Axiomatizations of the normalized Banzhaf value and the Shapley value

A cooperative game with transferable utilities– or simply a TU-game – describes a situation in which players can obtain certain payoffs by cooperation. A solution concept for these games is a function which assigns to every such a game a distribution of payoffs over the players in the game. Famous solution concepts for TU-games are the Shapley value and the Banzhaf value. Both solution concepts have been axiomatized in various ways. An important difference between these two solution concepts is the fact that the Shapley value always distributes the payoff that can be obtained by the `grand coalition' consisting of all players cooperating together while the Banzhaf value does not satisfy this property, i.e., the Banzhaf value is not efficient. In this paper we consider the normalized Banzhaf value which distributes the payoff that can be obtained by the `grand coalition' proportional to the Banzhaf values of the players. This value does not satisfy certain axioms underlying the Banzhaf value. In this paper we introduce some new axioms that characterize the normalized Banzhaf value. We also provide an axiomatization of the Shapley value using similar axioms. Received: 10 April 1996 / Accepted: 2 June 1997     

Going to Pieces: Paul Monette and the Fragments of the Tribe

Author of the highly acclaimed Borrowed Time: An AIDS Memoir (1988) and winner of the 1992 National Book Award for his autobiography Becoming a Man: Half a Life Story, Paul Monette died of complications from AIDS in Los Angeles on February 12, 1995. His most recent work, Last Watch of the Night: Essays Too Personal and Otherwise (1994), is his third volume in a trilogy of autobiographical writing on growing up gay, coming-out, and living with AIDS. A graduate of Phillips Academy and Yale University, Monette received a number of awards for his writing and his work as an outspoken voice in the battle against AIDS, including the National Book Award, three Lambda Literary awards, the PEN Center West Freedom to Write Award, and three honorary doctorate degrees, from Wesleyan University, the City University of New York, and the State University of New York at Oswego. A memorial service was held for Monette on Sunday, February 19, 1995, at the Directors Guild of America on Sunset Boulevard in Los Angeles. Paul Monette was 49.     

Hospital-sponsored networks. The rush to consolidate and the future of medical practice

As the medical delivery system undergoes fundamental change, there is a growing pressure on hospitals to form networks with physicians. The prime motivation for these entities is to preserve market share and fill beds. There is likewise intense pressure on physicians to join them, even if these networks do not serve their best interests, or the goal of fostering physician-centered practice. A transformation is under way, however, that may well place doctors again in the central role of guiding the new modes of medical practice in the United States.     

Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem

In the binary single constraint Knapsack Problem, denoted KP, we are given a knapsack of fixed capacity c and a set of n items. Each item j, j = 1,...,n, has an associated size or weight w_j and a profit p_j. The goal is to determine whether or not item j, j = 1,...,n, should be included in the knapsack. The objective is to maximize the total profit without exceeding the capacity c of the knapsack. In this paper, we study the sensitivity of the optimum of the KP to perturbations of either the profit or the weight of an item. We give approximate and exact interval limits for both cases (profit and weight) and propose several polynomial time algorithms able to reach these interval limits. The performance of the proposed algorithms are evaluated on a large number of problem instances.     

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Dual Career Couples als eine Variante von Work-Life-Integration

Dual Career Couples as a form of work-life-integrationThe author discusses the situation of dual career couples, when both are university graduates following an own career. Basing on a respective publication she delineates the current, mostly American research and reports on several German research projects, which endeavour to analyse the relation between gender and inequality in dual career couples.     

Von der Supervision zur Mediation und zurück

From supervision to mediation and vice versaMediation in organizations becomes more and more important because of increasing conflicts. The question is, which competencies of the counsellor are necessary, and above all, whether mediation is a particular method. The author explains the method of mediation and illustrates his concept of “patchwork-mediation”. This procedure allows to build a bridge between supervision and mediation.     

Ebert. Wolfgang (2001): Systemtheorien in der Supervision — Bestandsaufnahme und Perspektiven

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