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.     

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.     

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.     

Stability when mobility is restricted by the existing coalition structure

In many social and economic situations the optimal solution requires the formation of coalitions that partition the set of players. When the individual player is small relative to the size of the existing coalitions, it seems realistic to assume that the prevailing coalition structure dictates the set of possible blocking coalitions. Specifically, it is assumed that an individual does not consider forming any coalition, but rather joining an already existing one. Two solution concepts for these games are investigated: structural equilibrium and stable payoffs, which are derived from the application of ψ-stability to the core and to the bargaining set, respectively. To this end an extension of the bargaining set to games without side payments is offered. Both solution concepts are shown to exist for some coalition structure. However, while structural equilibrium may fail to exist for any non trivial coalition structure, for every coalition structure there exists a stable payoff.     

Blame-game politics in a coalition government

Delays in the adoption of reforms is an important question in political economics. This paper explores this issue in the context of a representative democracy where the government is a coalition and citizens observe neither the decision-making process, nor politicians' preferences for a reform. We show that a coalition member who favors a reform may nonetheless choose to veto its adoption (thus delaying it until after the next election) and let his coalition partners share the blame for the non-adoption. We refer to this strategy as blame-game politics. We then identify three reasons for a politician to play the blame-game. One is to make an issue salient in the next election. A second reason is to avoid a split in his electorate, which is accomplished by hiding his stance on an issue. A third reason is to enhance ‘bargaining power’ during the formation of the next government.     

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.     

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.     

Dynamic coalitional equilibrium

We study coalition formation processes of Konishi and Ray (2003) [27]. It is shown that an absorbing and deterministic process of coalition formation that also forms an equilibrium - satisfies a coalitional one-deviation property - does exist if one allows the process to be history dependent. All such dynamic equilibrium processes of coalition formation are characterized. Absorbing outcomes of dynamic equilibrium processes are also identified. It is shown that they always constitute a subset of the largest consistent set of Chwe (1994) [11]. A procedure that identifies a dynamic equilibrium process of coalition formation in finite time is constructed.     

Stability of coalition governments in Western Europe: 1945–1986

The duration and type of coalition governments in twelve European countries in the period 1945–1986 are considered. It is argued that the distribution of party size, on a one-dimensional policy dimension, gives an indication of the qualitative features of the bargaining process between parties and that this determines the type of coalition that forms and the average duration of government. On this basis the twelve countries are divided into four groups (namely unipolar, bipolar, multipolar and fragmented systems).     

Common agency lobbying over coalitions and policy

This paper presents a theory of common agency lobbying in which policy-interested lobbies can first influence the choice of a proto-coalition and then influence the legislative bargaining over policy within that coalition. The equilibrium policy in the legislative bargaining stage maximizes the aggregate policy utility of the coalition members and the lobbies, but lobbying can also lead to the preservation of the status quo and lobby-induced gridlock. When the status quo does not persist, the policy outcome is largely determined by the selection of a coalition, since legislative bargaining under unanimity within the coalition leads to a coalition-efficient policy regardless of the identity of the proposer. An example is presented to identify the types of equilibria and provide a full characterization of an equilibrium.     

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.     

A bargaining approach to the Owen value and the Nash solution with coalition structure

The mechanism by Hart and Mas-Colell (1996) for non-transferable utility (NTU) games is generalized so that a coalition structure among players is taken into account. The new mechanism yields the Owen value for transferable utility (TU) games with coalition structure as well as the consistent value (Maschler and Owen 1989, 1992) for NTU games with trivial coalition structure. Furthermore, we obtain a solution for pure bargaining problems with coalition structure which generalizes the Nash (1950) bargaining solution.     

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.     

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.     

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.     

Coalition governments and comparative constitutional design

In this paper we present a structural approach to the study of government formation in multi-party parliamentary democracies. The approach is based on the estimation of a stochastic bargaining model which we use to investigate the effects of specific institutional features of parliamentary democracy on the formation and dissolution of coalition governments. We illustrate our methodology by presenting the results of two (counterfactual) experiments of comparative constitutional design.     

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.     

Gamson's Law versus non-cooperative bargaining theory

We compare Gamson's Law, a popular empirical model of legislative bargaining, with two non-cooperative bargaining models in three players divide the dollar games in which no player has enough votes to form a winning coalition on their own. Both of the game theoretic models better organize the comparative static data resulting from changes in nominal bargaining power than does Gamson's Law. We also identify deviations from the point predictions of the non-cooperative bargaining models. Namely, proposer power is not nearly as strong as predicted under the Baron–Ferejohn model, and a significant number of bargaining rounds tend to take more than two steps under demand bargaining and more than one stage under Baron–Ferejohn, counter to the models' predictions. Regressions using the experimental data provide results similar to the field data, but fail to do so once one accounts for predictions regarding coalition composition under Gamson's Law.     

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.     

RISKY VERSUS RISKLESS BARGAINING PROCEDURES: THE AUMANN‐ROTH CONTROVERSY REVISITED*

In a series of papers, Aumann and Roth discussed a game in which players can cooperate in pairs and two of them prefer to form a coalition with each other. Roth argued that the only rational outcome is that the players who prefer each other form a coalition; Aumann argued that all three coalitions are possible because the players have a problem of expectation coordination. A non‐cooperative analysis provides additional support for Aumann's arguments and shows that the difference between Aumann's and Roth's views can be traced back to a difference (risky versus/riskless) in the bargaining procedure.