Spatial pillage game

A pillage game is a coalitional game as a model of Hobbesian anarchy. The spatial pillage game introduces a spatial feature into the pillage game. Players are located in regions and can travel from one region to another. The players can form a coalition and combine their power only within their destination regions, which limits the exertion of the power of each coalition. Under this spatial restriction, a coalition can pillage less powerful coalitions without any cost. The feasibility of pillages between coalitions determines the dominance relation that defines stable states in which powers among the players are endogenously balanced. With the spatial restriction, the set of stable states changes. However, if the players have forecasting ability, then the set of stable states does not change with the spatial restriction. Core, stable set, and farsighted core are adopted as alternative solution concepts.     

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.     

On the continuity of representations of effectivity functions

An effectivity function assigns to each coalition of individuals in a society a family of subsets of alternatives such that the coalition can force the outcome of society’s choice to be a member of each of the subsets separately. A representation of an effectivity function is a game form with the same power structure as that specified by the effectivity function. In the present paper we investigate the continuity properties of the outcome functions of such representation. It is shown that while it is not in general possible to find continuous representations, there are important subfamilies of effectivity functions for which continuous representations exist. Moreover, it is found that in the study of continuous representations one may practically restrict attention to effectivity functions on the Cantor set. Here it is found that general effectivity functions have representations with lower or upper semicontinuous outcome function.     

Endogenous timing of managerial delegation contracts in a unionized duopoly

In a multiple‐stage duopoly game with strategic delegation and unionized labor market, this paper analyzes whether firms' owners decide managerial incentive contracts sequentially or simultaneously. When firms compete in quantities, firms' owners can choose incentive contracts simultaneously or sequentially, depending on the unions' relative bargaining power and the degree of product differentiation. Instead, when firms compete in prices, firms' owners set incentive contracts sequentially with substitute goods and simultaneously with complement goods.     

Gains and losses at core allocations

The search for a coalition which can possibly improve upon a given allocation and the redistribution of endowments within such a coalition are conducted through the use of prices. Prices permit the expression of how much every agent gains or loses in the allocation. With any feasible allocation one can associate a price system such that either the total loss of all losers does not exceed a certain bound independent of the number of agents or the losers can improve. The definition of gains and losses that we use implies that the total gain is also bounded in core allocations. Our theorem is closely related to that of Vind (1965).     

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。     

Representation of non-transferable utility games by coalition production economies

We prove that every compactly generated non-transferable utility (NTU) game can be generated by a coalition production economy. The set of Walrasian payoff vectors for our induced coalition production economy coincides with the inner core of the balanced cover of the original game. This equivalence depends heavily on our representation. We exemplify that this equivalence need not hold in other representations. We also give a sufficient condition for the existence of a Walrasian equilibrium for our induced coalition production economy.     

Every member of the core is as respectful as any other

We strategically separate different core outcomes. The natural counterparts of a core allocation in a strategic environment are the α-core, the β-core and the strong equilibrium, modified by assuming that utility is transferable in a strategic context as well. Given a core allocation ω of a convex transferable utility (TU) game \(v\), we associate a strategic coalition formation game with \( \left( {v, \omega } \right) \) in which ω survives, while most other core allocations are eliminated. If the TU game is strictly convex, the core allocations respected by the TU-α-core, the TU-β-core and the TU-strong equilibrium shrink to ω only in the canonical family of coalition formation games associated with \( \left( {v, \omega } \right) \). A mechanism, which strategically separates core outcomes from noncore outcomes for each convex TU game according to the TU-strong equilibrium notion is reported.     

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.     

Set-valued solution concepts using interval-type payoffs for interval games

Uncertainty is a daily presence in the real world. It affects our decision making and may have influence on cooperation. Often uncertainty is so severe that we can only predict some upper and lower bounds for the outcome of our actions, i.e., payoffs lie in some intervals. A suitable game theoretic model to support decision making in collaborative situations with interval data is that of cooperative interval games. Solution concepts that associate with each cooperative interval game sets of interval allocations with appealing properties provide a natural way to capture the uncertainty of coalition values into the players’ payoffs. In this paper, some set-valued solution concepts using interval payoffs, namely the interval core, the interval dominance core and the interval stable sets for cooperative interval games, are introduced and studied. The main results contained in the paper are a necessary and sufficient condition for the non-emptiness of the interval core of a cooperative interval game and the relations between the interval core, the interval dominance core and the interval stable sets of such a game.     

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.     

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 decentralized and informationally efficient mechanism realizing fair outcomes in economies with public goods

We present a decentralized mechanism (called Lindahl Egalitarian), which yields Pareto efficient and envy free allocations (i.e. fair outcomes). We show that the mechanism is informationally efficient in general production economies with an arbitrary, but finite, number of private and public goods, and a finite number of agents. The mechanism reduces to the Walrasian mechanism starting from equal wealth when no agent cares about public goods. We also prove that the set of Public Competitive equilibrium allocations (from equal endowments and proportional taxation), and the set of the Lindahl Egalitarian equilibrium allocations are the same. We are grateful to Xavier Calsamiglia and Albert Marcet for helpful conversations, and to A. de la Fuente, I. Macho, and an anonimous referee for useful suggestions. A. Manresa’s research has been supported by the grant CICYT PB90-0172. J. Aizpurua acknowledges financial support from the Government of Navarra.     

Convergence to competitive equilibria and elimination of no-trade (in a strategic market game with limit prices)

The strategic market games literature contains many results that predict Walrasian equilibria in the competitive limit. However, they usually come at the expense of ad hoc assumptions that rule out “pathological” no trade equilibria. This paper studies a strategic market game with limit prices. The set of Nash equilibrium allocations of this game converges to the set containing all competitive equilibria and no-trade, when players are replicated. Moreover, two rounds of iterated deletion of weakly dominated strategies eliminate the no-trade equilibria. Hence, replication paired with two rounds of iterated dominance gives a clean prediction of competitive equilibrium.     

Rivalry Restraint as Equilibrium Behavior

Rivalry restraint has received a lot of attention as a theory of profits in recent research on business strategy. Its economic rationale is explained as the consequences of either exogenous or endogenous anticompetitive forces present in different industries. In this paper, we use a dynamic oligopolistic industry model and show that rivalry restraint emerges as equilibrium behavior among firm owners who delegate decisions to managers. In the corresponding two‐stage game, managers choose optimal production rates in a dynamic Cournot market and owners set incentives for managers, acting sequentially rational. Equilibrium incentives correspond to rivalry restraint, that is, managers are less aggressive in the product market with lower outputs and increasing profits for all firms in the industry.     

Implementation of marginal cost pricing equilibrium allocations with transfers in economies with increasing returns to scale

This paper considers implementation of marginal cost pricing equilibrium allocations with transfers for production economies with increasing returns to scale. We present a mechanism whose Nash equilibrium allocations coincide with the set of marginal cost pricing equilibrium allocations with transfers that characterizes Pareto efficient allocations for economies with non-convex production technologies. We allow production sets and preferences to be unknown to the planner. The mechanism has some nice properties such as feasibility, continuity, and finite-dimension of message space. Furthermore, it works not only for three or more agents, but also for two-agent economies.     

The airport problem with capacity constraints

The original airport problem is concerned with the cost sharing of an airstrip among airplanes assuming that one airstrip is sufficient to serve all airplanes. In this paper, we generalize the original airport problem by imposing capacity constraints to consider the situation when one airstrip cannot serve all airplanes and investigate how to share the cost among airplanes. We introduce the sequential equal contributions rule for our problem and show that it coincides with the Shapley value of the corresponding airport game when the worth of a coalition is defined to be the minimum cost of serving all members of the coalition. The sequential equal contributions rule requires each airplane to contribute equally to the cost of a given section of any airstrip as long as the length of the section is less than or equal to its desired length even though the airplane cannot use the airstrip. Each airplane’s contribution is the sum of terms, one for each section of the airstrip whose length is less than or equal to its desired length. We also present an axiomatic characterization of the rule by imposing the axioms of efficiency, the equal share lower bound, smaller-cost monotonicity, and population fairness.     

Stable cost sharing in production allocation games

Suppose that a group of agents have demands for some good. Every agent owns a technology which allows them to produce the good, with these technologies varying in their effectiveness. If all technologies exhibit increasing returns to scale (IRS) then it is always efficient to centralize production of the good, whereas efficiency in the case of decreasing returns to scale (DRS) typically requires to spread production. We search for stable cost allocations while differentiating allocations with homogeneous prices, in which all units produced are traded at the same price, from allocations with heterogeneous prices. For the respective cases of IRS or DRS, it is shown that there always exist stable cost sharing rules with homogeneous prices. Finally, in the general framework (under which there may exist no stable allocation at all) we provide a sufficient condition for the existence of stable allocations with homogeneous prices. This condition is shown to be both necessary and sufficient in problems with unitary demands.     

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.     

The veto mechanism in atomic differential information economies

We establish new characterizations of Walrasian expectations equilibria based on the veto mechanism in the framework of differential information economies with a complete finite measure space of agents. We show that it is enough to consider the veto power of a single coalition, consisting of the entire set of agents, to obtain the Aubin private core. Moreover, we investigate on the veto power of arbitrarily small and big coalitions, providing an extension to mixed markets of well known Schmeidler (1972) and Vind’s (1972) results in terms of Aubin private core allocations.