The Efficiency Principle in Non-Cooperative Coalitional Bargaining

Applying the non-cooperative theory of coalitional bargaining, I examine a widely held view in economic literature that an efficient outcome can be agreed on in voluntary bargaining among rational agents in the absence of transaction costs. While this view is not always true, owing to the strategic formation of subcoalitions, I show that it can hold under the possibility of successive renegotiations of agreements. Renegotiation may, however, motivate bargainers to form a subcoalition first and to exploit the first-mover rent. This strategic behaviour in the process of renegotiation may distort the equity of an agreement.
JEL Classification Numbers: C72, C78, D23, D61, D63.     

Rubinstein Auctions: On Competition for Bargaining Partners

This paper analyzes the effect of competition for bargaining partners on the prices that prevail in thin markets, as well as how the matches are simultaneously determined. Three trading processes or bargaining procedures are described. In all the variants that we consider, except for one case of public offers, either there is no pure strategy subgame perfect equilibrium or such equilibria exhibit delay in reaching agreement.Journal of Economic LiteratureClassification Numbers: C72, D43.     

下游竞争、买方谈判能力与上游产品差异化

基于零售商谈判能力的差异,构建完全信息动态博弈模型,考察下游竞争程度、买方谈判能力对上游产品差异化策略激励的影响.结果表明,下游市场竞争与买方谈判能力对产品差异化的激励不存在替代效应;当零售商不具有买方谈判能力时,市场竞争程度通过影响上游利润激励供应商的产品差异化策略,竞争程度不影响批发价格;当主导零售商具有买方谈判能力时,谈判能力通过影响批发价格激励供应商的产品差异化策略;市场竞争削弱了消费者效用水平,而买方谈判能力改善了消费者效用水平.     

Coalitional Colonel Blotto Games with Application to the Economics of Alliances

In Borel’s Colonel Blotto game two players simultaneously allocate their respective endowments of a resource across n battlefields, the higher allocation wins each battlefield, and players maximize the number of battlefields won. Here we examine two players who may form an alliance before separately competing in two disjoint Colonel Blotto games against a common adversary. Despite a lack of common interests, unilateral transfers—in a direction consistent with the exploitation hypothesis—arise for a range of parameter configurations. Such transfers alter the adversary’s strategy and the combination of the direct and strategic effects benefits both allies.     

Education Signalling with Preemptive Offers

We analyse a version of Spence's job market signalling model in which firms can make job offers before workers complete their education. Workers cannot commit to turning down such offers. Offers are private, so that workers are unable to use one firm's offer in an attempt to elicit better offers from other firms. In the unique sequential equilibrium outcome of the model with unproductive education, there is no wasteful education. When education is productive, the standard model predicts that more able individuals become overeducated to separate themselves from less able workers. In our model, less able workers become overeducated to (partially) pool with more able workers. The pooling mutes the incentives of high ability workers, who in consequence actually choose to become undereducated. We examine the robustness of our result to modifications to the basic model.     

Bargaining with subjective mixtures

This paper reconsiders the Bargaining Problem of Nash (Econometrica 28:155–162, 1950). I develop a new approach, Conditional Bargaining Problems, as a framework for measuring cardinal utility. A Conditional Bargaining Problem is the conjoint extension of a Bargaining Problem, conditional on the fact that the individuals have agreed on a “measurement event”. Within this context, Subjective Mixture methods are especially powerful. These techniques are used to characterise versions of the Nash and the Kalai–Smorodinsky solutions. This approach identifies solutions based only on the individuals’ tastes for the outcomes. It is therefore possible to do Bargaining theory in almost complete generality. The results apply to Biseparable preferences, so are valid for almost all non-expected utility models currently used in economics.     

Bargaining with endogenous information

This paper analyses information acquisition in ultimatum bargaining with common values. Because of an endogenous lemons problem the equilibrium payoffs of the agents are non-monotonic in the information cost. The mere possibility of information acquisition can cause no trade although the agents maintain symmetric information in equilibrium and the gain from trade is common knowledge. The agent responding to a take-it-or-leave-it offer may capture some or even the full trading surplus in a perfect Bayesian equilibrium. The implications for sequential bargaining are discussed.     

Bargaining Outcomes with Double-Offer Arbitration

Increasingly, arbitration is becoming used to resolve bargaining disputes in a variety of settings. Reducing dispute rates is often listed as a main goal in designing arbitration mechanisms. Conventional arbitration and final-offer arbitration are two commonly used procedures, but theoretical examinations of these arbitration procedures show that disputants’ final bargaining positions do not converge and disagreement is likely. This article contains results from a set of experiments designed to compare bargaining outcomes under the two commonly used arbitration procedures with outcomes under an innovative procedure called “double-offer” arbitration (Zeng et al., 1996). This procedure requires that disputants make two final offers at impasse: a primary and a secondary offer. The arbitrator evaluates the pairs of offers using a linear criterion function, and theory suggests the secondary offers converge to the median of the arbitrator’s preferred settlement distribution. Because the procedure’s rules are that convergence of offers generates a settlement at those offers, this theoretical convergence result implies that arbitration is not needed in the end. Experimental results indicate that dispute rates in double-offer arbitration are, on average, about the same as dispute rates in conventional arbitration. However, other results show reason to favor double-offer arbitration. Specifically, in repeated bargaining, there is concern over whether use of an arbitration procedure becomes addictive and makes bargainers more likely to use the procedure in the future-a “narcotic effect.” The data show that double-offer arbitration is non-addictive, whereas both conventional and final-offer arbitration are.     

Coalitional bargaining games with random proposers: Theory and application

We consider a non-cooperative coalitional bargaining game with random proposers in a general situation for which players differ in recognition probability and time preference. We characterize an efficient equilibrium as the generalized Nash bargaining solution that belongs to the core. The model is applied to wage bargaining between an employer and multiple workers. Although involuntary unemployment may occur in equilibrium, full employment emerges as players become sufficiently patient.     

Repeated Bargaining with Persistent Private Information

The paper analyses repeated contract negotiations involving the same buyer and seller where the contracts are linked because the buyer has persistent (but not full y permanent) private information. The size of the surplus being divided is specified as a two-state Markov chain with transitions that are synchronized with contract negotiation dates. Equilibrium involves information cycles triggered by the success or failure of aggressive demands made by the seller. Because there is persistence in the Markov chain generating the surplus, a successful demand induces the seller to make another aggressive demand in the next negotiation, since the buyer's acceptance reveals that the current surplus is large. Rejection of an aggressive demand, on the other hand, leads the seller to be pessimistic about the size of the surplus in the next contract, so the seller makes a soft offer that is sure to be accepted. Then, after several such offers have been accepted, the seller is optimistic enough to again make an aggressive demand, creating an information cycle. An interesting feature of this cycle is that the soft price is not constant, but declines as the cycle continues, so as to offset the buyer's option value of re-starting the cycle when the current state is bad. An explicit mapping is given for the relationship between the basic parameters and the equilibrium prices and quantities; in particular, there is a closed-form solution for the threshold belief that makes the seller indifferent between hard and soft offers.     

Bargaining with a possibly committed seller

We consider negotiations with an open time horizon where a buyer has private information about his valuation and does not know whether the seller is committed to the advertised price. This setting combines two common specifications made in the non-cooperative bargaining literature: one side is privately informed about its valuation, which is drawn from a continuum, and the other side is possibly committed to a fixed offer. We analyze the game both in discrete and in continuous time and show convergence of the two settings, which extends results from Abreu and Gul [2000. Bargaining and reputation. Econometrica 68, 85–117]. One interesting result is that as time proceeds, the non-committed seller becomes less likely to concede in a given period, i.e., it appears as if he becomes more “stubborn.” We further show that a seller may prefer to negotiate with a “worse” buyer as this enhances the value of his possible commitment.     

Bargaining with asymmetric information in non-stationary markets

Summary. The Rubinstein and Wolinsky bargaining-in-markets framework is modified by the introduction of asymmetric information and non-stationarity. Non-stationarity is introduced in the form of an arbitrary stochastic Markov process which captures the dynamics of market entry and pairwise matching. A new technique is used for establishing existence and characterizing the unique outcome of a non-stationary market equilibrium. The impact of market supply and demand on bilateral bargaining outcomes and matching probabilities is explored. The results are useful for examining such questions as why coordination failures and macroeconomic output fluctuations are correlated with real and monetary shocks. Received: July 22, 1994; revised version: January 21, 1998     

A Bargaining Experiment to Motivate Discussion on Fairness

The author presents a classroom version of the popular research game called the Ultimatum Game. Researchers are placing growing importance on how fairness affects behavior, and this experiment provides a useful, fun, and engaging way in which a day or two of class time can be spent on the topic. The appendix contains all of the materials necessary to conduct this experiment, and the experiment can highlight several items of interest for the instructor. First, different individuals place different subjective weights on concerns for fairness versus money. Second, theories that incorporate concerns for fairness into agents' preferences can often explain behavior better than those that do not. Finally, when it is relatively cheap to purchase fairness (or equality) individuals purchase more of it. The classroom results can motivate discussion of a downward sloping demand curve for fairness.     

Folk Theorem For Bilateral Bargaining with Vector Endowments

We analyse a bargaining game of two players on the division of the sum of their vector endowments, with alternating proposals and discounting of single period utilities. The pair of endowments is not weakly Pareto‐efficient. Until they reach an agreement, each of the parties can withdraw from bargaining and keep their endowments. Any strictly individually rational division of the sum of endowments can emerge in some subgame perfect equilibrium if discount factors are close enough to one. Each subgame perfect equilibrium, in which the parties’ decisions do not depend on past rejected proposals, leads to a weakly Pareto‐efficient agreement in the first period.     

Litigation with Symmetric Bargaining and Two-Sided Incomplete Information

We construct game-theoretic foundations for bargaining in theshadow of a trial. Plaintiff and defendant both have noisy signalsof a common-value trial judgment and make simultaneous offersto settle. If the offers cross, they settle on the average offer;otherwise, both litigants incur an additional cost and the judgmentis imposed at trial. We obtain an essentially unique Nash equilibriumand characterize its conditional trial probabilities and judgments.Some of the results are intuitive. For example, an increasein trial cost (or a decrease in the range of possible outcomes)reduces the probability of a trial. We obtain a precise nonlinearexpression for the relationship. Other results reverse findingsfrom previous literature. For example, trials are possible evenwhen the defendant's signal indicates a higher potential judgmentthan the plaintiff's signal, and when trial costs are low, middlingcases (rather than extreme cases) are more likely to settle.     

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.     

Bargaining with endogenous disagreement: The extended Kalai-Smorodinsky solution

Following Vartiainen (2007) we consider bargaining problems in which no exogenous disagreement outcome is given. A bargaining solution assigns a pair of outcomes to such a problem, namely a compromise outcome and a disagreement outcome: the disagreement outcome may serve as a reference point for the compromise outcome, but other interpretations are given as well. For this framework we propose and study an extension of the classical Kalai-Smorodinsky bargaining solution. We identify the (large) domain on which this solution is single-valued, and present two axiomatic characterizations on subsets of this domain.     

Rethinking Political Bargaining: Policymaking with a Single Proposer

Most political bargaining in the U.S. system has two featureswhich are constitutionally mandated: (1) only one actor canmake a formal proposal, and (2) he or she can make an indefinitenumber of proposals. Existing work in economics and politicalscience ignores at least one of these features. I constructa model incorporating both of these components of politicalbargaining. The main finding of this article is that time preferencesand the number of periods have no effect on the equilibriumpolicy outcomes, which are identical to those first stated byRomer and Rosenthal in a one-period model. This result suggeststhat impatience and time preferences may not be key featuresof political bargaining. This model has implications for constitutionaland statutory rules regarding bargaining: it can be appliedto presidential appointments, legislation, citizen initiatives,vetoes and filibusters (e.g., Krehbiel's pivotal politics model),and term limits.     

Bargaining Over Environmental Budgets: A Political Economy Model with Application to French Water Policy

In decentralized water management with earmarked budgets financed by user taxes and distributed back in the form of subsidies, net gains are often heterogeneous across user categories. This paper explores the role of negotiation over budget allocation and coalition formation in water boards, to provide an explanation for such user-specific gaps between tax payments and subsidies. We propose a bargaining model to represent the sequential nature of the negotiation process in water districts, in which stakeholder representatives may bargain upon a fraction of the budget only. The structural model of budget shares estimated from the data on French Water Agencies performs well as compared with reduced-form estimation. Empirical results confirm the two-stage bargaining process and provide evidence for systematic net gains from the system for agricultural water users.