Commitment and choice of partner in a negotiation with a deadline

This paper analyses the effects of partially revocable endogenous commitments of a seller in a negotiation with a deadline. In particular, we examine when commitment is a source of strength, a source of inefficiency and when it does not affect the bargaining outcome at all. We show that when commitment possesses a minimum amount of irrevocability this crucially determines the bargaining outcome. In the bilateral bargaining case, commitment becomes a source of inefficiency since it causes a deadline effect. In the choice of partner framework, however, the deadline effect disappears and there is an immediate agreement and, moreover, commitment becomes a source of strength since it increases the seller's equilibrium payoff by triggering off competition between the buyers.     

不对称雇主学习、外部选择与雇员谈判力

本文在非合作博弈（策略式）单边不对称信息讨价还价框架下,按照外部约束（而不是威胁点）的思路来模型化外部雇主的竞争,以分析不对称雇主学习的程度对处于信息劣势的通用性雇员谈判力的决定作用。本文提出的框架弥补了已有文献的一些不足,同时为不对称雇主学习这一劳动经济学概念提供了一个讨价还价理论基础。     

Partition function bargaining with public demands

In the partition function bargaining problem the value of a coalition depends on the coalition structure in which it is embedded. This paper applies the demand-making bargaining game of coalition formation to the three-player partition function bargaining problem. The values of some embedded coalitions appear to be strategically irrelevant. The strategically relevant values constitute a coalition function bargaining problem. A classification in terms of the associated coalition function bargaining problem is provided. For one of the three classes that are distinguished the set of equilibrium outcomes closely relates to the core of the associated coalitional problem. For another class of problems the equilibrium outcome corresponds to the Von Neumann-Morgenstern outcome. Received: February 14, 2000; revised version: December 13, 2002 RID="*" ID="*" I would like to thank Harold Houba and Gerard van der Laan for valuable discussions, and an anonymous referee for helpful comments. This research was conducted while I was at the Vrije Universiteit Amsterdam.     

Wage Indexation, Employment and Inflation

Price versus productivity-indexing is considered in a model of monetary policy with incomplete information and wage bargaining. In a perfectly price-indexed economy, the inflationary bias due to lack of credibility is eliminated. However, productivity-indexing is more appropriate to dampen macroeconomic fluctuations that are caused by real disturbances. We show that productivity-indexing alone guarantees both price and employment stability, provided the government's reputation is good enough and the union's bargaining power is not too strong. This reduces the degree of price indexation as the union becomes weaker and the government's reputation improves. Productivity-indexing is desirable with volatile productivity processes and weak unions.
JEL classification : E 24; E 52     

TRADE NEGOTIATIONS, INFORMATION AND DOMESTIC POLITICS: THE ROLE OF DOMESTIC GROUPS

A domestic ratification game nested within an international bargaining game establishes that domestic politics influences the outcome of international negotiations. When information on the domestic side is incomplete, an informational role of lobbies is established. Cooperation is more likely when domestic lobbies provide information to Congress about a treaty presented for ratification, especially when cooperation would not otherwise occur. As government becomes more divided, cooperation is less likely; when it does occur, the legislature is better off – internal divisions worsen the external leverage of states, while a united home front is the executive's best chance for obtaining her ideal agreement.     

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.     

Strategic union delegation and strike activity

Abstract.  We develop a model of wage determination with private information, in which the union has the option to delegate the wage bargaining to either surplus‐maximizing delegates or to wage‐maximizing delegates (such as senior union members). We show that the wage outcome in case of surplus‐maximizing delegates is not necessarily smaller than the wage outcome in case of wage‐maximizing delegates, even when the wage bargaining with private information is close to one with complete information. However, if it is commonly known that the union is stronger than the firm and the demand is sufficiently elastic, then delegating to wage‐maximizing delegates definitely increases the wage at equilibrium. The maximum delay in reaching an agreement is greater whenever the union chooses wage‐maximizing delegates instead of surplus‐maximizing delegates and remains finite even when the period length shrinks to zero. JEL classification: C70, C71, C72, C78     

A Decentralized Market with Common Values Uncertainty: Non-Steady States

We analyse a market where (i) trade proceeds by random and anonymous pairwise meetings with bargaining; (ii) agents are asymmetrically informed about the value of the traded good; and (iii) no new entrants are allowed once the market is open. We show that information revelation and efficiency never obtain in equilibrium, even as discounting is removed. This holds whether the asymmetry is two-sided or one-sided. In some cases there exist equilibria where a substantial amount goes untraded. This contrasts with the earlier literature, which was based on the steady-state equilibria of a model where agents enter the market every period.     

Alternating-offer bargaining over menus under incomplete information

Summary. This paper considers bargaining with one-sided private information and alternating offers where an agreement specifies both a transfer and an additional (sorting) variable. Moreover, both sides can propose menus. We show that for a subset of parameters the alternating-offer game has a unique equilibrium where efficient contracts are implemented in the first period. This stands in sharp contrast to the benchmarks of contract theory, where typically only the uninformed side proposes, and bargaining theory, where typically the agreement only specifies a transfer. Received: September 10, 2001; revised version: March 25, 2002 RID="*" ID="*" I benefitted from discussions with Benny Moldovanu, Holger Müller, and Roland Strausz, and from comments made by an anonymous referee.     

Union–firm bargaining: Order of play and efficiency

This paper shows that a modified alternating offers Rubinstein model can provide a Pareto superior outcome in the context of the right-to-manage union–firm bargaining. Two examples of bargaining protocols that yield a superior outcome are provided. In the first example, the parties engage in a game in which the order of play is determined as part of the bargaining. We show that the game has a unique subgame perfect equilibrium in which the firm always moves first in the wage bargaining game. The equilibrium wage is, therefore, unique. In the second example, we examine a two-part-tariff alternating offers bargaining protocol, where the parties bargain over the wage and transfer payments. We show that this bargaining protocol has a Pareto efficient, unique subgame perfect equilibrium. Thus, although the parties do not bargain over the level of employment, the outcome under this protocol is, nevertheless, socially optimal.     

Bargaining with Voluntary Transmission of Private Information: Does the Use of Final Offer Arbitration Impede Settlement?

We identify two features of final offer arbitration (FOA) whichmay impede settlement in a bargaining game where asymmetricinformation drives the failure to settle. First, under FOA theinformed party has an incentive to conceal private informationabout the expected outcome in arbitration from his bargainingpartner. Revealing this information allows the previously uninformedparty to submit a more advantageous offer to the arbitratorto the detriment of the informed party. Second, in a two-typemodel, the uninformed player may choose to arbitrate all cases,a result which never occurs in a simple litigation game. Eachplayer's offer directly affects the outcome of arbitration underFOA, and it is this feature that generates impediments to settlementthat are not observed in a simple litigation game. Both impedimentsto settlement are removed if bargaining is allowed to take placeafter potentially binding offers have been submitted to thearbitrator.     

Modeling longevity risk transfers as Nash bargaining problems: Methodology and insights

The problem of longevity risk has recently received considerable attention. In this paper, we apply economic modeling methods to longevity risk securitization, which is now regarded by pension and insurance industries as a solution to the problem. Specifically, we model the trade of a longevity security as a two-player bargaining game, and use Nash's bargaining solution to determine the outcome of it. Our work not only offers an alternative method for pricing longevity securities, but also reveals several properties about the market for longevity securities. First, a trade would occur if the longevity security is an effective hedging instrument, and the trade would benefit all agents involved. Second, a trade of longevity risk can reduce pension plans' bankruptcy risk, safeguarding the financial security of pension plan members. Finally, compared to the competitive equilibrium, Nash's bargaining solution yields higher trading prices. Therefore, as the market becomes more competitive, pension plans may hedge longevity risk at a lower cost.     

Property Rights and Efficiency of Voluntary Bargaining under Asymmetric Information

We show that in public good problems under asymmetric information, the success of voluntary bargaining is closely related to the structure of property rights. We characterize property rights structures and mediated bargaining procedures that either lead to an efficient voluntary resolution to public good problems, or achieve the efficient outcome but slightly coerce the agents into participation. In this respect, we identify "efficient" property rights structures.     

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.     

Bargaining and the observability of contractual commitments via third parties

This paper analyzes a two-stage model of bilateral bargaining where one of the agents has the option to delegate. A first approach is to assume that the contract between the agent and his representative is perfectly observable and can be renegotiated. Commitment effects arise although renegotiation is possible. Then, perfect observability of the contract is weakened to observe it with certain probability. Commitment effects as pure-strategy equilibria exist if this probability is sufficiently close to 1, in contrast to Bagwell's [1995] findings that imperfect observability undermines commitment. Considering the realistic case of the actual agreement between two parties being private information, the commitment value as equilibrium outcome disappears since having closed a renegotiation-proof contract offers costless self-insurance against strategic misunderstandings. The author is grateful for helpful comments from Vasco Santos, participants at the International Atlantic Economic Conference, October 7–10, 1999, Montreal, Canada, an anonymous referee, and David M. Aadland.     

Blindfolded vs. Informed Ultimatum Bargaining – A Theoretical and Experimental Analysis

This paper analyzes blindfolded vs. informed ultimatum bargaining where proposer and responder are both either uninformed or informed about the size of the pie. Considering the transition from one information setting to another suggests that more information induces lower (higher) price offers and acceptance thresholds when the pie is small (large). While our experimental data confirm this transition effect, risk aversion leads to diverging results in blindfolded ultimatum bargaining where task‐independent strategies such as ‘equal sharing’ or the ‘golden mean’ are implemented more frequently.     

N-PERSON NASH BNARGAINING WITH VARIABEL THREATS*

We consider two models of n-person bargaining problems with the endogenous determination of disagreement points. In the first model, which is a direct extension of Nash's variable threat bargaining model, the disagreement point is determined as an equilibrium threat point. In the second model, the disagreement point is given as a Nash equilibrium of the underlying noncooperative game. These models are formulated as extensive games, and axiomatizations of solutions are given for both models. It is argued that for games with more than two players, the first bargaining model does not preserve some important properties valid for two-person games, e.g., the uniqueness of equilibrium payoff vector. We also show that when the number of players is large, any equilibrium threat point becomes approximately a Nash equilibrium in the underlying noncooperative game, and vice versa. This result suggests that the difference between the two models becomes less significant when the number of players is large.     

Bargaining over a Menu of Wage Contracts

We investigate an infinite horizon bargaining problem in which a firm and a worker bargain over two dimensions, quality and wage. The worker has private information about his type. Only the uninformed firm makes an offer and it can offer a menu of quality-wage contracts instead of single one. We show that for all discount factors, the unique sequential equilibrium outcome is separating without delay; the firm separates the types of worker with a menu of contracts in the first period. Our result shows that in multi-dimensional bargaining, the "Coase Conjecture" holds in the sense that the game ends in the first period. But it fails in the sense that the uninformed party can preserve the entire bargaining power.     

Insiders and outsiders in labour market models

The monopoly union model and the wage bargaining model are analysed in light of the distinction between insiders and outsiders. It is shown that a possible outcome of the wage bargaining is the wage level where all insiders keep their job, but no outsiders are taken on. In this situation, small variations in the bargaining situation of the union will not affect the wage and employment outcome. Furthermore, it may even be the case that the union does not wish a higher wage, because this would lead to lay-offs among the insiders. Thus, the monopoly union model and the bargaining model may yield the same wage and employment levels.This paper is part of the research project Wage Formation and Unemployment at SAF Center for Applied Research at the Department of Economics, University of Oslo. Comments from Michael Hoel, Andrew Oswald, Åsa Rosén, Asbjørn Rødseth and an anonymous referee on earlier drafts are gratefully acknowledged.     

Existence and efficiency of a stationary subgame-perfect equilibrium in coalitional bargaining models with nonsuperadditive payoffs

We provide the existence theorem of stationary subgame-perfect equilibrium (SSPE) in a noncooperative coalitional bargaining game model with random proposers. Our model contains a bargaining situation where the coalitional game is nonsuperadditive. We also provide a necessary and sufficient condition for the existence of a pure-strategy SSPE satisfying the efficiency property when the discount factor is close to one. Furthermore, we provide examples where the delay in agreement occurs, even in a random-proposers model, when the game is nonsuperadditive. I am grateful to Akira Okada and an anonymous referee for their useful comments and helpful suggestions.