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  • 1
    Electronic Resource
    Electronic Resource
    Weighted Aumann-Shapley pricing (1998)
    Springer
    International journal of game theory 27 (1998), S. 511-523 
    Details
    ISSN: 1432-1270
    Keywords: Key words: Aumann-Shapley pricing ; cost allocation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. Cost allocation problems arise in many contexts in economics and management science. In a typical problem that we have in mind, a decision maker must decide how to allocate the joint cost of production among several commodities using prices. Furthermore, these prices must satisfy certain reasonable postulates among which is the requirement that total revenue associated with these prices must cover total cost. In this paper, we investigate a generalization of Aumann-Shapley pricing, called Weighted Aumann-Shapley pricing, that allows for asymmetric pricing of commodities even when those commodities affect costs in a symmetric fashion. Weighted AS pricing is a natural extension of (symmetric) Aumann-Shapley pricing, and may be considered a non-atomic analogue of Owen's modified diagonal formula (with respect to the multilinear extension) for the weighted TU Shapley Value.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001820050087
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Approximation theory for stochastic variational and Ky Fan inequalities in finite dimensions (1993)
    Springer
    Annals of operations research 44 (1993), S. 43-61 
    Details
    ISSN: 1572-9338
    Keywords: Variational inequality ; Ky Fan inequality ; monotone operator ; stochastic programming ; portfolio choice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The ideas of approximation and continuity have been extensively investigated both for optimization problems and variational inequalities. In this paper, we study approximation issues for a class of VIs, called Stochastic Variational Inequalities (SVIs), that arise, for example, in stochastic programming and portfolio choice problems. SVI problems are special cases of a more general class of problems that we will study first, called Stochastic Ky Fan Inequalities (SKFIs). We also analyze the role of monotonicity in the analysis of both SVIs and SKFIs. Our interest in these problems is motivated by recent research in the theory of portfolio choice for investors who are not classical expected utility maximizers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02073590
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  • 3
    Electronic Resource
    Electronic Resource
    An approach to the pricing of broadband telecommunications services (1993)
    Springer
    Telecommunication systems 2 (1993), S. 159-184 
    Details
    ISSN: 1572-9451
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, we describe two cost allocation methodologies which may be used to determine prices for a regulated telecommunications supplier offering heterogeneous services on a broadband network. Both methodologies can be characterized by sets of plausible axioms that one could argue should be satisfied by any pricing rule. One of the approaches leads to the Aumann-Shapley pricing rule, which is well known in the literature. The other approach leads to a pricing rule based on the Shapley value of a related cooperative game. While these approaches are similar in motivation, they differ in the technical requirements which must be imposed on the underlying cost function, and we argue that Shapley value pricing is more appropriate in a telecommunications context. We are able to explicitly determine Shapley value prices for customers who differ from one another in terms of their arrival rates, service rates, costs of lost work, and the number of simultaneous channels which they require.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02109856
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  • 4
    Electronic Resource
    Electronic Resource
    Reference functions and possibility theorems for cardinal social choice problems (1996)
    Springer
    Social choice and welfare 14 (1996), S. 65-78 
    Details
    ISSN: 1432-217X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Sociology , Economics
    Notes: Abstract.  In this paper, we provide axiomatic foundations for social choice rules on a domain of convex and comprehensive social choice problems when agents have cardinal utility functions. We translate the axioms of three well known approaches in bargaining theory (Nash 1950; Kalai and Smorodinsky 1975; Kalai 1977) to the domain of social choice problems and provide an impossibility result for each. We then introduce the concept of a reference function which, for each social choice set, selects a point from which relative gains are measured. By restricting the invariance and comparison axioms so that they only apply to sets with the same reference point, we obtain characterizations of social choice rules that are natural analogues of the bargaining theory solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003550050052
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  • 5
    Electronic Resource
    Electronic Resource
    Probabilistic value pricing (1996)
    Springer
    Mathematical methods of operations research 43 (1996), S. 73-95 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we consider the class of probabilistic value pricing mechanisms for cost allocation problems, which are related to probabilistic values for finite games with transferable utility. We characterize probabilistic value pricing axiomatically, as well as several related pricing mechanisms, including semivalue pricing (symmetric pricing without cost sharing), quasivalue pricing (cost sharing pricing without symmetry), and weighted Shapley value pricing. We also describe a class of problems in which (symmetric) Shapley value pricing coincides with Aumann-Shapley pricing, and a class of problems for which every quasivalue pricing mechanism is supportable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01303435
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  • 6
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    Approximation theory for stochastic variational and Ky Fan inequalities in finite dimensions (1993)
    Springer
    Details
    Publication Date: 1993-02-01
    Print ISSN: 0254-5330
    Electronic ISSN: 1572-9338
    Topics: Mathematics , Economics
    Published by Springer
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  • 7
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    Probabilistic value pricing (1996)
    Springer
    Details
    Publication Date: 1996-02-01
    Print ISSN: 1432-2994
    Electronic ISSN: 1432-5217
    Topics: Mathematics , Economics
    Published by Springer
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    PAPER CURRENT
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