Abstract
The potential approach of value theory is extended with respect to a new characterizing property called conservation giving a clear interpretation of the potential. Many analogues between game theory and physics are presented. Particularly, there is a theorem of conservation of energy analogous to the highly important one in classical mechanics. Moreover, the Shapley-Value gets a new interpretation as the marginal contribution to a certain average in contrast to that as an average marginal contribution instead. The Banzhaf-Index can also be uniquely characterized by this approach. Finally, all results are extended to games with a continuum of players of finitely many types.
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Initiated in January 1995 at the Institute of Mathematical Economics, University of Bielefeld, 33501 Bielefeld, Germany
Thanks to the anonymous referee for helpful comments.
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Ortmann, K.M. Conservation of energy in value theory. Mathematical Methods of Operations Research 47, 423–449 (1998). https://doi.org/10.1007/BF01198404
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DOI: https://doi.org/10.1007/BF01198404