The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure

The Shapley value assigns, to each game that is adequately represented by its characteristic function, an outcome for each player. An elaboration on the Shapley value that assigns, to characteristic function games, a “partition function” outcome is broadly established and accepted, but elaborations to encompass games with externalities (represented by partition functions) are not. Here, I show that simultaneous consideration of the two elaborations (“generalization” and “extension”) obtains a unique Shapley-type value for games in partition function form. The key requirement is that the “Extended, Generalized Shapley Value” (EGSV) should be “recursive”: the EGSV of any game should be the EGSV of itself. This requirement forces us to ignore all but the payoffs to bilateral partitions. The EGSV can be conceptualized as the ex ante value of a process of successive bilateral amalgamations. Previous Shapley value extensions, if generalized, are not recursive; indeed, they iterate to the EGSV.     

Sharing the surplus: An extension of the Shapley value for environments with externalities

Economic activities, both on the macro and micro level, often entail wide-spread externalities. This in turn leads to disputes regarding the compensation levels to the various parties affected. We propose a method of deciding upon the distribution of the gains (costs) of cooperation in the presence of externalities when forming the grand coalition is efficient. We show that any sharing rule satisfying efficiency, linearity, dummy player and a strong symmetry axioms can be obtained through an average game. Adding an additional axiom, we identify one unique rule satisfying these properties.     

Potential,value, and random partitions

We provide a new interpretation of the potential of the Shapley value as the expected worth of some random partition of the player set. Using this insight, we advocate the potential as an index of power concentration in simple monotonic games.     

Equivalence and axiomatization of solutions for cooperative games with circular communication structure

We study cooperative games with transferable utility and limited cooperation possibilities. The focus is on communication structures where the set of players forms a circle, so that the possibilities of cooperation are represented by the connected sets of nodes of an undirected circular graph. Single-valued solutions are considered which are the average of specific marginal vectors. A marginal vector is deduced from a permutation on the player set and assigns as payoff to a player his marginal contribution when he joins his predecessors in the permutation. We compare the collection of all marginal vectors that are deduced from the permutations in which every player is connected to his immediate predecessor with the one deduced from the permutations in which every player is connected to at least one of his predecessors. The average of the first collection yields the average tree solution and the average of the second one is the Shapley value for augmenting systems. Although the two collections of marginal vectors are different and the second collection contains the first one, it turns out that both solutions coincide on the class of circular graph games. Further, an axiomatization of the solution is given using efficiency, linearity, some restricted dummy property, and some kind of symmetry.     

Non-manipulable division rules in claim problems and generalizations

When resources are divided among agents, the characteristics of the agents are taken into consideration. A simple example is the bankruptcy problem, where the liquidation value of a bankrupt firm is divided among the creditors based on their claims. We characterize division rules under which no group of agents can increase the total amount they receive by transferring their characteristics within the group. By allowing agents’ characteristics to be multi-dimensional and choosing the meaning of variables appropriately, our model can subsume a number of existing and new allocation problems, such as cost sharing, social choice with transferable utilities, income redistribution, bankruptcy with multiple types of assets, probability updating, and probability aggregation. A number of existing and new results in specific problems are obtained as corollaries.     

A comparison between the core and the monopoly solutions in a mixed exchange economy

Summary. Using a mixed market model for analyzing imperfectly competitive economies, we maximize the oligopolists' Welfare Function, given individual rationality and feasibility constraints. We prove that solutions belong to the core for a large class of economies. This class includes, in particular, every monopoly having a single type of small traders. Note that all such solutions yield the large trader, utility-wise, strictly more than at any monopoly solution, where the monopolist plays strategically, and the ocean of small traders act as being as price-takers. Received: March 4, 1996; revised version July 7, 1996     

The museum pass game and its value

We discuss a game in which service providers (e.g., museums) team up in offering a limited time access pass allowing unlimited usage of their services. In this game, a natural way to allocate the joint income from the sale of passes among the service providers is by using the Shapley value. We show that, for the particular game considered, the Shapley value takes a very intuitive and computationally simple form.     

Market games with differential information and infinite dimensional commodity spaces: The core

Summary We provide an alternative proof of the existence of core allocations in exchange economies with differential information and infinite dimensional commodity spaces. We also identify a critical feature of information sharing rules that ensures nonemptiness of the core. In essence, the only condition we require on the sharing rules is that profitable insider trading be prohibited. In the absence of insider trading, balancedness is guaranteed and core nonemptiness follows.I thank Dan Arce, Erik Balder, Myrna Wooders, and Nicholas Yannelis for helpful comments. This paper is a greatly revised version of my paper entitled. A Variational Problem Arising in Market Games with Differential Information, written in August of 1991.     

Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms

There is a wide range of economic problems that involve the exchange of indivisible goods with no monetary transfers, starting from the housing market model of the seminal paper by Shapley and Scarf (1974) to problems such as the kidney exchange or the school choice problem. The classical solution to many of these models is to apply a mechanism called Top Trading Cycles, attributed to David Gale, which satisfies good properties for the case of strict preferences. In this paper, we propose a family of mechanisms, called Top Trading Absorbing Sets mechanisms, which generalize the Top Trading Cycles to the general case in which individuals are allowed to report indifferences, while preserving a maximal possible set of its desirable properties.     

Virtual utility and the core for games with incomplete information

The core is extended to games with incomplete information. The feasible set is characterized by incentive-compatible mechanisms. Blocking is organized at the interim stage by an incentive-compatible mediation plan. Membership of the blocking coalition itself may be determined randomly by the blocking mediator. Nonemptiness of an interim fine core is proven for games with a balanced structure, independent types, and sidepayments. An offer of severance payments may be needed to inhibit blocking. Core allocations are characterized in terms of virtual-utility scales that generalize the weighted-utility scales of the inner core. Mechanisms that achieve core allocations are coalitionally durable.     

Symmetry-based compromise and the Nash solution to convex bargaining problems

A new axiom, symmetry-based compromise, is introduced to study solutions to convex bargaining problems. It is shown that any efficient solution that is also scale invariant and satisfies symmetry-based compromise must be Nash.     

Linear efficient and symmetric values for TU-games: Sharing the joint gain of cooperation

Recently, Hermandez-Lamoneda et al. (2008) and independently Chameni and Andjiga (2008) gave an analytic formulation for all valued solutions to the n-person TU-games that satisfy linearity, efficiency and symmetry axioms. Our main purpose in this paper is to recast the proposed formulation to a more potentially interpretational one. We are focused on an interpretation based on the idea of marginal contribution, a concept already familiar in the Shapley value and the Solidarity value. A general null player axiom is introduced, and it turns out that any valued solution satisfying the three properties is characterized by a null player model.     

The weak core of simple games with ordinal preferences: implementation in Nash equilibrium

In a simple game, coalitions belonging to a given class are “absolutely powerful” while others have no power. We attempt to make this distinction operational. Toward this end, we propose two axioms on social choice correspondences, Strong Non-Discrimination and Exclusion. Strong Non-Discrimination describes circumstances under which certain coalitions, the losing coalitions, have no influence over social choice. Exclusion requires that there are situations in which certain coalitions, the winning coalitions, can exercise their power. We show that the weak core correspondence is the minimal correspondence satisfying Maskin Monotonicity and Strong Non-Discrimination. We also show that the weak core is the unique correspondence satisfying Nash implementability, Strong Non-Discrimination, and Exclusion.     

股东与经理人风险态度偏差所引发代理成本的抵减--EVA调整事项必要性的一个定量化解释

EV A调整事项是EVA区别于R I(R esidualIncom e)的重要标志,也是EV A倡导者所宣传的EV A重要“卖点”。在理论界,调整事项必要性的争论一直存在;在实务界,推行EV A管理模式的企业对待调整事项也是千差万别。本文有别于一般的研究思路,在构筑股东和经理人投资决策模型的基础上、在股东与经理人风险态度不一的假设下,采用数理推导的办法来论证EV A调整事项存在的必要性。本文的研究表明,由于经理人相对股东更容易回避风险,在投资项目的选择上,往往会放弃收益率小于经理人最低要求报酬率、但是N PV却大于零的投资项目,这样就损害了股东的利益,加大了代理成本。EV A调整事项使得费用(成本)的确认时间向后推移,从而能够产生对股东和经理人因风险态度偏差而引发代理成本的一种递减作用,保护股东的利益。     

Coordination on saddle-path solutions: the eductive viewpoint—linear multivariate models

We examine local strong rationality (LSR) in multivariate models with both forward-looking expectations and predetermined variables. Given hypothetical common knowledge restrictions that the dynamics will be close to those of a specified minimal state variable solution, we obtain eductive stability conditions for the solution to be LSR. In the saddlepoint stable case the saddle-path solution is LSR provided the model is structurally homogeneous across agents. However, the eductive stability conditions are strictly more demanding when heterogeneity is present, as can be expected in multisectoral models. Heterogeneity is thus a potentially important source of instability even in the saddlepoint stable case.     

Relationship between management ownership and firm value among the business group affiliated firms in Korea

In this paper, we revisit an old issue on the relation between management ownership and firm’s value. The Korean panel data on the business group firms, allows us to compute ownership right and control right separately for each business group affiliated firm. Our measures are different from the similar measures on the Korean firms as in Baek et al. (2004) or Joh (2003). Rather than confounding the two offsetting effects, this paper tests convergence of interest hypothesis and entrenchment hypothesis separately. Empirical findings show that, given control right, there is no clear-cut relation between firm value and the inside management ownership for most firms with the inside management ownership less than 42%, that there is a positive relation between firm value and the inside management ownership for those firms with the inside management ownership higher than 42%, and that, given ownership right, profitability decreases as control right increases.     

The treatment effect, the cross difference, and the interaction term in nonlinear “difference-in-differences” models

In any nonlinear “difference-in-differences” model with strictly monotonic transformation function, the treatment effect is the cross difference of the observed outcome minus the cross difference of the potential non-treatment outcome, which equals the incremental effect of the interaction term coefficient.     

浅析传统成本法与作业成本法的区别与联系

由于企业的竞争日趋激烈,一种能够有效控制成本的作业成本法应运而生.在西方国家,作业成本法得到了良好的实施并取得了一定的成效.本文分析了作业成本法与传统成本法的区别和联系,作业成本法从根本上解决了传统成本法的缺陷.以作业为基础的成本计算是成本会计科学发展的大趋势,在我国研究与推广作业成本法有着重大的理论与现实意义.