The inner core and the strictly inhibitive set
type: Item
instance of: scholarly article
title: The inner core and the strictly inhibitive set
zbMATH Open document ID: 0813.90139
published in: Journal of Economic Theory
publication date: 1993-06-29T00:00:00Z
review text: The relation between the inner core and the strictly inhibitive set is explored. Let \(G= (N, V)\) denote a game in characteristic function form where \(N\) is the (finite) set of agents and \(V\) is a map from the set of subsets \(S\) of \(N\) into \(R^ s\). \(V(S)\) stands for the set of (non transferable) payoff vectors members of the coalition \(S\) can achieve for themselves. A game \(G\) is compactly (resp. convexly) generated if it can be represented in a form \((N, F)\) where each \(F(S)\) is compact (resp. convex). It is also called polyhedral if each \(F(S)\) is a compact polyhedron. \(S\) is a blocking coalition against a payoff vector \(u\) in \(V(N)\) if there is \(u'\) in \(V(S)\) s.t. \(u_ i'> u_ i\), all \(i\) in \(S\). The core is the set of all payoff vectors in \(V(N)\) against which there is no blocking coalition. Given a point \(\lambda\) in the simplex in \(R^ N\), \(H^ S_ \lambda= \{u'\in R^ S\mid \lambda^ S\cdot u'= 0\}\) denotes the set of utility transfers possible according to the exchange rates in \(\lambda^ S\), the projection of \(\lambda\) in the coordinates of \(S\). \(G_ \lambda\) denotes the game with utility transfers according to \(\lambda\), derived from \(G\), denoted by \((N, V_ \lambda)\) where \(V_ \lambda\) is defined by \(V_ \lambda(S)= V(S)+ H^ S_ \lambda\) for each \(S\subseteq N\). The inner core of a compactly generated game \(G\) is defined as the set of payoff vectors \(u\) s.t., for some \(\lambda\), \(u\) is in the core of \(G_ \lambda\). A randomized blocking plan is denoted by a pair of functions \((p, w)\) defined on the set of all subsets of \(N\). \(p(S)\geq 0\) for all \(S\subseteq N\) and \(\sum_{S\subseteq N} p(S)= 1\). \(p(S)\) represents the probability that a mediator will make \(S\) a blocking coalition. \(W(S)\in V(S)\) for each \(S\) and is the payoff vector that members of \(S\) would get if they did form a blocking coalition. A payoff vector \(U\) is strictly blocked by a randomized blocking plan \((…
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 222134
zbMATH Keywords: inner core
zbMATH Keywords: strictly inhibitive set
zbMATH Keywords: blocking coalition
zbMATH Keywords: compactly generated game
zbMATH Keywords: randomized blocking plan
zbMATH Keywords: polyhedral games
zbMATH Keywords: dynamic matching process
author: Cheng-Zhong Qin
MaRDI profile type: Publication
full work available at URL: jeth.1993.1006
OpenAlex ID: W2095530470
DOI: 10.1006/JETH.1993.1006
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description: scientific article; zbMATH DE number 222134