-offs is inversely related to the aggregate bargaining power of the sellers.     

SEARCH,ADVERSE SELECTION,AND MARKET CLEARING

We examine a dynamic decentralized trading model with infinitesimal sellers and buyers to investigate whether or not the market fails to clear in the limit of search friction vanishing. A seller, who has private information about product quality, and a buyer are matched to bargain over price. They form a long‐term relationship if they reach agreement. They return to the matching pool if they fail to agree or the existing relationship is dissolved. The market fails to clear if and only if the ratio of agents' patience over the dissolution rate exceeds a threshold.     

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     

MONEY HOLDINGS,INFLATION, AND WELFARE IN A COMPETITIVE MARKET*

This article examines an environment where money is essential and agents exchange in perfectly competitive, Walrasian markets. Agents consume and produce a homogeneous good, but hold money to purchase consumption in the event of a relatively low productivity shock. A Walrasian market delivers a nondegenerate distribution of money holdings across agents and avoids some of the computational difficulties associated with the market assumption of bilateral bargaining common to search‐theoretic environments. The model is calibrated to long‐run U.S. velocity, and the welfare costs of inflation are assessed for variable buyer–seller ratios and persistent states of buying and selling.     

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.     

On Perceptions of Fairness: The Role of Valuations, Outside Options, and Information in Ultimatum Bargaining Games

This study examines fairness perceptions in ultimatum bargaining games with asymmetric payoffs, outside options, and different information states. Fairness perceptions were dependent on treatment conditions. Specifically, when proposers had higher chip values, dollar offers were lower than when responders had higher chip values. When responders had an outside option, offers were higher and were rejected less often than when proposers had an outside option. However, a given offer was rejected more often when responders had an outside option. Therefore, similar to the first mover advantage, the “advantaged” or “entitled” player received a higher monetary payoff than they would otherwise. When there was complete information about payoff amounts (payoff conversion rates and outside options), rejections occurred more often, and given offer amounts were rejected more often than when there was incomplete information. When there was incomplete information, offers were higher in the initial rounds than in the final rounds. These results suggest that proposers made offers strategically, making offers that would not be rejected, rather than out of a concern for fairness.     

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.     

Gradualism in Bargaining and Contribution Games

This paper identifies a source of gradualism in bargaining and contribution games. In the bargaining games we examine, each party can opt out at any time, and the outside option outcome is assumed to depend on the offers made in the negotiation phase. Specifically, we assume that (1) making a concession in the negotiation phase increases the other party's outside option pay-off and (2) the outside option outcome induces an efficiency loss as compared with a negotiated agreement. The main finding is that the mere presence of such history-dependent outside options forces equilibrium concessions in the negotiation phase to be gradual, and the degree of gradualism is characterized. The model also applies to contribution games in which the outside option may be interpreted as the option to implement a partial project using the total contributions made so far.     

BARGAINING AMONG FARMERS,GOODWILL, AND THE SUCCESS OF COOPERATIVES

A model of concessional bargaining among farmers explains the success (or lack thereof) of cooperative institutions in rural farm settings in the developing regions. Concessional bargaining in day‐to‐day interactions generates goodwill, which helps smoothen future dealings amongst farmers as well as with outside agents. In particular, we model the existence of goodwill amongst farmers as enhancing their ability to collectively bargain with an outside dealer that buys their farm produce. Results suggest that when dealing with each other, farmers offer higher concessions when the risk of loss or reversal in bargaining power is high; however, the level of concession is also influenced by the degree of reciprocity and parameters that affect bargaining surplus. Findings provide further insights over the success of cooperative institutions in rural farm settings where inter‐farmer goodwill dynamics determines the cooperative's bargaining outcomes. Specifically, when farmers generously reciprocate each other's goodwill gestures, it leads to better outcomes through increasing their cooperative reservation price. In contrast, when the degree of reciprocity is lower, or when the risk of bargaining power switching is higher, farmers extract more surplus from other farmers, and this also lowers the cooperative's bargaining outcomes and makes the cooperative arrangement unviable in the long term.     

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).     

MARRIAGE,DIVORCE, AND ASYMMETRIC INFORMATION

We use data on people's valuations of options outside marriage and beliefs about spouses' options. The data demonstrate that, in some couples, one spouse would be happier and the other spouse unhappier outside of some marriages, suggesting that bargaining takes place and that spouses have private information. We estimate a bargaining model with interdependent utility that quantifies the resulting inefficiencies. Our results show that people forgo some utility in order to make their spouses better off and, in doing so, offset much of the inefficiency generated by their imperfect knowledge. Thus, we find evidence of asymmetric information and interdependent utility in marriage.     

Quality distortions in vertical relations

This paper examines how delivery tariffs and private quality standards are determined in vertical relations that are subject to asymmetric information. We consider an infinitely repeated game where an upstream firm sells a product to a downstream firm. In each period, the firms negotiate a delivery contract comprising the quality of the good as well as a non-linear tariff. Assuming asymmetric information about the actual quality of the product and focusing on incentive compatible contracts, we show that from the firms’ perspective delivery contracts lead to more efficient contracts and thus higher overall profits the lower the firms’ outside options, i.e. the higher their mutual dependency. Buyer power driven by a reduced outside option of the upstream firm enhances the efficiency of vertical relations, while buyer power due to an improved outside option of the downstream firm implies less efficient outcomes.     

Wage Bargaining,Privatisation, Ability to Pay and Outside Options: Evidence from Hungary

This article examines the determinants of short-term wage dynamics, using a sample of large Hungarian companies for 1996–99. We test the basic implications of an efficient contract model of bargaining between incumbent employees and managers, which the data do not reject. In particular, there are structural differences between the ownership sectors consistent with our prior knowledge on relative bargaining strength and unionisation measures. Stronger bargaining position of workers leads to higher ability to pay elasticity of wages, and lower outside option elasticity. Our results indicate that while bargaining position of workers in domestic privatised firms may be weaker than in the state sector, the more robust difference relates to state sector workers versus privatised firms with majority foreign ownership.     

The impact of bargaining on markets with price takers: Too many bargainers spoil the broth

In this paper we study how bargainers impact on markets in which firms set a list price to sell to those consumers who take prices as given. The list price acts as an outside option for the bargainers, so the higher the list price, the more the firms can extract from bargainers. We find that an increase in the proportion of consumers seeking to bargain can lower consumer surplus overall, even though new bargainers receive a lower price. The reason is that the list price for those who do not bargain and the bargained prices for those who were already bargaining rise: sellers have a greater incentive to make the bargainers’ outside option less attractive, reducing the incentive to compete for price takers. Competition Authority exhortations to bargain can therefore be misplaced. We also consider the implications for optimal seller bargaining.     

Sequential bargaining,external effects of agreement,and public intervention

In some bargaining situations, agreement has implications for agents beyond the parties involved, and if so, delays in reaching an agreement or failing to reach an agreement, when this would be profitable, may imply significant welfare losses. The question raised in this paper is whether the intervention of a government, who has a positive valuation of agreement and therefore offers a subsidy, will reduce such delays and inabilities to reach agreement? Based on a perfect Bayesian equilibrium in a sequential bargaining game with intervention, we show that in equilibrium intervention always reduces the ex ante equilibrium inefficiency and conditionally reduces expected delays in trade. However, for intervention in the form of a subsidy to take place, the aggregate of the seller’s reservation price and the externalities must be (almost) as high as the buyer’s upper valuation limit.     

Exit options in incomplete contracts with asymmetric information

This paper analyzes bilateral contracting in an environment with contractual incompleteness and asymmetric information. One party (the seller) makes an unverifiable quality choice and the other party (the buyer) has private information about its valuation. A simple deterministic exit option contract, which allows the buyer to refuse trade, achieves the first-best in the benchmark cases where either quality is verifiable or the buyer?s valuation is public information. But, when unverifiable and asymmetric information are combined, deterministic contracts are necessarily inefficient. The first-best can be achieved, however, through simple message games with stochastic terms of trade as off-equilibrium outcomes.     

Signaling bargaining power: Strategic delay versus restricted offers

Summary. I study the first-round separating equilibrium of a buyer-seller bargaining game, extended to allow for asymmetric information, strategically delayed offers and offers restricted to a portion of the good. When bargaining is over a consumption good, in equilibrium the “strong” buyer uses a restricted offer if his optimal consumption path is conservative relative to the “weak” buyer. A pure restricted offer may even be a costless, efficient signal. When the good is durable, a pure strategic delay is involved in signaling a strong bargaining position if the discount factor is high. Received: June 24, 1998; revised version: May 30, 1999     

Private information,Coasian bargaining,and the second welfare theorem

Most of the debate about Coasian bargaining in the presence of externalities relates to the First Welfare Theorem: is the outcome under bargaining efficient? This debate has involved the definition and importance of transaction costs, the significance of private information, and the effect of entry. There has been little analysis of how Coasian bargaining relates to the Second Welfare Theorem: even if the bargaining outcome is efficient, does the process limit the set of Pareto optimal allocations which can be achieved?We consider a model in which individuals utilize a common resource and may affect each other's output. The individuals differ in their productivities or tastes and this information is private to each of them. The government can manage the common resource and use nonlinear taxes to correct for the externality or it can turn the common resource over to a private owner who can charge individuals to utilize it with a nonlinear fee schedule. The government and the owner have the same information about tastes and productivities of the individuals. Except for the private information, there are no bargaining or administrative costs for collecting the taxes or fees. Whether there is public or private ownership, the government desires to redistribute, but it faces self-selection constraints.We show that the outcome of Coasian bargaining is constrained Pareto efficient. That is, given the information constraints, no Pareto improvement is possible. However, private ownership may limit what Pareto optimal allocations the government can achieve. The private owner in seeking to maximize profits always proposes contracts which counteract the government's attempts to redistribute across individuals with different characteristics. Under public management, any Pareto optimum can be sustained. In this context, private ownership, while not inefficient, does limit the government's ability to redistribute.