Multilateral Bargaining Problems

In many situations in economics and political science there are gains from forming coalitions but conflict over which coalition to form and how to distribute the gains. This paper presents an approach to suchmultilateral bargaining problems. Asolutionto a multilateral bargaining problem specifies an agreement for each coalition that is consistent with the bargaining process in every coalition. We establish the existence of such solutions, show that they are determined by reservation prices, and characterize these reservation prices as the payoffs ofsubgame perfect equilibrium outcomesof a non-cooperative bargaining model.Journal of Economic LiteratureClassification Numbers: C71, C72, C78.     

Timing of endogenous bargaining over costs and firms’ locations

This work analyzes a duopoly in which firms choose their locations and then bargain over wages with their unions. The timing of the bargaining process is endogeously determined. We obtain that bargaining is simultaneous if and only if both firms decide when negotiations take place. Otherwise negotiation takes place sequentially. Under simultaneous or sequential negotiations, the market is equally shared and both firms have the same price-cost margins and profits. When bargaining is sequential firms have higher profits, the leader locates closer to the market than in the simultaneous case, the follower locates further away and the distance between the two firms is greater.      

ON THE NEUTRALITY OF COALITION FORMATION IN A PURE BARGAINING PROBLEM*

We consider the sequential bargaining game à la Stahl–Binmore–Rubinstein with random proposers, juxtaposing an ex ante coalition formation stage to their bargaining game. On the basis of the expected outcomes in the negotiation over how to split a dollar, players can form coalitions in a sequential manner, within each of which they can redistribute their payoffs. It turns out that the grand coalition does form, and that each player receives his discounted expected payoff, which is obtained by playing as a single player in the negotiation, although there could be many equilibria in the bargaining stage.     

INTERNATIONAL TRADE BARGAINING AND THE MOST-FAVORED-NATION CLAUSE*

This paper advances a model of multilateral trade negotiations to analyze the effects of the most-favored-nation clause (MFN) on international trade agreements. Negotiations are modeled in a three player, non-cooperative, dynamic bargaining framework that admits the possibility of both bilateral and multilateral agreements. The central result is that bargaining in the presence of MFN results in Pareto efficient, mutually advantageous, multilateral trade agreements. The free-rider problem commonly attributed to the presence of MFN does not arise, and, under a condition of symmetry, each country receives equal gains (or reciprocity) from the agreement. In the absence of MFN, many of these properties may not hold. Examples are given in which at most two of the three countries benefit from agreement. These results suggest that many of the criticisms levied against the MFN clause are misplaced; moreover, attempts to replace unconditional MFN with conditional MFN may sacrifice many of the long-held values of the GATT.     

A Closed Form Characterization of the Stationary Outcome in Multilateral Bargaining

In this paper we consider infinite horizon multilateral bargaining with alternate offers. We prove that there exists only one stationary subgame perfect equilibrium outcome and it corresponds to the unique invariantmeasure of a column stochastic matrix. We characterize this stationary subgame perfect equilibrium outcome in a closed form, and also extend the approach to the multilateral bargaining with random moves.     

R&D INVESTMENTS AND SEQUENTIAL WAGE NEGOTIATIONS*

This paper analyses how the structure of wage bargaining affects R&D investment by firms that increases the productivity of labour in a Cournot duopoly. We find that total expenditure on R&D is greater when wages are set simultaneously than when they are set sequentially. Thus sequential wage negotiations reduce the incentive for firms to innovate and affect the productivity of labour. When wage negotiations are sequential the productivity of labour is greater (lower) in the follower (leader) firm than when negotiations are simultaneous. We also obtain that for same parameter values it is possible for the firm with the lower productivity to end up paying a higher wage than the firm with the higher level of labour productivity.     

Pattern Bargaining and Wage Leadership in a Small Open Economy*

Pattern bargaining with the tradables (manufacturing) sector as the wage leader is common in Europe. We question the conventional wisdom that such bargaining produces wage restraint. In our model, all forms of pattern bargaining give the same outcomes as uncoordinated bargaining under inflation targeting. Under a monetary union, wage leadership for the non‐tradables sector is conducive to wage restraint, whereas wage leadership for the tradables sector is not. Comparison thinking might lead the follower to set the same wage as the leader. Such equilibria can arise when the leader sector is the smaller sector, and these can promote high employment.     

Multilateral bargaining: conditional and unconditional offers

Summary. We present a game in which n persons split a cake, where a distinction between conditional and unconditional offers is made. This distinction sheds light on the contrasting results obtained in the previous literature of multilateral bargaining. By allowing the proposer to make both conditional and unconditional offers, we show that the game has a unique subgame perfect Nash equilibrium outcome. Received: March 14, 2000; revised version: March 13, 2001     

Private takings

This paper examines the implications associated with a recent Supreme Court ruling, Kelo v. City of New London (2005). Kelo can be interpreted as supporting eminent domain as a means of transferring property rights from one set of private agents—landowners—to another private agent—a developer. Under voluntary exchange, where the developer sequentially acquires property rights from landowners via bargaining, a holdout problem arises. Eminent domain gives all of the bargaining power to the developer and, as a result, eliminates the holdout problem. This is the benefit of Kelo. However, landowners lose all their bargaining power and, as a result, their property investments become more inefficient. This is the cost of Kelo. A policy of eminent domain increases social welfare compared to voluntary sequential exchange only when the holdout problem is severe, and this occurs only if the developer has very little bargaining power. We propose an alternative government policy that eliminates the holdout problem but does not affect the bargaining power of the various parties. This alternative policy strictly dominates a policy of eminent domain, which implies that eminent domain is an inefficient way to transfer property rights between private agents.     

Valuations and dynamics of negotiations

This paper analyzes three‐party negotiations in the presence of externalities. We obtain a closed‐form solution for the Markov perfect equilibrium of a multilateral non‐cooperative bargaining model, yielding an equilibrium value and dynamics of negotiations that are supported by experimental studies. Players’ values are monotonically increasing (or decreasing) in the amount of negative (or positive) externalities that they impose on others. Moreover, players’ values are continuous and piecewise linear on the worth of bilateral coalitions, and are inextricably related to their negotiation strategies: the equilibrium value is the Nash bargaining solution when no bilateral coalitions form; the Shapley value when all bilateral coalitions form; or the nucleolus, when either one bilateral coalition among “natural partners” or two bilateral coalitions including a “pivotal player” form.     

UNION–FIRM BARGAINING AGENDA REVISITED: WHEN UNIONS HAVE DISTINCT PREFERENCES

In this paper we revisit the issue of the scope of bargaining between firms and unions by considering a more general union's utility function with distinct preferences and sequential negotiations. First, we compare exogenously given labour market institutions; i.e., right‐to‐manage (RTM) and sequential efficient bargaining (SEB). We show that the conventional wisdom, which states that firms always prefer RTM, no longer holds. In fact, when unions are adequately wage aggressive and have strong enough bargaining power, firms may prefer SEB negotiations; however, firms switch their preference to RTM when unions are very strong. Moreover, we show that a conflict of interest between the parties may emerge when unions are sufficiently employment oriented as well as sufficiently wage aggressive and not too strong or too weak in bargaining. Second, we analyse the endogenous choice of the bargaining agenda. We show that a rich plethora of equilibria may occur and new situations of conflict/agreement of interests between the bargaining parties arise in particular when unions are sufficiently wage‐aggressive.     

Incomplete contract, bargaining and optimal divisional structure

When complete contracting is not possible, allocating control structure becomes the second-best arrangement. This paper analyzes the design of optimal divisional structure within an organization where ex post bargaining between the potential divisional managers is possible. In much the same light as Aghion and Tirole (J Political Econ 105(1):1?C29, 1997), we study the control problem in the context of search for projects. Our model shows that when the managers cannot bargain with one another, internal integration is preferred to internal separation. Where bargaining is possible, formal divisional structure defines both the ex post bargaining position of the two managers and their incentive to search ex ante. When the managers tend to arrive at a more favorable project to the principal via bargaining, the general leader of a firm may want to choose separation instead to increase the probability of bargaining, as the symmetrical incentive requires both managers to search and get informed.     

Uniqueness of Stationary Equilibrium Payoffs in the Baron-Ferejohn Model

We consider a multilateral sequential bargaining model in which the players may differ in their probability of being selected as the proposer and the rate at which they discount future payoffs. For games in which agreement requires less than unanimous consent, we characterize the set of stationary subgame perfect equilibrium payoffs. With this characterization, we establish the uniqueness of the equilibrium payoffs. For the case where the players have the same discount factor, we show that the payoff to a player is nondecreasing in his probability of being selected as the proposer. For the case where the players have the same probability of being selected as the proposer, we show that the payoff to a player is nondecreasing in his discount factor. Journal of Economic Literature Classification numbers: C72, C78, D70.     

On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.     

Rationalizability and equilibrium in N-person sequential bargaining

Summary. This paper deals with N-person sequential bargaining games with complete information. For N-person sequential bargaining games, uniqueness of the SPE has been obtained by allowing the players to exit with partial agreements. Adopting a non-equilibrium approach, we show that N-person sequential bargaining games with exit are solvable by a refinement of rationalizability for multi-stage games (trembling-hand rationalizability) whatever the impatience of the players. That is, once we adopt the non-equilibrium approach, the exit opportunity still fulfils its original aim: we achieve a unique solution by introducing the exit opportunity. Moreover, this unique solution is the unique SPE. Received: October 30, 1996; revised version: July 7, 1998     

Multi-player bargaining with endogenous capacity

We study equilibrium prices and trade volume in a market with several identical buyers and a seller who commits to an inventory and then offers goods sequentially. Prices are determined by a strategic costly bargaining process with a random sequence of proponents. A unique subgame perfect equilibrium exists, characterized by no costly delays and heterogeneous sale prices. In equilibrium constraining capacity is a bargaining tactic the seller uses to improve a weak bargaining position. With capacity constraints, sale prices approach the outcome of an auction as bargaining costs vanish. The framework provides a building block for price formation in models of equilibrium search with multilateral matching, and offers a rationale for the adoption of single-unit auctions with fixed reservation price.     

Developing-Country Benefits from MFN Relative to Regional/Bilateral Trade Arrangements

Using a general‐equilibrium model of world trade, this paper evaluates the benefits of most‐favored‐nation (MFN) treatment to developing countries in multilateral relative to bilateral or regional trade agreements, from three sources. First, developing countries may be able to free‐ride on bilateral tariff concessions exchanged between larger countries in MFN‐based GATT/WTO rounds. Second, MFN benefits developing countries by restricting discriminatory retaliatory actions by other countries, evaluated here by a non‐ cooperative Nash tariff game. Finally, MFN changes threat points in bargaining and hence affects the bargaining solution of multilateral MFN‐based trade negotiation compared to a bilateral/regional arrangement. The authors find that the benefits to developing countries are small in the first case as the tariff rates are already low, and the benefits are small in the second case as the optimal tariffs under unconstrained retaliation are not very asymmetric. Benefits from the third case are large as large countries can extract large side‐payments if they bargain bilaterally.     

Non-cooperative support for the asymmetric Nash bargaining solution

We study a model of non-cooperative multilateral unanimity bargaining on a full-dimensional payoff set. The probability distribution with which the proposing player is selected in each bargaining round follows an irreducible Markov process. If a proposal is rejected, negotiations break down with an exogenous probability and the next round starts with the complementary probability. As the risk of exogenous breakdown vanishes, stationary subgame perfect equilibrium payoffs converge to the weighted Nash bargaining solution with the stationary distribution of the Markov process as the weight vector.     

A Note on Multi-Issue Two-Sided Bargaining: Bilateral Procedures

This note considers a two-sided multi-issue bargaining problem in which players that belong to the same “side” may have conflicting priorities regarding the different negotiated issues. The note examines different bilateral bargaining procedures and shows the different equilibrium settlements that they yield. In particular the note examines the possibility that group heterogeneity (conflicting priorities) may be exploited in order to gain a better settlement. The different potential outcomes that are implied by the different procedures explain why we often observe such intense negotiation over bargaining procedures. Moreover, the conflict over procedure can be substantial, among parties with common interest as well as between opposing players. Journal of Economic Literature Classification Number: C7.