Power and efficiency in production pillage games

A pillage game is a formal model of Hobbesian anarchy as a coalitional game. The technology of pillage is specified by a power function that determines the power of each coalition as a function of its members and their wealth. A coalition can despoil any other coalition less powerful than itself. The present paper studies the problem of achieving an efficient allocation of resources when the required reallocation changes the distribution of power. For example, land redistribution may increase total production, but may also deprive the original owners of the power they need to compel compensation. In this case the original owners would block the redistribution. Previous work on pillage games has focused on the stable set (von Neumann–Morgenstern solution) as a representation of a stable balance of power. However, the balance of power is typically too delicate to support all efficient allocations. The present paper shows that for a large class of power functions, a recently developed extension of the stable set, called the legitimate set, can be rich enough to support all efficient allocations.      

Majority rule with dollar voting

Consider a majority game in which each player's voting strength is equal to the player's payoff. In this game, wealth is the only source of power, and any coalition with more than half the wealth can take everything. Only extreme concentrations of wealth, in which one player owns everything or two players each own half the total wealth are undominated, and thus constitute the core. However, the stable set (von Neumann-Morgenstern solution) is significantly larger. Allocations in which one player has half the wealth, or which divide the total wealth equally among a number of players equal to a power of two, constitute the unique stable set. The stable set thus provides a formal model of an endogenous balance of power.     

Cores of effectivity functions and implementation theory

In a committee where cooperative voting occurs, effectivity functions describe the blocking power of coalitions. It is a binary relation that says for each coalition T and each subset of outcomes B whether or not T can force the final outcome within B. The corresponding cooperative stability notion generalizes the familiar core of a simple game. We study those effectivity functions yielding a non-empty core for all preference profiles, of which additive effectivity functions are an example. This proves to be closely related to implementation by means of the strong equilibrium concept.     

Coalition formation in general NTU games

A general nontransferable utility (NTU) game is interpreted as a collection of pure bargaining games that can be played by individual coalitions. The threatpoints or claims points respectively, in these pure bargaining games reflect the players' opportunities outside a given coalition. We develop a solution concept for general NTU games that is consistent in the sense that the players' outside opportunities are determined by the solution to a suitably defined reduced game. For any general NTU game the solution predicts which coalitions are formed and how the payoffs are distributed among the players.     

A theory of coalition formation in committees

Let G = (N,W) be a strong weighted majority game and let A be a set of alternatives. Denote by L the set of linear orders on A. A social choice function F:L^N → A is a representation of G if the simple game G¹(F) associated with F equals G. A coalition S is determining in G if it satisfies the following condition. Let F be a representation of G and let R^N ? L^N. Then, if a simple majority of the members of S consider an alternative x to be their best choice, then S can ‘enforce’ x to be a Nash equilibrium payoff in the resulting non-cooperative voting game g(F,R^N). In this paper we generalize the above notion of a determining coalition to committees (i.e., proper and monotonic simple games), and give a complete characterization of the set of determining coalitions of a committee. Furthermore, we discuss our notion of a determining coalition in the light of some real-life data on formation of coalitions in town councils in Israel.     

Locally lipschitz cooperative games

A locally Lipschitz cooperative generalized game is described by its coalition worth function v defined on the set [0, 1]ⁿ of generalized (or fuzzy) coalitions of n players. We assume that v is positively homogeneous and locally Lipschitz. We propose the Clarke's generalized gradient ∂v(c^N) of v at the coalition c^N=(1,…,1) of all players as a set of solutions, and we study its property. We point out that it coincides with the core when v is super–additive and to the Shapley value when v is smooth.     

Stability of Climate Coalitions in a Cartel Formation Game

This paper analyses the formation and stability of coalitions to form international environmental agreements. We present and apply the Stability of coalitions model to assess the internal and external stability of all possible coalition structures in a cartel formation game; first under the assumption that no transfers take place and second for a transfer scheme. One important novelty of this paper is the analysis of the incentive structure of twelve regions for all possible combinations of (cartel) coalitions in an empirical setting with asymmetric regions. We show that stable coalitions can emerge only if benefits from global abatement are sufficiently high or if an appropriate transfer scheme is introduced.The authors acknowledge the support of Juan-Carlos Altamirano-Cabrera, Eligius Hendrix, Niels Olieman, Pepijn van Oort, Arjan Ruijs and Hans-Peter Weikard in the analysis. Furthermore, the comments by two anonymous referees are gratefully acknowledged. The usual disclaimer applies.     

International cooperation on biodiversity conservation when spatial structures matter

International cooperation on biodiversity conservation when spatial structures matter. Spatial Economic Analysis. This paper considers the stability of international environmental agreements (IEAs) for biodiversity conservation with an explicit spatial structure. It studies the impact of distance between countries on coalition stability. It analyses a circular spatial structure with different spatial patterns. Robust results are obtained for a wide range of cost-and-benefit parameters: stable coalitions have a maximum size of two members. The best global payoff is obtained when coalitions are composed of neighbouring countries with the smallest possible distance. A ‘remoteness effect’ is observed, i.e., some coalitions of two members are unstable when one of the signatory countries is far away from the other coalition member and from the singletons.     

Cooperative game with nondeterministic returns

We study a non-traditional cooperative game where returns from coalitions are nondeterministic. The long-standing concept of core can be generalized to reflect players’ contentment with their allocations. It is now imperative to formalize the restrictions, such as those pertaining to information, on allocations. The latter are also at times more conducive to fractional representations. With probabilistic structures added, nondeterministic returns become random variables, utility functions attain risk-attitude connotations, and the timing of players’ allocation resolutions gains significance. Under various conditions for utility functions, we show how various core concepts of the general game can be related to its traditionally defined auxiliaries. These developments help pave the way for our illustrations, within two distinct settings, that players’ increased risk aversion would promote the formation of the grand coalition.     

A core equivalence theorem with an arbitrary communication structure

We formalize the concept of a communication structure by identifying it with a partition of the set of agents. Thus, a coalition can form if and only if it belongs to the given partition. Within this framework we are able to show that for every integer J≧2, if we put the uniform distribution on the space of partitions that contain exactly (or, no more than) J coalitions, the probability that such a partition will contain a blocking coalition for any Pareto optimal allocation which is bounded away from being competitive, is arbitrarily close to 1, as the number of individuals increases.     

国际环境合作的经济学分析

本文利用现代经济学理论与方法，构筑了一个分析国际环境合作问题的经济学框架。分析的中心是建立一个静态模型来寻求作为一个联盟形态的国际环境合作的内部和外部稳定性条件，主要结论是稳定的国际环境合作是由模型给定的参数内生地决定的。与当前大多数研究的一个重要不同是，我们的模型没有采用通常的减少污染排放这一分析参数，而是选用了更为直接的污染排放量这一指标。在运用联盟理论对两类情形即不合作和完全合作进行模型化处理的基础上，本文导出了联盟成员国与非成员国福利水平和污染排放量的若干命题，并建立起国际环境合作稳定性的条件。     

On the formation of coalitions in infinite player games

This paper investigates the problem of determining when an infinite player game can be partitioned into countably many stable coalitions. An example is given of asuperadditive scalar measure game for which this is not possible and several positive results are presented. The final section of the paper takes up the problem of when a process of successive coalition formation can eventually lead to a division of all available resources. A theorem and a counterexample are presented for countable player games and the positive result is applied to the vector measure games considered earlier in the paper.     

Equilibria in a class of aggregative location games

Consider a multimarket oligopoly, where firms have a single license that allows them to supply exactly one market out of a given set of markets. How does the restriction to supply only one market influence the existence of equilibria in the game? To answer this question, we study a general class of aggregative location games where a strategy of a player is to choose simultaneously both a location out of a finite set and a non-negative quantity out of a compact interval. The utility of each player is assumed to depend solely on the chosen location, the chosen quantity, and the aggregated quantity of all other players on the chosen location. We show that each game in this class possesses a pure Nash equilibrium whenever the players’ utility functions satisfy the assumptions negative externality, decreasing marginal utility, continuity, and Location–Symmetry. We also provide examples exhibiting that, if one of the assumptions is violated, a pure Nash equilibrium may fail to exist.     

Selection institutions and war aims

We explore how the sizes of the winning coalition and selectorate influence the war aims of states. Leaders who answer to a small winning coalition are more likely to seek territorial gain as a way to increase state resources. Nonterritorial war aims produce a commitment problem in that after the war the defeated state may not comply with the victor's demands. States with large winning coalitions are more willing to continue the war to remove the enemy leader as a solution to this commitment problem. We test our hypotheses against the Militarized Interstate Dispute data set, and we find some support for our argument. Received: June 2004, Accepted: April 2005, Correspondence to: James D. Morrow     

Representation of transferable utility games by coalition production economies

We prove that, by the method of construction of a coalition production economy due to Sun et al. [Sun, N., Trockel, W., Yang, Z., 2008. Competitive outcomes and endogenous coalition formation in an n$n$-person game. Journal of Mathematical Economics 44, 853–860], every transferable utility (TU) game can be generated by a coalition production economy. Namely, for every TU game, we can construct a coalition production economy that generates the given game. We briefly discuss the relationship between the core of a given TU game and the set of Walrasian payoff vectors for the induced coalition production economy.     

Stable and efficient coalitional networks

We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network specifies the nature of the relationship each individual has with her coalition members and with individuals outside her coalition. To predict the coalitional networks that are going to emerge at equilibrium we propose the concepts of strong stability and of contractual stability. Contractual stability imposes that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. Requiring the consent of coalition members under the simple majority or unanimity decision rule may help to reconcile stability and efficiency. Moreover, this new framework can provide insights that one cannot obtain if coalition formation and network formation are tackled separately and independently.     

An equivalence theorem for a differential information economy

In a pure exchange economy with differential information and a finite set of traders, physical commodities and states of nature, we characterize the Walrasian expectations or Radner equilibria by using the veto power of the grand coalition. We prove that an allocation x is a Radner equilibrium allocation if and only if it is “privately non-dominated” by the grand coalition in every economy obtained by perturbing the original initial endowments in the direction of x. The first and second welfare theorems become particular cases of our main result. Since the deterministic Arrow–Debreu–McKenzie model is a special case of the differential information economy model we also provide a new characterization of the Walrasian equilibria.     

An axiomatization of the core of cooperative games without side payments

Let M be a set of m players, m≧3, and let Γ be the set of all (finite) games (without side payments) that have a non-empty core. When M is finite, the following four (independent) axioms fully characterize the core on Γ: (i) non-emptiness, (ii) individual rationality, (iii) the reduced game property, and (iv) the converse reduced game property. If M is infinite, then the converse reduced game property is redundant.     

Multilateral negotiations and formation of coalitions

This paper analyses properties of games modeling multilateral negotiations leading to the formation of coalitions in an environment with widespread externalities. The payoff generated by each coalition is determined by an exogenous partition function (the parameter space). We show that in almost all games, except in a set of measure zero of the parameter space, the Markov perfect equilibrium value of coalitions and the state transition probability that describe the path of coalition formation is locally unique and stable. Therefore, comparative statics analysis are well-defined and can be performed using standard calculus tools. Global uniqueness does not hold in general, but the number of equilibria is finite and odd. In addition, a sufficient condition for global uniqueness is derived, and using this sufficient condition we show that there is a globally unique equilibrium in three-player superadditive games.