Reduced game and converse consistency

The initiating points of the current paper are the axiomatic characterizations, in terms of consistency, of the equal allocation of nonseparable cost value (by Moulin), the Shapley value (by Hart and Mas-Colell), and the prenucleolus (by Orshan). The basic axioms are the same, but three different reduced games can be used to distinguish these three solutions. The main purpose of the paper is to illustrate that besides the definitions of reduced games are different, the axiom converse consistency also plays an important role to distinguish these three solutions.     

The separability axiom and equal-sharing methods

A quasi-linear social choice problem is defined as selecting one (among finitely many) indivisible public decision and a vector of monetary transfers among agents to cover the cost of this decision. This decision is based upon individual preferences, which are assumed to be additively separable and linear in money. The Separability axiom is a consistency property for choice methods on societies with variable size: the decision is not affected if we remove an arbitrary agent under the condition that he be guaranteed his original utility level and the cost to the remaining agents is modified accordingly. Thus the utility level assigned by the social choice function to agent i is the price at which the other agents are unanimously willing to buy agent is share of the decision power. A general characterization of choice methods satisfying this axiom is provided. Three subclasses of particular interest are characterized by additional milder axioms. Those are: (i) equal sharing of the surplus left over some reference utility (e.g., the utility at a status quo decision), (ii) utilitarian methods that merely select the efficient public decision and perform no monetary transfers, and (iii) equal allocation of nonseparable costs, which divides equally the surplus left over from the utility derived from the pivotal mechanism (also known as the Vickrey-Clarke-Groves mechanism).     

Cost Manipulation Games in Oligopoly, With Costs of Manipulating

We analyze a class of two-stage games where rival firms incur real resource costs in manipulating their marginal costs, so as to influence the outcome of the game they want to play in stage two. Marginal costs may be manipulated by various means, such as redistribution of productive assets, choice of location, or creation of an internal input market. A general formulation of the game is provided, and several applications are analyzed. We show that the optimal allocation of resources within an oligopoly can be asymmetric, even for ex-ante symmetric firms. This is an additional explanation of heterogeneity in oligopoly.     

The Split Core for Sequencing Games

The split core is a refinement of the core for sequencing games. The split core arises from a generalization of the equal gain splitting (EGS) rule that is introduced byCuriel et al. (1989). It is pointed out that the split core is the convex hull of permutation-based gain splitting allocations and the EGS allocation is in the barycenter of the split core. Finally, an axiomatic characterization of the split core is provided.Journal of Economic LiteratureClassification Number: 026.     

Production-inventory games: A new class of totally balanced combinatorial optimization games

In this paper we introduce a new class of cooperative games that arise from production-inventory problems. Several agents have to cover their demand over a finite time horizon and shortages are allowed. Each agent has its own unit production, inventory-holding and backlogging cost. Cooperation among agents is given by sharing production processes and warehouse facilities: agents in a coalition produce with the cheapest production cost and store with the cheapest inventory cost. We prove that the resulting cooperative game is totally balanced and the Owen set reduces to a singleton: the Owen point. Based on this type of allocation we find a population monotonic allocation scheme for this class of games. Finally, we point out the relationship of the Owen point with other well-known allocation rules such as the nucleolus and the Shapley value.     

Average Monotonic Cooperative Games

A subclass of monotonic transferable utility (T.U.) games is studied: average monotonic games. These games are totally balanced. We prove that the core coincides with both the bargaining set à la Davis and Maschler and the bargaining set à la Mas-Colell. To obtain this result a technique based on reduced games is used. Journal of Economic Literature Classification Number: C71     

Extendable Cooperative Games

A (TU) cooperative game is extendable if every core allocation of each subgame can be extended to a core allocation of the game. It is strongly extendable if any minimal vector in the upper core of any of its subgames can be extended to a core allocation. We prove that strong extendability is equivalent to largeness of the core. Further, we characterize extendability in terms of an extension of the balanced cover of the game. It is also shown how this extension can unify the analysis of many families of games under one roof.     

Market Games in Large Economies with a Finite Number of Types

We study market games derived from an exchange economy with a continuum of agents, each having one of finitely many possible types. The type of agent determines his initial endowment and utility function. It is shown that, unlike the well-known Shapley–Shubik theorem on market games (Shapley and Shubik in J Econ Theory 1:9–25, 1969), there might be a (fuzzy) game in which each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a game needs also to be homogeneous. We also study investment games – which are fuzzy games obtained from an economy with a finite number of agents cooperating in one or more joint projects. It is argued that the usual definition of the core is inappropriate for such a model. We therefore introduce and analyze the new notion of comprehensive core. This solution concept seems to be more suitable for such a scenario. We finally refer to the notion of feasibility of an allocation in games with a large number of players. Some of the results in this paper appear in a previous draft distributed by the name “Cooperative investment games or Population games”. An anonymous referee of Economic Theory is acknowledged for his/her comments     

Common Pool Games are Convex Games

For the class of cooperative common pool games the paper focuses on the question of how, during the preplay negotiation process, the ability of coalitions to enforce their claims imposes externalities on the opposition by having an impact on the jointly produced resource. One of our main results is that common pool games are clear games. Based on this result we are able to derive sufficient conditions for the convexity of the characteristic function, which establishes the second main result in the paper, namely that cooperative common pool games are characterized by increasing returns with respect to the coalition size.     

Nash Equilibria of Repeated Games with Observable Payoff Vectors

We study a model of repeated games with imperfect monitoring where the payoff vector is observable. In this situation, any profitable deviation is detectable by all the players but the identity of the deviator may be unknown. We design collective punishments directed against the set of potential deviators. A particular class of signals is studied for which a characterization of the set of equilibrium payoffs is obtained. Journal of Economic Literature Classification Numbers: C73.     

Balanced Contributions Axiom in the Solution of Cooperative Games

In a gamevin characteristic function form, suppose the Banzhaf value ψ is used to pay a coalitionSalready formed. Then coalitionSno longer receivesv(S); instead it receivesR^ψ(S) = ∑_{i ∈ S}ψ_i(v_s), wherev_Sdenotes the subgame of coalitionS. Surprisingly, the Shapley value of this new game Sh(N, R^ψ) is equal to the Banzhaf value ofv. In this paper we establish a similar result for all values satisfying balanced contributions axiom. Additionally, we introduce player's weights to obtain the corresponding result in the nonsymmetric case.Journal of Economic LiteratureClassification Number: C71     

Strong Equilibrium in Congestion Games

[6]introduced the class of congestion games and proved that they always possess a Nash equilibrium in pure strategies. Here we obtain conditions for the existence of a strong equilibrium in this class of games, as well as for the equivalence of Nash and strong equilibria. We also give conditions for uniqueness and for Pareto optimality of the Nash equilibrium. Except for a natural monotonicity assumption on the utilities, the conditions are expressed only in terms of the underlying congestion game form. It turns out that avoiding a certain type of bad configuration in the strategy spaces is essential to positive results.Journal of Economic LiteratureClassification Numbers: C71, C72, D62.     

Cost allocation in spanning network enterprises with stochastic connection costs

This paper considers the problem of network formation and cost allocation that arises when customers need to be connected to a single service provider through a (communication) network. The cost of a connection consists of both the construction costs and the maintenance costs. Since the latter costs are unknown ex ante connection costs are represented by random variables. It is shown how an ‘optimal’ network is determined and that the core of the corresponding stochastic spanning tree game is non-empty. A two stage Bird allocation is defined and shown to be a core allocation of stochastic spanning tree games.     

Associated consistency and equal allocation of nonseparable costs

Summary. We modified the definition of associated game with respect to Hamiache (2001) to characterize the equal allocation of nonseparable costs (EANS) by means of Pareto Optimality(PO), Translation Covariance (TC), Symmetry (SYM), Associated Consistency(AC) and Continuity(CONT).Received: 8 April 2004, Revised: 9 May 2005, JEL Classification Numbers: C71.The author is indebted to Clement Wen for many helpful comments and he is also very grateful to a referee who proposed several helpful comments to improve the paper.     

Gradualism in Bargaining and Contribution Games

This paper identifies a source of gradualism in bargaining and contribution games. In the bargaining games we examine, each party can opt out at any time, and the outside option outcome is assumed to depend on the offers made in the negotiation phase. Specifically, we assume that (1) making a concession in the negotiation phase increases the other party's outside option pay-off and (2) the outside option outcome induces an efficiency loss as compared with a negotiated agreement. The main finding is that the mere presence of such history-dependent outside options forces equilibrium concessions in the negotiation phase to be gradual, and the degree of gradualism is characterized. The model also applies to contribution games in which the outside option may be interpreted as the option to implement a partial project using the total contributions made so far.     

Games of Status

A status game is a cooperative game in which the outcomes are rank orderings of the players. They are a good model for certain situations in which players care about how their "status" compares with that of other players.
We present several formal models within this class. Included are authoritarian status games (where coalitions may assign positions in the rank ordering to nonmembers) and oligarchic status games (where they are unableto do so). We consider the issues of a value concept for authoritarian games and that of core existence for oligarchic games. We then add a transferable resource to the models, obtaining "games of wealth and status."
Finally, we consider an interesting variant, called a "secession game," where coalitions have the right to secede from the grand coalition and form their own smaller "subsocieties," each with its own hierarchy.     

Information and incentives in labor-managed economies

The incentive problems that result in labor-managed economies from attempting to eliminate the inefficient allocation of labor due to this institutional arrangement are discussed. Games are searched for such that, at an equilibrium, firms have revealed truthful information and labor is allocated efficiently. It is shown that such games do not exist if output is not observable, and even if aggregate deficits or surpluses are permitted. By contrast, if output is observable, balanced games exist in which it is dominant strategy for each firm to be truthful.     

A dual description of the class of games with a population monotonic allocation scheme

A vector of balanced weights infers an inequality that games with a nonempty core obey. This paper gives a generalization of the notion ‘vector of balanced weights.’ Herewith, it provides necessary and sufficient conditions to determine whether a TU-game has a population monotonic allocation scheme or not. Furthermore, it shows that every four-person integer valued game with a population monotonic allocation scheme has an integer valued population monotonic allocation scheme and it gives an example of a seven-person integer valued game that has only noninteger valued population monotonic allocation schemes.     

政府产业重组规划、信号博弈与企业兼并行为

文章以2009年我国腾中重工公司兼并通用公司"悍马"品牌为现实索引,为水平兼并不存在"整合效应"的负盈利资产提供两种基于信号博弈的理论解释.第一种解释基于限制性定价的思路,说明在成本信息不对称的企业进行产量竞争背景下和在一定的市场环境下,总会对应一定负盈利水平的资产,使得低成本类型企业宁愿选择收购非盈利资产,以向竞争者显示其成本类型而得益.另一种解释引入政府推进产业重组的因素,当高效重组不同成本类型企业的概率条件和资产负盈利水平满足一定条件时,存在使低成本类型企业选择收购非盈利资产,以避免在产业重组中可能被低效兼并的分离均衡.     

Assignment Games Satisfy the CoMa-Property

A balanced game satisfies the CoMa-property if and only if the extreme points of its core are marginal vectors. In this note we prove that assignment games satisfy the CoMa-property. Journal of Economic Literature Classification Numbers: C71, C78.