The Component Fairness Solution for Cycle- Free Graph Games

In this paper we study cooperative games with limited cooperation possibilities, representedby an undirected cycle-free communication graph. Players in the game can cooperate if andonly if they are connected in the graph, i.e. they can communicate with one another. Weintroduce a new single-valued solution concept, the component fairness solution. Our solution is characterized by component efficiency and component fairness. The interpretationof component fairness is that deleting a link between two players yields for both resultingcomponents the same average change in payoff, where the average is taken over the players in the component. Component fairness replaces the axiom of fairness characterizing the Myerson value, where the players whose link is deleted face the same loss in payoff. Thecomponent fairness solution is always in the core of the restricted game in case the gameis superadditive and can be easily computed as the average of n specific marginal vectors,where n is the number of players. We also show that the component fairness solution canbe generated by a specific distribution of the Harsanyi-dividends.operations research and management science;

The Average Tree Solution for Cooperative Games with Communication Structure

We study cooperative games with communication structure, represented by an undirectedgraph. Players in the game are able to cooperate only if they can form a network in the graph. A single-valued solution, the average tree solution, is proposed for this class ofgames. Given the graph structure we define a collection of spanning trees, where eachspanning tree specifies a particular way by which players communicate and determines a payoff vector of marginal contributions of all the players. The average tree solution is defined to be the average of all these payoff vectors. It is shown that if a game has acomplete communication structure, then the proposed solution coincides with the Shapleyvalue, and that if the game has a cycle-free communication structure, it is the solutionproposed by Herings, van der Laan and Talman (2008). We introduce the notion of linkconvexity, under which the game is shown to have a non-empty core and the average tree solution lies in the core. In general, link-convexity is weaker than convexity. For games with a cycle-free communication structure, link-convexity is even weaker than super-additivity.operations research and management science;

Optimal provision of infrastructure using public-private partnership contracts

This paper deals with the optimal provision of infrastructure by means of public-private partnership contracts.In the economic literature infrastructure is characterized as a large, indivisible and non-rival capital good that produces services for its users.Users can be both consumers and producers. Consumers may derive utility from infrastructure, either indirectly, because it facilitates the use of some particular private good, or directly, because it is available for this facility.Examples are roads that facilitate the use of private cars, or computer systems facilitating the use of personal computers. Producers may use infrastructure as one of their production factors.The non-rivalness or nonexcludability of the infrastructure and the large costs to produce and maintain the infrastructure causes it to be a public good.On the other hand, infrastructure also possesses characteristics of a private commodity because it facilitates of the use of a complementary private commodity.Modern information-technological developments open new possibilities to eveal the need of individual users for a specific public infrastructure, by monitoring the private use they make of it.Consequently, a large part of the public financing of infrastructure can be privatised.That forms the base for public private partnerships to establish and maintain infrastructure.In this paper we discuss the design of an operational system to finance the costs of infrastructure.It will be shown that the system basically can result in an economically efficient level of infrastructure.The basic idea is that use of infrastructure is constrained by the availability of the infrastructure being provided.Therefore users who are hampered by too small a provision of the infrastructure are willing to pay for the use of infrastructure.

Transverse-Longitudinal Coupling by Space Charge in Cyclotrons

A method is presented that enables to compute the parameters of matched beams with space charge in cyclotrons with emphasis on the effect of the transverse-longitudinal coupling. Equations describing the transverse-longitudinal coupling and corresponding tune-shifts in first order are derived for the model of an azimuthally symmetric cyclotron. The eigenellipsoid of the beam is calculated and the transfer matrix is transformed into block-diagonal form. The influence of the slope of the phase curve on the transverse-longitudinal coupling is accounted for. The results are generalized and numerical procedures for the case of an AVF cyclotron are presented. The algorithm is applied to the PSI Injector II and Ring cyclotron and the results are compared to TRANSPORT.Comment: 8 pages, 2 figure

Religious people only live longer in religious cultural contexts: A gravestone analysis.

Religious people live longer than non-religious people according to a staple of social science research. Yet, are those longevity benefits an inherent feature of religiosity? To find out, we coded gravestone inscriptions and imagery in order to assess the religiosity and longevity of 6,400 deceased people from religious and non-religious U.S. counties. We show that in religious cultural contexts, religious people lived 2.2 years longer than did non-religious people. In non-religious cultural contexts, however, religiosity conferred no such longevity benefits. Evidently, a longer life is not an inherent feature of religiosity. Instead, religious people only live longer in religious cultural contexts where religiosity is valued. Our study answers a fundamental question on the nature of religiosity and showcases the scientific potential of gravestone analyses

Measuring the Power of Nodes in Digraphs

Many economic and social situations can be represented by a digraph. Both axiomatic and iterative methods to determine the strength or power of all the nodes in a digraph have been proposed in the literature. We propose a new method, where the power of a node is determined by both the number of its successors, as in axiomatic methods, and the powers of its successors, as in iterative methods. Contrary to other iterative methods, we obtain a full ranking of the nodes for any digraph. The new power function, called the positional power function, can either be determined as the unique solution to a system of equations, or as the limit point of an iterative process. The solution is also explicitly characterized. This characterization enables us to derive a number of interesting properties of the positional power function. Next we consider a number of extensions, like the positional weakness function and the position function.mathematical economics and econometrics ;

Socially Structured Games and Their Applications

In this paper we generalize the concept of a non-transferable utility game by introducing the concept of a socially structured game. A socially structured game is given by a set of players, a possibly empty collection of internal organizations on any subset of players, for any internal organization a set of attainable payoffs and a function on the collection of all internal organizations measuring the power of every player within the internal organization. Any socially structured game induces a non-transferable utility game. In the derived non-transferable utility game, all information concerning the dependence of attainable payoffs on the internal organization gets lost. We show this information to be useful for studying non-emptiness and refinements of the core.For a socially structured game we generalize the concept of π-balancedness to social stability and show that a socially stable game has a non-empty socially stable core. In order to derive this result, we formulate a new intersection theorem that generalizes the KKM-Shapley intersection theorem. The socially stable core is a subset of the core of the game. We give an example of a socially structured game that satisfies social stability, whose induced non-transferable utility game therefore has a non-empty core, but does not satisfy π-balanced for any choice of πThe usefulness of the new concept is illustrated by some applications and examples. In particular we define a socially structured game, whose unique element of the socially stable core corresponds to the Cournot-Nash equilibrium of a Cournot duopoly. This places the paper in the Nash research program, looking for a unifying approach to cooperative and non-cooperative behavior in which each theory helps to justify and clarify the other.microeconomics ;

Cooperative Games in Graph Structure

By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payoffs for each coalition that is a nonempty subset of the grand coalition of all players. It is well-known that balancedness is a sufficient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. For this result any information on the internal organization of the coalition is neglected.In this paper we generalize the concept of coalitional games and allow for organizational structure within coalitions. For a subset of players any arbitrarily given structural relation represented by a graph is allowed for. We then consider non-transferable utility games in which a possibly empty set of payoff vectors is assigned to any graph on every subset of players. Such a game will be called a cooperative game in graph structure or shortly graph game. A payoff vector lies in the core of the game if there is no graph on a group of players which can make all of its members better off.We define the balanced-core of a graph game as a refinement of the core. To do so, for each graph a power vector is determined that depends on the relative positions of the players within the graph. A collection of graphs will be called balanced if to any graph in the collection a positive weight can be assigned such that the weighted power vectors sum up to the vector of ones. A payoff vector lies in the balanced-core if it lies in the core and the payoff vector is an element of payoff sets of all graphs in some balanced collection of graphs. We prove that any balanced graph game has a nonempty balanced-core and therefore a nonempty core. We conclude by some examples showing the usefulness of the concepts of graph games and balanced-core. In particular these examples show a close relationship between solutions to noncooperative games and balanced-core elements of a well-defined graph game. This places the paper in the Nash research program, looking for a unifying theory in which each approach helps to justify and clarify the other.microeconomics ;

A General Existence Theorem of Zero Points

Let X be a non-empty, compact, convex set in R and an upper semi-continuous mapping from X to the collection of non-empty, compact, convex subsets in R. Its is well knwon that such a mapping has a stationary point in X, i.e. there exists a point in X satisfying that its image under has a non-empty intersection with the normal cone of X at the point. In case for every point in X it holds that the intersection of the image under with the normal cone of X at the point is either empty or contains the origin 0, then must have a zero point on X, i.e. there exists a point in X satisfying that 0 lies in the image of the point. Another well-known condition for the existence of a zero point follows from Ky Fan''s coincidence theorem, which says that if for every point in the intersection of the image with the tangent cone of X at the point is non-empty, the mapping must have a zero point. In this paper we extend all these existence results by giving a general zero point existence theorem, of which the two results are obtained as special cases. We also discuss what kind of solutions may exist when no further conditions are stated on the mapping . Finally, we show how our results can be used to establish several new intersection results on a compact, convex set.Economics ;