Abstract
In this paper, it is shown that both the Semivalues and the Least Square Values of cooperative transferable utilities games can be expressed in terms of n 2 averages of values of the characteristic function of the game, by means of what we call the Average per capita formulas. Moreover, like the case of the Shapley value earlier considered, the terms of the formulas can be computed in parallel, and an algorithm is derived. From these results, it follows that each of the two values mentioned above are Shapley values of games easily obtained from the given game, and this fact gives another computational opportunity, as soon as the computation of the Shapley value is efficiently done.
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Dragan, I. On the Semivalues and the Least Square Values Average Per Capita Formulas and Relationships. Acta Math Sinica 22, 1539–1548 (2006). https://doi.org/10.1007/s10114-005-0818-8
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DOI: https://doi.org/10.1007/s10114-005-0818-8