Trade Negotiations under Alternative Bargaining Structure

We build a bargaining model, in which a country (leader) decides whether or not to form a free trade agreement with other nations (followers), either through a sequential or a multilateral bargaining procedure. Unlike Aghion et al. ( 2007 , Journal of International Economics, 73, 1–30), in our specification of multilateral bargaining, the leader can collude with all those follower countries who agree to its offer. This has important implications for the choice of sequential and multilateral bargaining by the leader in presence of coalition externalities. Moreover, this bargaining procedure ensures that “stumbling block” equilibrium will never occur.     

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.     

Subbalanced games and bargaining sets

Summary. In defining a bargaining set, it is desirable to require that a counterobjecting coalition has a non-empty intersection with the objecting coalition. We refer to this as the intersection property and define a bargaining set, MB ₁, that imposes this property on a variant of the bargaining set defined by Vohra (1991). To study the existence of MB ₁, a new version of the KKM theorem is proposed and the concept of a subbalanced game is introduced. We also provide conditions for the non-emptiness of MB ₂, a bargaining set introduced by Zhou (1994) which imposes the additional restriction that the objecting coalition not be a subset of the counterobjecting coalition.Received: 9 December 2002, Revised: 6 December 2004, JEL Classification Numbers: C71. Correspondence to: Chih ChangThe authors are very grateful to a referee who proposes many helpful comments on both substantive matters and exposition which much improve the paper.     

A Theory of Endogenous Coalition Structures

Consider an environment with widespread externalities, and suppose that binding agreements can be written. We study coalition formation in such a setting. Our analysis proceeds by defining on a partition function an extensive-form bargaining game. We establish the existence of a stationary subgame perfect equilibrium for such a game. Our main results are concerned with the characterization of equilibriumcoalition structures. We develop an algorithm that generates (under certain conditions) an equilibrium coalition structure. Our characterization results are especially sharp forsymmetricpartition functions. In particular, we provide a uniqueness theorem and apply our results to a Cournot oligopoly.Journal of Economic LiteratureClassification Numbers: C71, C72, C78, D62.     

On the Least Core and the Mas-Colell Bargaining Set

We show that the least core of a TU coalitional game with a finite set of players is contained in the Mas-Colell bargaining set. This result is extended to games with a measurable space of players in which the worth of the grand coalition is at least that of any other coalition in the game. As a consequence, we obtain an existence theorem for the Mas-Colell bargaining set in TU games with a measurable space of players. Journal of Economic Literature Classification Number: C71.     

Inefficiency and social exclusion in a coalition formation game: experimental evidence

This paper experimentally investigates the impact of reciprocal behavior in multilateral bargaining and coalition formation. Our results show that reciprocal fairness strongly affects the efficiency and equity of coalition formation. In a large majority of cases, inefficient and unfair coalitions are chosen when their coalition values are relatively high. Up to one third of the experimental population is excluded from bargaining and earns nothing. In monetary terms economically significant efficiency losses occur. We find that the interplay of selfish and reciprocal behavior unavoidably leads to this undesirable consequences. We also compare the predictions of recently developed models of social preferences with our experimental results. We find that some of these models capture the empirical regularities surprisingly well.     

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.     

The Evolutionary Stability of Auctions over Bargaining

This paper considers equilibrium in transaction mechanisms. In an environment with homogeneous buyers and sellers, which eliminates the advantage auctions possess of matching buyers and sellers, both auctions and bargaining are equilibria. However, only auctions are evolutionarily stable. This identifies a new advantage of auctions over bargaining, arising from the division of the gains from trade.Journal of Economic LiteratureClassification Numbers: C78, C73, D44.     

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.     

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.     

Coalition Stability in Public Goods Provision: Testing an Optimal Allocation Rule

We test the canonical model of international environmental agreements (IEAs) in a laboratory setting with asymmetric agents. IEA participation represents coalition formation and public good provision where there are gains to cooperation, but an incentive to free-ride. We test four competing methods of dividing the coalition’s worth: a recently proposed optimal rule which accounts for subjects’ payoffs as a single free-rider, the Shapley value, the Nash bargaining solution, and an equal split. Each treatment generates the theoretically predicted coalition size more often than not. The shares of the potential gains to cooperation achieved by each rule are: 51, 36, 40 and 13%, respectively. These results highlight the importance of using an optimal rule to improve IEAs, and more broadly for voluntary public good provision.     

A Theory of Gradual Coalition Formation

We study noncooperative multilateral bargaining games, based on underlying TU games, in which coalitions can renegotiate their agreements. We distinguish between models in which players continue to bargain after implementing agreements ("reversible actions") and models in which players who implement agreements must leave the game ("irreversible actions"). We show that renegotiation always results in formation of the grand coalition if actions are reversible, but that the process may otherwise end with smaller coalitions. On the other hand, we show that the grand coalition cannot form in one step if the core of the game is empty, irrespective of the reversibility of actions.     

COMPETITIVE PRICING AND EFFICIENCY IN SEARCH EQUILIBRIUM*

We consolidate and generalize some results on price determination and efficiency in search equilibrium. Extending models by Rubinstein and Wolinsky and by Gale, heterogeneous buyers and sellers meet according to a general matching technology and prices are determined by a general bargaining condition. When the discount rate r and search costs converge to 0, we show that prices in all exchanges are the same and equal the competitive, market clearing, price. Given positive search costs, efficiency obtains iff bargaining satisfies Hosios' condition and r=0. When prices are set by third‐party market makers, however, we show that search equilibrium is necessarily efficient.     

Barriers to Global Free Trade through Bilateral Agreements

This paper examines the formation of bilateral free trade agreements (FTAs) in the context of a dynamic noncooperative bargaining game with a random proposer. We show that global free trade (a grand coalition) does not necessarily occur unless transfer payments among countries are allowed. When transfer payments are possible, bilateral FTAs always achieve global free trade, but the ex‐ante and ex‐post inequalities of social welfare among countries are larger than those when all countries are independent because of the strategic bargaining behavior.     

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.     

Spatial Competition with an Outside Good and Distributed Reservation Prices

In this paper, we analyze spatial competition within the framework of a Hotelling model with quadratic transportation costs and an outside option. The new feature of our approach is that consumers are uniformly distributed not only along the Hotelling line but also with regard to reservation prices. It turns out that in this particular model, duopolists always locate their shops exactly at the first and third quartile of the consumer distribution – i.e., at the socially optimal locations. Moreover, with uniformly distributed reservation prices, less than seventy percent of the consumers buy the good, and profits are less than fifteen percent of those in the standard model without an outside option. Received February 7, 2001; revised version received March 27, 2002 Published online: November 11, 2002     

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.     

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.     

Paying the expected externality for a price quote achieves bargaining efficiency

A seller and buyer have reservation prices x and y. Each has a subjective distribution on the other's reservation price. Paying an offer or the expected benefit the other participant receives from his offer induces honest price quotations, hence efficiency: sale iff y> x.