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.     

Participation constraints of matching mechanisms

Matching mechanisms have been proposed to improve public good provision in voluntary contributions. However, such decentralized subsidizing mechanisms may not be Pareto‐improving and may suffer from incomplete information and incredible commitment. This paper examines participation constraints of matching mechanisms with small matching rates in two cases of equilibria. At interior equilibria, there always exist small Pareto‐improving matching schemes regardless of preferences. This universal existence is useful for cooperation among heterogeneous players in the context without global information of preferences or at the international level without central governments. At corner equilibria, matching schemes work in different ways and have distinct welfare effects in certain cases, and the existence of Pareto‐improving matching schemes is not universal but is possible under certain conditions. The paper further characterizes Pareto‐improving matching schemes, and shows that it is easier to reach Pareto‐improving matching outcomes if players value more on public goods and have stronger substitution between private and public goods.     

The Stability of Hedonic Coalition Structures

We consider the partitioning of a society into coalitions in purely hedonic settings, i.e., where each player's payoff is completely determined by the identity of other members of her coalition. We first discuss how hedonic and nonhedonic settings differ and some sufficient conditions for the existence of core stable coalition partitions in hedonic settings. We then focus on a weaker stability condition: individual stability, where no player can benefit from moving to another coalition while not hurting the members of that new coalition. We show that if coalitions can be ordered according to some characteristic over which players have single-peaked preferences, or where players have symmetric and additively separable preferences, then there exists an individually stable coalition partition. Examples show that without these conditions, individually stable coalition partitions may not exist. We also discuss some other stability concepts, and the incompatibility of stability with other normative properties. Journal of Economic Literature Classification Numbers: C71, A14, D20.     

Public good agreements under the weakest‐link technology

We analyze the formation of public good agreements under the weakest‐link technology. Whereas policy coordination is not necessary for symmetric players, it matters for asymmetric players; however, this fails in the absence of transfers. By contrast, with a transfer scheme, asymmetry may be an asset for cooperation. We characterize various types and degrees of asymmetry and relate them to the stability of self‐enforcing agreements. Asymmetric distributions of autarky public good provision levels (also representing asymmetric interests in cooperation) that are positively skewed tend to be conducive to the stability of agreements. We show that under such conditions, even a coalition including all players can be stable. However, asymmetries that foster stability (instability) tend to be associated with low (high) gains from cooperation.     

Matching soulmates

We study iterated matching of soulmates (IMS), a recursive process of forming coalitions that are mutually preferred by members to any other coalition containing individuals as yet unmatched by this process. If all players can be matched this way, preferences are IMS-complete. A mechanism is a soulmate mechanism if it allows the formation of all soulmate coalitions. Our model follows Banerjee, Konishi, and Sönmez, except reported preferences are strategic variables. We investigate the incentive and stability properties of soulmate mechanisms. In contrast to prior literature, we do not impose conditions that ensure IMS-completeness. A fundamental result is that, (1) any group of players who could change their reported preferences and mutually benefit does not contain any players who were matched as soulmates and reported their preferences truthfully. As corollaries, (2) for any IMS-complete profile, soulmate mechanisms have a truthful strong Nash equilibrium, and (3) as long as all players matched as soulmates report their preferences truthfully, there is no incentive for any to deviate. Moreover, (4) soulmate coalitions are invariant core coalitions—that is, any soulmate coalition will be a coalition in every outcome in the core. To accompany our theoretical results, we present real-world data analysis and simulations that highlight the prevalence of situations in which many, but not all, players can be matched as soulmates. In the Appendix we relate IMS to other well-known coalition formation processes.     

Outside options,component efficiency,and stability

In this paper, we introduce a component efficient value for TU games with a coalition structure which reflects the outside options of players within the same structural coalition. It is based on the idea that splitting a coalition should affect players who stay together in the same way. We show that for all TU games there is a coalition structure that is stable with respect to this value.     

The biodiversity conservation game with heterogeneous countries

Biodiversity is an essential resource, which we classify as conditionally-renewable. In order to achieve conservation and sustainable use of biodiversity virtually all nation states signed the United Nations Convention on Biological Diversity. In this paper we investigate how the heterogeneity of countries in regard to ecosystems and wealth influences the stability of international biodiversity conservation agreements both without and with transfers. We further examine the effect of different degrees of ecosystem substitutability. We model a coalition formation game with players that have a continuous conservation choice. The conservation benefit is dependent on wealth and ecosystem quality. Aggregation of global benefits respects differences in ecosystem substitutability. In case of transfers, a fund redistributes coalition benefits according to a sharing rule. The main finding is that in the absence of transfers, compared to the homogeneous situation, heterogeneity in ecosystems and wealth reduces the size of a stable coalition. The destabilising effect is stronger the higher the ecosystem substitutability. Optimal transfers facilitate a large stable coalition.     

Imitation and selective matching in reputational games

This paper investigates imitation and selective matching in reputational games with an outside option. We identify two classes of such games, ultimatum and trust games. By selective matching we mean that short-run players have the possibility of selecting the long-run player they play against. We find that selective matching (unlike random matching) favors the equilibrium associated to reputation in the ultimatum game, but not in the trust game.     

Toward Farsightedly Stable International Environmental Agreements

The stability of International Environmental Agreements (IEA) is analyzed by using game theory. The integrated assessment model FUND provides the cost-benefit payoff functions of pollution abatement for sixteen different world regions. The farsighted stability concept of Chwe (1994) is used and solved by combinatorial algorithms. Farsighted stability assumes perfect foresight of the players and predicts which coalitions can be formed when players are farsighted. All farsightedly stable coalitions are found, and their improvement to environment and welfare is considerable. The farsightedly stable coalitions are refined further to preferred farsightedly stable coalitions, which are coalitions where the majority of coalition members reach higher profits in comparison with any other farsightedly stable coalitions. Farsightedly stable coalitions contribute more to the improvement of environment and welfare in comparison to D'Aspremont et al.'s (1983) stable ones. Considering multiple farsighted stable coalitions, participation in coalitions for environmental protection is significantly increased, which is an optimistic result of our game theoretical model.     

Corruption and Reputation

This paper examines corruption in a random matching game where past actions are imperfectly observed and players have the option to continue trading with their existing partners. It shows that the effect of individual reputations for honesty may outweigh the effect of a bad collective reputation depending on the expected value of a continued match relative to the corruption gain.     

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.     

Global public goods and unilateral matching mechanisms

While conventional agreements on international public goods require bilateral or multilateral cooperation, we show that unilateral action through matching mechanisms with a self‐commitment device can possibly generate Pareto‐improving outcomes. Even without commitment, unilateral matching may also benefit both players at corner situations. We further characterize the conditions under which this desirable outcome is achieved, particularly highlighting the role of the income distribution and its interplay with the preferences. Moreover, we propose a variant of unilateral matching that can generate Pareto‐improving outcomes regardless of the preferences and the income distribution, indicating that income inequality may not be an obstacle for improving public good provision through unilateral matching.     

A note on stable and sustainable global tax coordination with Leviathan governments

Itaya et al. (2014) study the conditions for sustainability and stability of capital tax coordination in a repeated game model with tax-revenue maximizing governments. One of their major results is that the grand tax coalition is never stable and sustainable. The purpose of this note is to prove that there are conditions under which the grand tax coalition is stable and sustainable in Itaya et al.'s model.     

Convex Games and Stable Sets

It is well known that the core of a convex coalitional game with a finite set of players is the unique von Neumann–Morgenstern stable set of the game. We extend the definition of a stable set to coalitional games with an infinite set of players and give an example of a convex simple game with a countable set of players which does not have a stable set. But if a convex game with a countable set of players is continuous at the grand coalition, we prove that its core is the unique von Neumann–Morgenstern stable set. We also show that a game with a countable (possibly finite) set of players which is inner continuous is convex iff the core of each of its subgames is a stable set.Journal of Economic LiteratureClassification Numbers: C70, C71.     

Collusion, Exclusion, and Inclusion in Random-Order Bargaining

This paper examines the profitability of three types of integration in a cooperative game solved by a random-order value ( e.g. the Shapley value). Collusion between players  i  and  j  is a contract merging their resources in the hands of one of them, say  i  . This contract can be represented as a combination of exclusion, which lets  i  exclude  j  's resource but not use it himself, and inclusion, which lets  i  use  j  's resource but not exclude  j  from it. This representation yields a third-difference condition on the characteristic function that determines the profitability of collusion, generalizing existing results for specific games. Namely, collusion is profitable [unprofitable] when the complementarity of the colluding players is reduced [increased] by other players.     

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.     

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.     

A game-theoretic model of coalition formation among primates

This paper models the coalition formation process among primates as a sequential game. The population consists of individuals having distinct social ranks which is determined by the individual’s resource holding potential. Each member of the population is interested in gaining access to a food resource, either individually or via a coalition. At any given stage of the game, a player can either propose a specific coalition or he can be proposed to in order to join one. Hence, the strategy of a player consists of a sequence of decisions regarding who to propose to for the formation of a coalition and which proposals to accept or reject. We derive the preferences of the players over the various coalition structures under the assumption that the probability of a coalition to obtain the resource is given by a logistic distribution as a function of relative strengths of the players. We show that, given the primates’ strategic behavior, a variety of different coalition structures can emerge in equilibrium.      

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.     

Forming and Dissolving Partnerships in Cooperative Game Situations

A group of players in a cooperative game are partners (e.g., as in the form of a union or a joint ownership) if the prospects for cooperation are restricted such that cooperation with players outside the partnership requires the accept of all the partners. The formation of such partnerships through binding agreements may change the game implying that players could have incentives to manipulate a game by forming or dissolving partnerships. The present paper seeks to explore the existence of allocation rules that are immune to this type of manipulation. An allocation rule that distributes the worth of the grand coalition among players is called partnership formation‐proof if it ensures that it is never jointly profitable for any group of players to form a partnership and partnership dissolution‐proof if no group can ever profit from dissolving a partnership. The paper provides results on the existence of such allocation rules for general classes of games as well as more specific results concerning well‐known allocation rules.