dr. Irinel DRAGAN
Professor of Mathematics
Department of Mathematics, University of Texas at Arlington
Arlington, Texas
S.U.A.
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Average per capita formulas for Shapley values and semivalues
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ABSTRACT
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We introduce by an example the classical problem of fairly dividing the
worth of the grand coalition. The Shapley value is one of the most
popular solution. In 1981, Dubey-Neyman-Weber introduced axiomatically
the Semivalues, which satisfy some of the axioms of the Shapley value,
but the efficiency is lost. In 1992, we proved a so called Average per
capita formula, which allows a parallel computation of the Shapley
value. For a Semivalue we proved a similar formula in a joint paper with
Martinez-Legaz, (2001), from which a similar algorithm can be derived.
In the presentation, after introducing the two types of values, we show
that the computation of the Semivalues by means of a Shapley value is
possible. In fact, the Efficient normalization of a Semivalue is the
Shapley value of a game obtained by rescaling from the given game. This
is proved by means of the Average per capita formulas. Then, the
Semivalue is reduced to the Shapley value by adding an additive game to
the rescaled game. This gives another method for computing the
Semivalues. What we call the Inverse problem can benefit from this
relationship.
          
SHORT CV
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Dr.Irinel Dragan is Professor of Mathematics at Department of Mathematics, 
University of Texas at Arlington, Texas, USA.
His research focuses on Algebra, Geometry, and Game Theory. 
Dr.Dragan held a research and teaching position at 
University Al. I. Cuza (Iasi, Romania), 
Faculty of Mathematics until 1980. Dr.Dragan completed his PhD in 1961 at the 
University Al. I. Cuza (Iasi, Romania).