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This paper makes the point on a well known property of capital allocation rules, namely the
one called no-undercut. Its desirability in capital allocation stems from some stability game theoretical
features related to the notion of core, both for finite and infinite games. We review these aspects,
by relating them to the properties of the risk measures involved in capital allocation problems. We
also discuss some problems and possible extensions arising when we deal with non-coherent risk
measures
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