Abstract
A power index provides a reliable forecast of the expected division of power in a committee, where the “weights” of the participants are known. Among the numerous indices, the most well known and applied are those of Shapley-Shubik and Banzhaf-Coleman. Interesting applications of power indices are found when it is necessary to study what variations in the index of a certain player would be produced by changes in his weight. For example, in finance, a shareholder can evaluate the outcome of a potential take-over bid, by knowing a priori how the configuration of a major shareholding would change. He could also estimate how his controlling position would change, if he were to buy a block of shares from another major shareholder.
This paper extends an existing algorithm for the computation of the variations of the Shapley-Shubik index in the above quoted cases, to the Banzhaf-Coleman index, and consequently provides a rapid method for the calculation of the latter.
This paper has been jointly financed by MURST (40 and 60 percent) and Committee 10 of C.N.R. The author would like to thank Barbara Botti, Stefania Mercanti and Sonia Mora for their contributions.
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Gambarelli, G. (1996). Takeover Algorithms. In: Bertocchi, M., Cavalli, E., Komlósi, S. (eds) Modelling Techniques for Financial Markets and Bank Management. Contributions to Management Science. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-51730-3_13
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DOI: https://doi.org/10.1007/978-3-642-51730-3_13
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