Inheritance of Convexity for Partition Restricted

Alexandre Skoda ()
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Alexandre Skoda: Centre d'Economie de la Sorbonne, https://centredeconomiesorbonne.univ-paris1.fr

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

Abstract: A correspondence P associates to every subset A ? N a partition P(A) of A and to every game (N,v), the P-restricted game (N,vP) defined by vP(A) = ? (F ? P(A)) v(F) for all A ? N. We give necessary and sufficient conditions on P to have inheritance of convexity from (N,v) to (N,vP). The main condition is a cyclic intersecting sequence free condition. As a consequence, we only need to verify inheritance of convexity for unanimity games and for the small class of extremal convex games (N,vS) (for any Ø ? S ? N) defined for any A ? N by vS(A) = |A ? S | ? 1 if |A ? S | ? 1, and vs(A) = 0 otherwise. In particular when (N,v) corresponds to Myerson's network-restricted game inheritance of convexity can be verified by this way. For the Pmin correspondence (Pmin(A) is built by deleting edges of minimum weight in the subgraph GA of a weighted communication graph G, we show that inheritance of convexity for unanimity games already implies inheritance of convexity. Assuming only inheritance of superadditivity, we also compute the Shapley value of the restricted game (N,vP) for an arbitrary correspondence P

Keywords: communication network; cooperative game; restricted game; partitions (search for similar items in EconPapers)
JEL-codes: C6 C61 C7 C71 (search for similar items in EconPapers)
Pages: 33 pages
Date: 2016-05
New Economics Papers: this item is included in nep-gth
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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:16040

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