On the predictive efficiency of the core solution in side-payment games

This paper reports the first cross-study competitive test of thecore solution in side-payment games where the core is nonempty and nonunique (i.e., larger than a single point). The core was tested against five alternative theories including the Shapley value, the disruption nucleolus, the nucleolus, the 2-center, and the equality solution. A generalized Euclidean distance metric which indexes the average distance between an observed payoff vector and the entire set of predicted payoff vectors (Bonacich, 1979) was used as the measure of goodness-of-fit. Analysis of data assembled from six previously reported studies (encompassing a total of 1,464 observations over 56 3-person and 4-person side-payment games) showed the core to predict less accurately than the Shapley value, disruption nucleolus, and nucleolus solutions (p < 0.01). These findings are consistent with previous empirical results that show the core to have a low level of predictive accuracy in side-payment games.This research was supported by grants SOC-7726932 and SES-8015528 from the National Science Foundation. Data analysis was performed at the Madison Academic Computing Center.     

Procedural and optimization implementation of the weighted ENSC value

The main purpose of this article is to introduce the weighted ENSC value for cooperative transferable utility games which takes into account players’ selfishness about the payoff allocations. Similar to Shapley’s idea of a one-by-one formation of the grand coalition [Shapley (1953)], we first provide a procedural implementation of the weighted ENSC value depending on players’ selfishness as well as their marginal contributions to the grand coalition. Second, in the spirit of the nucleolus [Schmeidler (1969)], we prove that the weighted ENSC value is obtained by lexicographically minimizing a complaint vector associated with a new complaint criterion relying on players’ selfishness.

     

A test of the characteristic function and the Harsanyi function in N-person normal form sidepayment games

This paper reports the results of a laboratory experiment investigating sidepayment games represented in normal form. Attempts to predict payoff allocations via the application of solution concepts (such as the Shapley value or the nucleolus) encounter a problem in games of this form, because the game must first be transformed into some other form. Commonly, this other form is a set function defined over coalitions, such as the von Neumann-Morgenstern characteristic function. Because there are numerous possible transformations, the question arises as to which one provides the most accurate basis for prediction of payoffs.The laboratory experiment tested three such transformations - the mixed strategy characteristic function, the pure strategy characteristic function, and the Harsanyi threat function. Payoff predictions from two solution concepts (Shapley value, nucleolus) were computed on the basis of each of these transformations, making a total of six theories under test.Results of the study show, in general, that payoff predictions based on the Harsanyi threat function and on the mixed strategy characteristic function were more accurate than those based on the pure strategy characteristic function. The most accurate theories were the Shapley value computed from the Harsanyi function, the nucleolus computed from the Harsanyi function, and the Shapley value computed from the mixed strategy characteristic function. Less accurate were the nucleolus computed from the mixed strategy characteristic function and both the nucleolus and the Shapley value computed from the pure strategy characteristic function.This research was supported by grants SOC-7726932 and SES-8319322 from the National Science Foundation. The authors express appreciation to Yat-Tuck See, Jyh-Jen Horng Shiau, and Raymond Wong for assistance in computer programming, and to Jennifer Brandt, Young C. Choi, David C. Dettman, Laurel Dettman, Stephen B. Geisheker, Irving J. Ginsberg, Mike P. Griffin, Kimberly Ihm, Todd Isaacson, Christy Kinney, Mary Kohl, Sue Pope, Tammy Schmieden, Jill Schwarze, Susan Winter, and Kenneth Yuen for assistance in data collection and analysis.     

Three-valued simple games

In this paper we study three-valued simple games as a natural extension of simple games. We analyze to which extent well-known results on the core and the Shapley value for simple games can be extended to this new setting. To describe the core of a three-valued simple game we introduce (primary and secondary) vital players, in analogy to veto players for simple games. Moreover, it is seen that the transfer property of Dubey (1975) can still be used to characterize the Shapley value for three-valued simple games. We illustrate three-valued simple games and the corresponding Shapley value in a parliamentary bicameral system.     

Evaluating Cooperative Game Theory in water resources

Two empirical applications of Cooperative Game Theory concerned with regional cooperation in the use of irrigation water are presented. Both studies attempt to derive income maximizing solutions for the participants and the related income allocation schemes. Distinction is made between transferable and non-transferable utility situations. The reasonableness and the acceptability of the schemes derived are later critically evaluated. Main findings are: (1) use of utility functions leads to problems in gains allocations, (2) the Core concept may be useless in this application because since it is either difficult to calculate or is empty in many cases, (3) gains allocation and the derived core are heavily dependent on probabilities of coalitions formation in the Shapley value or the Generalized Shapley Value.During the course of this research in The Hebrew University of Jerusalem.On leave from The Hebrew University of Jerusalem.     

Cooperative provision of indivisible public goods

A community faces the obligation of providing an indivisible public good that each of its members is able to provide at a certain cost. The solution is to rely on the member who can provide the public good at the lowest cost, with a due compensation from the other members. This problem has been studied in a non-cooperative setting by Kleindorfer and Sertel (J Econ Theory 64:20–34, 1994). They propose an auction mechanism that results in an interval of possible individual contributions whose lower bound is the equal division. Here, instead we take a cooperative stand point by modelling this problem as a cost sharing game that turns out to be a ‘reverse’ airport game whose core is shown to have a regular structure. This enables an easy calculation of the nucleolus that happens to define the upper bound of the Kleindorfer–Sertel interval. The Shapley value instead is not an appropriate solution in this context because it may imply compensations to non-providers.     

Choices Under Ambiguity With Familiar And Unfamiliar Outcomes

This paper considers a decision-making process under ambiguity in which the decision-maker is supposed to split outcomes between familiar and unfamiliar ones. She is assumed to behave differently with respect to unfamiliar gains, unfamiliar losses and customary (familiar) outcomes. In particular, she is supposed to be pessimistic on gains, optimistic on losses and ambiguity neutral on the familiar outcomes. A generalization of the usual Choquet Integral is formalized when the decision maker holds capacities and probabilities. A characterization of the decision-maker’s behavior is provided for a specific subset of capacities, in which it is shown that the decision-maker underestimates the unfamiliar outcomes while is linear in probabilities on customary ones.     

Constrained egalitarianism in a simple redistributive model

The paper extends a result in Dutta and Ray's (1989) theory of constrained egalitarianism initiated by relying on the concept of proportionate rather than absolute equality. We apply this framework to redistributive systems in which what the individuals get depends on what they receive or pay qua members of generally overlapping groups. We solve the constrained equalization problem for this class of models. The paper ends up comparing our solution with the alternative solution based on the Shapley value, which has been recommended in some distributive applications.     

Quasi stable outcomes in the assignment game

There is a great deal of literature on matching, theoretical, and empirical, concerning stable assignments and mechanisms that achieve them. The starting point of this study is an interesting question about assignment procedures: given a situation where some agents (the senior workers) on one side have a priority status, which changes the classical theory. The core of game may not be stable. We prove the existence of a quasi stable constrained core. This constrained core may not be a lattice but it is a finite and disjoint union of complete lattices that check the properties of the core’s classical assignment game. We study the manipulability questions that derive.     

Estimating Merging Costs by Merger Preconditions

This article provides a method for estimating the bounds of transaction costs in horizontal mergers. Consider, for example, a completed monopoly merger in linear Cournot oligopolies with 10 symmetric firms. The method shows that its transaction costs are at most 25% (78%) of total premerger profits if there is zero (100%) excess capacity. Such estimations can be extended in a straightforward manner to other mergers and other oligopoly models. The estimation is based both on the profitability precondition, and on the non-empty core precondition, which postulates that the split of a merger’s profits be in its core. The article shows that the core in linear Cournot oligopolies has a non-empty interior, and indicates that the non-empty core precondition also sheds new lights on understanding important issues such as the stylized fact that mergers are likely to occur in markets plagued by excess capacities; why profitable mergers might not be formed; and why completed mergers might break up in the future.      

Population monotonic path schemes for simple games

A path scheme for a game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path. A path scheme is called population monotonic if a player’s payoff does not decrease as the path coalition grows. In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand. Obviously, each Shapley path scheme of a game is population monotonic if and only if the Shapley allocation scheme of the game is population monotonic in the sense of Sprumont (Games Econ Behav 2:378–394, 1990). We prove that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced. Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition. We also show that each Shapley path scheme of a simple game is population monotonic if and only if the set of veto players of the game is a winning coalition. Extensions of these results to other efficient probabilistic values are discussed.     

A Banzhaf share function for cooperative games in coalition structure

A cooperative game with transferable utility–or simply a TU-game– describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. In this paper we consider TU-games in which the players are organized into a coalition structure being a finite partition of the set of players. The Shapley value has been generalized by Owen to TU-games in coalition structure. We redefine this value function as a share function and show that this solution satisfies the multiplication property that the share of a player in some coalition is equal to the product of the Shapley share of the coalition in a game between the coalitions and the Shapley share of the player in a game between the players within the coalition. Analogously we introduce a Banzhaf coalition structure share function. Application of these share functions to simple majority games show some appealing properties.     

Digraph Competitions and Cooperative Games

Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided in terms of game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed.     

制度分析视角下的服务型政府建设

公正是社会制度的首要价值。作为公民导向型的治理模式,服务型政府将社会公正视为核心价值取向。制度是公正的保障。服务型政府的基本职能就在于制度供给,通过制度供给满足民众的社会需求。这种服务意识和公正理念的倡导,就要求进行制度创新。     

Hyperplane games,prize games and NTU values

The Shapley value is a well-known solution concept for TU games. The Maschler–Owen value and the NTU Shapley value are two well-known extensions of the Shapley value to NTU games. A hyperplane game is an NTU game in which the feasible set for each coalition is a hyperplane. On the domain of monotonic hyperplane games, the Maschler–Owen value is axiomatized (Hart Essays in game theory. Springer, 1994). Although the domain of hyperplane game is a very interesting class of games to study, unfortunately, on this domain, the NTU Shapley value is not well-defined, namely, it assigns an empty set to some hyperplane games. A prize game (Hart Essays in game theory. Springer, 1994) is an NTU game that can be obtained by “truncating” a hyperplane game. As such, a prize game describes essentially the same situation as the corresponding hyperplane game. It turns out that, on the domain of monotonic prize games, the NTU Shapley value is well-defined. Thus, one can define a value which is well-defined on the domain of monotonic hyperplane games as follows: given a monotonic hyperplane game, first, transform it into a prize game, and then apply the NTU Shapley value to it. We refer to the resulting value as the “generalized Shapley value” and compare the axiomatic properties of it with those of the Maschler–Owen value on the union of the class of monotonic hyperplane games and that of monotonic prize games. We also provide axiomatizations of the Maschler–Owen value and the generalized Shapley value on that domain.

     

论非核心价值体系对构建和谐社会的作用

社会价值体系有核心价值体系、非核心价值体系以及错误和腐朽思想。社会主义核心价值体系引领社会思潮,是一定的社会系统得以运转,一定的社会秩序得以维持的最基本的精神依托。而非核心价值体系的存在也是必然的,我们不能忽视它的作用。非核心价值体系的优秀资源可以丰富核心价值体系,例如,把传统价值观念加以改造,就能形成具有时代精神的价值观念。非核心价值是建设多元化社会发展的需要;也是保护文化多样性的需要,对构建和谐社会具有积极意义。     

Ambiguity and the value of information

The value of information is studied in a non-expected utility model of ambiguity with second-order probabilities. Information that reduces ambiguity has a positive value for ambiguity-averse decision makers, and the value of information that resolves ambiguity increases with greater ambiguity and with greater ambiguity aversion. Since information that resolves risk is valuable, and must also resolve ambiguity, the value of such information for ambiguity averters increases with greater ambiguity and with greater ambiguity aversion.     

Is the Disposition of Constrained Maximization Chosen Rationally?

One of the most important issues in moral philosophy is whether morality can be justified by rationality. The purpose of this study is to examine Gauthier’s moral theory, focusing on the disposition of constrained maximization, which is the main thrust of his project to justify morality rationally. First of all, I shall investigate Gauthier’s assumption and condition for the rationality of the disposition of constrained maximization so as to disclose that the disposition of constrained maximization is not necessarily chosen by rational agents. Then I shall explore his other arguments including ones for the reinterpretation of rationality and the self-critical reflection of rational beings, which can be considered as his further efforts to make the disposition of constrained maximization a rational choice. By exploring them, I shall attempt to indicate that those arguments are not valid so long as he clings to the maximizing conception of rationality and thereby this conception of rationality itself is not enough to provide morality with a basis.     

Class and gender inequalities in different types of welfare states: the Social Citizenship Indicator Program (SCIP)

Korpi W. Class and gender inequalities in different types of welfare states: the Social Citizenship Indicator Program (SCIP) Int J Soc Welfare 2010: ??: ??–??© 2010 The Author(s), Journal compilation © 2010 Blackwell Publishing Ltd and International Journal of Social Welfare. This article considers the role of legislated welfare state institutions as mediators of effects of political and structural forces on citizens' levels of living of relevance to inequalities in health and mortality. The focus is on institutional structures of welfare state programmes relevant to class inequality, as indicated by income inequalities, and to gender inequality, conceived of as differences in agency. I introduce the Social Citizenship Indicator Program, a database providing quantitative and qualitative information on structures of main social insurance programmes in 18 countries from 1930 to 2000, on about 300,000 data points. It is used to delineate types of distributive institutions of relevance for income inequality. Institutions relevant for gendered agency inequality affect choices by women, especially mothers, between unpaid and paid work. Driving forces behind the emergence of differences in distributive institutions are discussed, and patterns of class and gender inequalities are outlined.