Convex vNM-Stable Sets for a Semi Orthogonal Game. Part II: Rich Central Commodity

Abstract

This paper constitutes the second part in a series dealing with vNM-Stable sets for (cooperative) linear production games with a continuum of players, see J. Rosenmuller, Convex vNM–Stable Sets for a Semi Orthogonal Game. Part I: epsilon–Relevant Coalitions [IMW Working Paper no. 483 (2013)]. The coalitional function is generated by r 1 “production factors” (non atomic measures). R factors are given by orthogonal probabilities (“cornered” production factors) while factor r 1^th is provided “across the corners” of the market. We consider convex vNM-Stable Sets of this game. Within the second part we present an economy reflecting relative abundance of the “central” commodity. In this situation the model allows for a vNM-Stable Set including but not equal to the core of the game. Rather there is an additional imputation such that the vNM-Stable Set is the convex hull of this imputation and the core. This imputation is essentially described by the density of the r 1^st production factor – mutatis mutandis.