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Summary: Marginalist and efficient values for TU games
Anna B. Khmelnitskaya
St.Petersburg Institute for Economics and Mathematics Russian Academy of Sciences,
Tchaikovsky st. 1, 191187 St.Petersburg, RUSSIA
Abstract
We derive an explicit formula for a marginalist and efficient value for TU game which
possesses the null-player property and is either continuous or monotonic. We show that
every such a value has to be additive and covariant as well. It follows that the set of all
marginalist, efficient, and monotonic values possessing the null-player property coincides
with the set of random-order values, and thereby the last statement provides an axiom-
atization without the linearity axiom for the latter which is similar to that of Young for
the Shapley value. Another axiomatization without linearity for random-order values is
provided by marginalism, efficiency, monotonicity, and covariance.
Keywords: Transferable utility game; Value; Axiomatic characterization; Efficiency; Mar-
ginalism
Anna B.Khmelnitskaya
Department of Game Theory and Decision Making,
St.Petersburg Institute for Economics and Mathematics Russian Academy of Sciences,
Tchaikovsky st. 1, 191187 St.Petersburg, RUSSIA
Fax: +7 (812) 273 7953
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