We prove that the Burkill-Cesari integral i.e. the refinement derivative of Epstein-Marinacci at the empty set, is a value on a subspace of $AC$. Through this, we define a value on a subspace of $AC$ which strictly contains pNA. We discuss the continuity of our operator both w.r.t. the BV and the Lipschitz norm. As a consequence we provide and an existence result of a Lipschitz continuous value, different from the Aumann and Shapley's one, on a subspace of $AC_\infty$.
The Burkill-Cesari integral on spaces of absolutely continuous games
MARTELLOTTI, Anna
2014
Abstract
We prove that the Burkill-Cesari integral i.e. the refinement derivative of Epstein-Marinacci at the empty set, is a value on a subspace of $AC$. Through this, we define a value on a subspace of $AC$ which strictly contains pNA. We discuss the continuity of our operator both w.r.t. the BV and the Lipschitz norm. As a consequence we provide and an existence result of a Lipschitz continuous value, different from the Aumann and Shapley's one, on a subspace of $AC_\infty$.File in questo prodotto:
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