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.     

Coalitional stability under perfect foresight

Summary. We analyze strategic social environments where coalitions can form through binding or nonbinding agreements and actions of a coalition may impose externalities upon the welfare of the rest of the players. We define a solution concept that (1) captures the perfect foresight of the players that has been overlooked in the literature (e.g., Harsanyi [10] and Chwe [6]) and (2) identifies the coalitions that are likely to form and the “stable” outcomes that will not be replaced by any coalition of rational (and hence farsighted) players. The proposed solution concept thereby offers a notion of agreements and coalition formation in complex social environments. Received: February 12, 1996; revised version: March 3, 1997     

The Fatter the Tail, the Fatter the Climate Agreement

International climate negotiations take place in a setting where uncertainties regarding the impacts of climate change are very large. In this paper, we examine the influence of increasing the probability and impact of large climate change damages, also known as the ‘fat tail’, on the formation of an international mitigation agreement. We systematically vary the shape and location of the distribution of climate change damages using the stochastic version of the applied game-theoretical STACO model. Our aim is to identify how changes to the distributional form affect the stability of coalitions and their performance. We find that fatter upper tails increase the likelihood that more ambitious coalitions are stable as well as the performance of these stable coalitions. Fatter tails thus imply more successful, or ‘fatter’, international climate agreements.     

Coalitions, agreements and efficiency

If agents negotiate openly and form coalitions, can they reach efficient agreements? We address this issue within a class of coalition formation games with externalities where agents’ preferences depend solely on the coalition structure they are associated with. We derive Ray and Vohra's [Equilibrium binding agreements, J. Econ. Theory 73 (1997) 30-78] notion of equilibrium binding agreements using von Neumann and Morgenstern [Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944] abstract stable set and then extend it to allow for arbitrary coalitional deviations (as opposed to nested deviations assumed originally). We show that, while the extended notion facilitates the attainment of efficient agreements, inefficient agreements can nevertheless arise, even if utility transfers are possible.     

Coalition-Proof Nash Equilibria I. Concepts

In an important class of “noncooperative” environments, it is natural to assume that players can freely discuss their strategies, but cannot make binding commitments. In such cases, any meaningful agreement between the players must be self-enforcing. Although the Nash best-response property is a necessary condition for self-enforceability, it is not sufficient—it is in general possible for coalitions arrange plausible, mutually beneficial deviations from Nash agreements. We provide a stronger definition of self-enforceability, and label the class of efficient self-enforcing agreements “coalition-proof.”     

Do binding agreements solve the social dilemma?

We investigate experimentally whether “binding agreements” can provide a solution to the social dilemma that arises in the presence of pure public goods. Signing a binding agreement can prevent players from free riding on the contributions to the public good. However, a well known theoretical result is that the outcome of the endogenous formation of agreements is not necessarily efficient. Our setting is a bargaining game in which agreements form sequentially. The individual level of contribution to the public good increases with the size of the coalition reaching an agreement and the global agreement is always the socially optimal structure. There are two equilibrium outcomes, the global agreement and an asymmetric structure, which consists of two coalitions of different sizes, the small one free riding on the contributions of the larger one. We run an experiment which lends force to the theoretical result that outcomes may be inefficient. However, subjects do not play Nash and the experimental outcome is, on average, even more inefficient than the theory predicts. Our analysis leads to the conclusion that different types of behaviour co-exist.     

Stability of international climate coalitions — A comparison of transfer schemes

This paper studies the impact of pragmatic and optimal transfer schemes on the incentives for regions to join international climate agreements. With an applied model that comprises twelve world regions we investigate: (i) a benchmark without transfers, (ii) scenarios with allocation-based rules where coalition members receive tradable emission permits proportional to initial or future emissions, (iii) scenarios with outcome-based rules where the coalition surplus is distributed proportional to emissions, and (iv) a scenario based on an optimal sharing rule where the coalition surplus is distributed proportional to outside option payoffs.We find that well-designed transfer schemes can stabilise larger coalitions and increase global abatement levels. In our applied setting we find that for allocation-based and outcome-based rules only small coalitions are stable, and, in the case of grandfathered emission permits, there is no stable coalition at all. Some obstacles associated with grandfathered emission permits can be overcome by incorporating the expected growth of emissions in developing countries in the distribution of emission permits. For the optimal transfer scheme we find that larger coalitions, which include key players such as the United States and China, can be stable, but no transfer scheme is capable of stabilising the Grand Coalition.     

A Risk‐Dominant Allocation: Maximizing Coalition Stability

This paper presents a rule to allocate a coalition’s worth for superadditive games with positive externalities. The allocation rule awards each member their outside payoff, plus an equal share of the surplus. The resulting allocation maximizes coalition stability. Stable coalitions are Strong Nash equilibria since no subset of members has an incentive to leave. Similarly, no subset of non‐members has an incentive to join a stable coalition if the game is concave in this region. The allocation is risk‐dominant. All stable coalitions are robust to the maximum probability of 50% that players’ deviate from their individual best‐responses. The paper compares the allocation to the Shapley value and the Nash bargaining solution, and illustrates why these traditional rules result in small coalitions when applied to issues such as international environmental agreements.     

Optimal sin taxes

We investigate “sin taxes” on unhealthy items, such as fatty foods, that people may (by their own reckoning) consume too much of. We employ a standard optimal-taxation framework, but replace the standard assumption that all consumers have 100% self control with an assumption that some consumers may have some degree of self-control problems. We show that imposing taxes on unhealthy items and returning the proceeds to consumers can generally improve total social surplus. Because such taxes counteract over-consumption by consumers with self-control problems while at the same time they naturally redistribute income to consumers with no self-control problems (who consume less), such taxes can even create Pareto improvements. Finally, we demonstrate with some simple numerical examples that even if the population exhibits relatively few self-control problems, optimal taxes can still be large.     

应正确理解与运用WTO金融审慎措施

WTO框架内以GATS及其金融附件等多边协定组成的有关金融服务贸易的规则体系,是推行金融服务贸易自由化的最重要的国际协定.而金融监管与金融自由化看似矛盾的两者在WTO框架之中是通过金融审慎措施进行协调的.金融审慎措施的正确理解和运用既是履行WTO义务的要求,也是维护一国利益的需要.     

The weak core of simple games with ordinal preferences: implementation in Nash equilibrium

In a simple game, coalitions belonging to a given class are “absolutely powerful” while others have no power. We attempt to make this distinction operational. Toward this end, we propose two axioms on social choice correspondences, Strong Non-Discrimination and Exclusion. Strong Non-Discrimination describes circumstances under which certain coalitions, the losing coalitions, have no influence over social choice. Exclusion requires that there are situations in which certain coalitions, the winning coalitions, can exercise their power. We show that the weak core correspondence is the minimal correspondence satisfying Maskin Monotonicity and Strong Non-Discrimination. We also show that the weak core is the unique correspondence satisfying Nash implementability, Strong Non-Discrimination, and Exclusion.     

Climate Change,Heterogeneities, and Stability of International Fiscal Harmonization

This paper analyzes the instability introduced into multilateral agreements by two types of heterogeneity: heterogeneity of countries (size and number of producing members) and heterogeneity of lobbies (asymmetric influence at the national versus the international level). The work extends theoretical prospective analyses on environmental taxation, as illustrated by the harmonization of fuel taxes. We show that the acceptability of the tax set at the multilateral level depends on the type of coalitions that participate in the multilateral negotiation (size and number of producing countries) and the asymmetry in the local (state-level) power of lobbies during negotiations.     

CAPITAL CONTROLS AND CONFLICT OF INTERESTS

This paper is a normative analysis of the legal restrictions on international financial movements based on a formal model which analyzes the empirical observation that the degree of financial protectionism is associated with changes in the distribution of welfare among agents. The strategic interactions among four types of agents (a trade union, a firm manager, a financial investor and a government) are analyzed, and the optimal amount of capital control is derived as a Nash perfect equilibrium of a non-cooperative game with imperfect information. I conclude that a financial liberalization proposal can be supported by different coalitions of agents, according to the covariance of domestic and foreign returns and the degree of profitability of domestic industrial projects.     

A Strategic Analysis of Eutrophication Abatement in the Baltic Sea

Cooperation between the littoral countries of the Baltic Sea to mitigate eutrophication has proven difficult in the past. In this study, we explore the countries’ incentives to free-ride on agreements, find stable coalitions where free-riding is deterred, and propose alternative ways of designing stable agreements that would reduce eutrophication in the sea. We conclude that strong free-riding incentives for some countries preclude the socially optimal solution in the absence of an enforcing authority. A stable agreement can, however, be formed with some loss in efficiency. The research shows that a treaty with modest abatement targets between all the littoral countries would be more efficient than a coalition between fewer countries but with more ambitious targets. We compare the two international institutions involved in the protection of the Baltic Sea—the intergovernmental Helsinki Commission and the partly supranational European Union—and show that the European Union would not benefit from enforcing an agreement among its member states on the Baltic without Russia being involved in the conservation efforts. Our results suggest that efficient abatement and full participation could be achieved by using the power the European Union has to enforce such an agreement among its members and, simultaneously, negotiating with Russia within the Helsinki Commission.     

International Environmental Agreements under Endogenous Uncertainty

This paper explores the implications of the possibility of a shift in environmental damages on the participation in environmental treaties. Using a two‐period model where the probability of a regime shift increases in the first‐period pollution stock, we examine the issue of coalition formation under both fixed and dynamic membership. Our analysis suggests that endogenous uncertainty may increase participation. We find that full cooperation may be sustained, but only in the presence of endogenous uncertainty. Interestingly, when the shift in the environmental damage is large enough, the model provides a way to solve the “puzzle of small coalitions” found in the literature related to international environmental agreements. We also find that in period 1 (period 2) endogenous uncertainty leads to a lower (higher) pollution stock under dynamic membership as compared to the fixed membership case.     

Unique stability in simple coalition formation games

We investigate the uniqueness of stable coalition structures in a simple coalition formation model, for which specific coalition formation games, such as the marriage and roommate models, are special cases that are obtained by restricting the coalitions that may form. The main result is a characterization of collections of permissible coalitions which ensure that there is a unique stable coalition structure in the corresponding coalition formation model. In particular, we show that only single-lapping coalition formation models have a unique stable coalition structure for each preference profile, where single-lapping means that two coalitions cannot have more than one member in common, and coalitions do not form cycles. We also give another characterization using a graph representation, explore the implications of our results for matching models, and examine the existence of strategyproof coalition formation rules.     

Size inequality,coordination externalities and international trade agreements

Developing countries now account for a significant fraction of world trade and two-thirds of the membership of the World Trade Organization (WTO). However, many are still individually small and thus have a limited ability to bilaterally extract and enforce trade concessions from larger developed economies even though as a group they would be able to do so. We show that this coordination externality generates asymmetric outcomes under agreements that rely on bilateral threats of trade retaliation – such as the WTO – but not under agreements extended to include certain financial instruments. In particular, we find that an extended agreement generates improvements in global efficiency and equity if it includes the exchange of bonds prior to trading but not if it relies solely on ex post fines. Moreover, a combination of bonds and fines generates similar improvements even if small countries are subject to financial constraints that prevent them from posting bonds.     

A simple model of coalitional bidding

Summary. We analyze a model of coalitional bidding in which coalitions form endogenously and compete with each other. Since the nature of this competition influences the way in which agents organize themselves into coalitions, our main aim is to characterize the equilibrium coalition structure and the resulting bids. We do so in a simple model in which the seller may have good reason to allow joint bidding. In particular, we study a model in which the agents are budget constrained, and are allowed to form coalitions to pool their finances before engaging in the first price auction. We show that if the budget constraint is very severe, the equilibrium coalition structure consists of two coalitions, one slightly larger than the other; interestingly, it is not the grand coalition. This equilibrium coalition structure is one which yields (approximately) the maximum expected revenue. Thus the seller can induce the optimal (revenue maximizing) degree of cooperation among budget constrained buyers simply by permitting them to collude. Received: June 25, 1999; revised version: November 13, 2000     

Equilibrium binding agreements: a comment

To construct their Equilibrium Binding Agreements, Ray and Vohra (J. Econ. Theory, 73 (1997) 30-78) define a concept of an equilibrium between coalitions and prove its existence for any coalition structure. We show that this result crucially depends on the quasi-concavity of the utility functions, which in turn depends on the type of mixed strategies used by the coalitions. When coalitions use uncorrelated mixed strategies utility functions may not be quasi-concave and an equilibrium may not exist. However, if coalitions use correlated strategies, an equilibrium always exist.     

“Better off,as judged by themselves”: a comment on evaluating nudges

Many nudges are designed to make people better off, as judged by themselves. This criterion, meant to ensure that nudges will increase people’s welfare, contains some ambiguity. It is useful to distinguish among three categories of cases: (1) those in which choosers have clear antecedent preferences, and nudges help them to satisfy those preferences (often by increasing “navigability”); (2) those in which choosers face a self-control problem, and nudges help them to overcome that problem; and (3) those in which choosers would be content with the outcomes produced by two or more nudges, or in which ex post preferences are endogenous to nudges, so that without additional clarification or work, the “as judged by themselves” criterion does not identify a unique solution for choice architects. Category (1) is self-evidently large. Because many people agree that they suffer self-control problems, category (2) is large as well. Cases that fall in category (3) create special challenges, which may lead us to make direct inquiries into welfare or to explore what informed, active choosers typically select.