Coalition Formation and Stability

This paper studies a class of NTU coalition formation games in which every player’s payoff depends only on the members of her coalition. We identify four natural conditions on individuals’ preferences and show that, under each condition, stable (core) allocations exists.     

Measuring influence in command games

In the paper, we study a relation between command games proposed by Hu and Shapley and an influence model. We show that our framework of influence is more general than the framework of the command games. We define several influence functions which capture the command structure. These functions are compatible with the command games, in the sense that each commandable player for a coalition in the command game is a follower of the coalition under the command influence function. Some of the presented influence functions are equivalent to the command games, that is, they are compatible with the command games, and additionally each follower of a coalition under the command influence function is also a commandable player for that coalition in the command games. For some influence functions we define the equivalent command games. We show that not for all influence functions the compatible command games exist. Moreover, we propose a more general definition of the influence index and show that under some assumptions, some power indices, which can be used in the command games, coincide with some expressions of the weighted influence indices. Both the Shapley–Shubik index and the Banzhaf index are equal to a difference between the weighted influence indices under some influence functions, and the only difference between these two power indices lies in the weights for the influence indices. An example of the Confucian model of society is broadly examined. The authors wish to gratefully thank two anonymous referees for useful suggestions concerning this paper.     

A note on the paradox of smaller coalitions

We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy’s (Int J Game Theory 8:133–164, 1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (Social Choice Welfare 18:135–153, 2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy’s paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy’s paradox is not present for at least one minimal winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.     

Agenda control in coalition formation

Theoretical models of government formation in political science usually assume that the head of state is non-strategic. In this paper, we analyze the power of an agenda setter who chooses the order in which players are recognized to form coalitions in simple games. We characterize those sets of players which can be imposed in the equilibrium coalition and show that the only decisive structures where the agenda setter can impose the presence of any minimal winning coalition are apex games, where a large player forms a winning coalition with any of the small players. Keywords: Government Formation, Agenda Control, Coalitional Bargaining, Finite Bargaining Rules. Received: 26 January 2001/Accepted: 31 July 2001     

Gamson’s law and hedonic games

This note adds one celebrated coalition formation game due to Gamson (Am Soc Rev 26:373–382 1961a, Am Soc Rev 26:565–573, 1961b) in the list of applications of the theory of hedonic games explored by Banerjee et al. (Soc Choice Welf 18:135–153, 2001) and Bogomolnaia and Jackson (Games Econ Behav 38: 204–230, 2002). We apply their results to study the original Gamson game and offer extensions both to a multi-dimensional characteristics space and to an infinite number of players.     

Core in a simple coalition formation game

We analyze the core of a class of coalition formation game in which every player's payoff depends only on the members of her coalition. We first consider anonymous games and additively separable games. Neither of these strong properties guarantee the existence of a core allocation, even if additional strong properties are imposed. We then introduce two top-coalition properties each of which guarantee the existence. We show that these properties are independent of the Scarf-balancedness condition. Finally we give several economic applications. Received: 31 July 1999/Accepted: 5 January 2000     

A Matrix Approach to TU Games with Coalition and Communication Structures

The aim of this article is to present a technique to construct extensions of the Shapley value. Only basic matrix algebra is used. We concentrate on TU games with coalition structures and with communication structures. We define an efficient Aumann–Drèze value and an efficient Myerson value. We also define two families of values for TU games, the first being a convex combination of the efficient Aumann–Drèze value and of the Shapley value and the second a convex combination of the efficient Myerson value and of the Shapley value. We show that the Myerson value, the Aumann–Drèze value, the Shapley value and the four new solutions above are linked by a relationship of “similarity”.     

Spoilers,blocking coalitions,and the core

This paper surveys non-cooperative implementations of the core which tell an intuitive story of coalition formation. Under the core solution concept, if a blocking coalition exists those agents abandon the current allocation without regard for the consequences to players outside the blocking coalition. Yet in certain circumstances, these players have an incentive to prevent formation of any blocking coalition; a game analyzed in Lagunoff (Games Econ Behav 7:54–61, 1994) is vulnerable to such circumstances. To obtain all core allocations and only core allocations, a mechanism must either restrict the actions of non-members of a proposed coalition, or ensure that non-members are unharmed by the departure of the coalition. These requirements illustrate the core’s nonchalance toward agents not in blocking coalitions. The author gives special thanks to Beth Allen and Andy McLennan for their direction, and gratefully acknowledges valuable discussions with Roger Lagunoff, Hugo Sonnenschein, John Ledyard, Myrna Wooders, Nuray Akin, as well as comments from participants at the 2004 Spring Midwest Economic Theory and the Society for Economic Design conferences and from anonymous referees. All errors remain my own. Partial funding came from National Science Foundation grants DMI-0070257 and DMI-0217974.     

Social movement coalitions: Formation,longevity, and success

Social movements rely on coalitions to help mobilize the mass numbers of people necessary for success. In this article, we review the literature on social movement coalition formation, longevity, and success. We identify five factors critical to coalition formation: (a) social ties; (b) conducive organizational structures; (c) ideology, culture, and identity; (d) the institutional environment; and (e) resources. Next, we explore the extent to which coalition survival is influenced by these same factors and argue that emergent properties of the coalition, such as commitment and trust, also facilitate longevity. Our review of the literature reveals that two factors specific to coalitions influence their success: coalition form and the nature of institutional targets. Interaction, communication technology, and the availability of physical and virtual spaces that facilitate communication are themes that run throughout our discussion, as they undergird many of the elements that shape coalition formation and survival. We conclude by evaluating the state of the research area and suggesting directions for further research.     

Progress and conservation under Rawls's maximin principle

I argue the compatibility of progress with Rawls's maximin principle when applied to individual utility functions which are “nonaltruistic” in the sense that any transfer of consumption goods from old to young (resp. from young to old) lowers (resp. increases) old people's utility. The paper shows that necessary conditions for that compatibility are: (A) a bound on the feasible transfers from young to old, and (B) a positive intergenerational stock externality. The analysis implies that the maximin principle has the drawback of making, under mild assumptions, conservation incompatible with progress. Received: 15 December 1999/Accepted: 17 April 2000     

NETWORK STRUCTURE IN A LINK FORMATION GAME: AN EXPERIMENTAL STUDY

In this article, we use an experiment to evaluate the performance of alternative refinements in a Myersonian link formation game with a supermodular payoff function. Our results show that a non‐cooperative refinement, the global games (GG) approach, outperforms alternative cooperative refinements (strong Nash equilibrium, coalition‐proof Nash equilibrium, and pairwise stable Nash equilibrium) in explaining the observed experimental behavior in the static game of complete information with three players. The results are robust to some comparative statics and the GG approach shows a high predictive power under incomplete information. However, under repeated interaction or with a greater number of players, the GG approach loses predictive power, but so do the cooperative refinements. The results illustrate the importance of coordination failure in practice and the need to design mechanisms to reduce this effect in practical decision‐making problems. (JEL C70, C92, D20, D44, D82)     

The partnered core of a game with side payments

An outcome of a game is partnered if there are no asymmetric dependencies between any two players. For a cooperative game, a payoff is in the partnered core of the game if it is partnered, feasible and cannot be improved upon by any coalition of players. We show that the relative interior of the core of a game with side payments is contained in the partnered core. For quasi-strictly convex games the partnered core coincides with the relative interior of the core. When there are no more than three partnerships, the sums of the payoffs to partnerships are constant across all core payoffs. When there are no more than three players, the partnered core satisfies additional properties. We also illustrate our main result for coalition structure games.     

A value for games with coalition structures

This paper presents an axiomatization of a value for games with coalition structures which is an alternative to the Owen Value. The motor of this new axiomatization is a consistency axiom based on an associated game, which is not a reduced game. The new value of an n-player unanimity game is the compound average of the new values of all the (n-1)-player unanimity games. The new value of a unanimity game allocates to bigger coalitions a larger share of the total wealth. Note that the Owen value allocates to all the coalitions the same share independently of their size.     

Linear cost share equilibria and the veto power of the grand coalition

We consider pure exchange economies with finitely many private goods involving the choice of a public project. We discuss core-equivalence results in the general framework of non-Euclidean representation of the collective goods. We define a contribution scheme to capture the fraction of the total cost of providing the project that each blocking coalition is expected to cover. We show that for each given contribution scheme defined over the wider class of Aubin coalitions, the resulting core is equivalent to the corresponding linear cost share equilibria. We also characterize linear cost share equilibria in terms of the veto power of the grand coalition. It turns out that linear cost share equilibria are exactly those allocations that cannot be blocked by the grand coalition with reference to auxiliary economies with the same space of agents and modified initial endowments and cost functions. Unlike the Aubin-type equivalence and results presented in Diamantaras and Gilles (Soc Choice Welf 15:121–139, 1998), this characterization does not depend on a particular contribution scheme.     

A General Equilibrium Model of Multi-Party Competition

The paper introduces a generalized spatial model that is motivated by the frequent changes in party identity and electoral laws that characterize transitional party systems. In this model, parties may (1) change their platforms, (2) their identities through coalitions and splits and (3) if they form a winning coalition, the electoral law. The equilibrium is defined as a state such that no party or coalition can strictly benefit from changing the electoral law, its platform, or from splitting or coalescing. The results show that while there are games with no institutional or coalitional-split equilibria, such equilibria do exist under relatively undemanding conditions. The main finding is that once an institutional and identity equilibrium is achieved, it is generically robust against small trembles in party platforms or voter preferences. This robustness facilitates greater stability in terms of institutions and party identities in mature party systems where such trembles are smaller than in transitional systems.     

Constitutions, voting and democracy: A review

This review of William Riker's work suggests that his interest in rational choice theory was based on his desire to understand profound constitutional transformation in U.S. political history. Although he argued that “anything can happen in politics,” his use of the notion of heresthetic allowed him to focus on key contingent events. Indeed his later work added depth to his inductive generalizations on the nature of “federal bargains” and coalition formation.  Recent work by Austen-Smith and Banks, Merrill and Grofman, and Lijphart is also discussed in the light of Riker's earlier ideas on voting and democracy. Received: 25 February 2000/Accepted: 16 March 2000     

Existence of a coalitionally strategyproof social choice function: A constructive proof

This paper gives a concrete example of a nondictatorial, coalitionally strategyproof social choice function for countably infinite societies. The function is defined for those profiles such that for each alternative, the coalition that prefers it the most is “describable.” The “describable” coalitions are assumed to form a countable Boolean algebra. The paper discusses oligarchical characteristics of the function, employing a specific interpretation of an infinite society. The discussion clarifies within a single framework a connection between the negative result (the Gibbard-Satterthwaite theorem) for finite societies and the positive result for infinite ones. Received: 10 August 1998/Accepted: 29 February 2000     

On the social stability of coalitional property rights regimes

We present a model of coalitional property rights (CPR) regimes– regimes in which ownership of a good is attributable to coalitions of various sizes. Specifically, for each good, we define a legal structure that specifies the legal coalitions of individuals that share a communal claim to that good. Generally, each legal coalition may use exclusionary rules to allocate its holdings internally. These rules allow eligible subcoalitions to recontract by expropriating some fraction of the legal coalition's endowment. We then ask: what types of CPR regimes are socially stable in the sense of having a nonempty core? We give conditions on the legal structure and the primitives of the economy that achieve social stability in this sense. We emphasize two cases of particular interest. ( I ) Unanimity. Unanimity is required for a legal coalition to recontract against (block) the status quo. In this case, the core is nonempty under standard assumptions. Each agent's ability to veto an alternative allocation allows a partial characterization in terms of the economies that are privatized by dividing up the communal endowment among the members of each legal coalition. We show that in some economies' collective vs private ownership matters in terms of social stability. ( II ) Exclusion. Many eligible subcoalitions can expropriate the legal coalition's entire endowment. An example is the collection of simple majorities. The presence of cycles can easily lead to social instability. We show that if endowment holdings are sufficiently “specialized” and each agent's “veto power” sufficiently large, then stability can be achieved despite the presence of cycles in some goods. Received: 30 June 1993/Accepted: 28 February 1998     

Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization

The concept of coalition proof Nash equilibrium was introduced by Bernheim et al. [5]. In the present paper, we consider the representation problem for coalition proof Nash equilibrium: For a given effectivity function, describing the power structure or the system of rights of coalitions in society, it is investigated whether there is a game form which gives rise to this effectivity function and which is such that for any preference assignment, there is a coalition proof Nash equilibrium.  It is shown that the effectivity functions which can be represented in coalition proof Nash equilibrium are exactly those which satisfy the well-known properties of maximality and superadditivity. As a corollary of the result, we obtain necessary conditions for implementation of a social choice correspondence in coalition proof Nash equilibrium which can be formulated in terms of the associated effectivity function. Received: 24 June 1999/Accepted: 20 September 2000