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In this paper, we introduce situations involving the linear transformation of products (LTP). LTP situations are production situations where each producer has a single linear transformation technique. First, we approach LTP situations from a (cooperative) game theoretical point of view. We show that the corresponding LTP games are totally balanced. By extending an LTP situation to one where a producer may have more than one linear transformation technique, we derive a new characterization of (nonnegative) totally balanced games: each totally balanced game with nonnegative values is a game corresponding to such an extended LTP situation. The second approach to LTP situations is based on a more economic point of view. We relate (standard) LTP situations to economies in two ways and we prove that the economies are standard exchange economies (with production). Relations between the equilibria of these economies and the cores of cooperative LTP games are investigated. 相似文献
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Jeroen Suijs Peter Borm Herbert Hamers Marieke Quant Maurice Koster 《Annals of Operations Research》2005,137(1):117-140
This paper focuses on sharing the costs and revenues of maintaining a public network communication structure. Revenues are
assumed to be bilateral and communication links are publicly available but costly. It is assumed that agents are located at
the vertices of an undirected graph in which the edges represent all possible communication links. We take the approach from
cooperative game theory and focus on the corresponding network game in coalitional form which relates any coalition of agents
to its highest possible net benefit, i.e., the net benefit corresponding to an optimal operative network. Although finding
an optimal network in general is a difficult problem, it is shown that corresponding network games are (totally) balanced.
In the proof of this result a specific relaxation, duality and techniques of linear production games with committee control
play a role. Sufficient conditions for convexity of network games are derived. Possible extensions of the model and its results
are discussed.
The research of Jeroen Suijs has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. 相似文献
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