Competitive outcomes and the inner core of NTU market games

Weighted values and the core in NTU games

The purpose of this paper is to extend the following result by Monderer et al. (1992): the set of weighted Shapley values includes the Core in TU games. We extend the result to the class of uniformly positively smooth NTU games. We focus on two solution concepts which extend the weighted Shapley value. First, we focus on the weighted Egalitarian solution introduced by Kalai and Samet (1985). We...

New Conditions for Core Existence in Coalitional NTU Games*

Strong convexity of NTU games

In this paper, we provide an alternative definition of NTU convexity, strongly ordinal convexity. We show that if a game is strongly ordinal convex, then any marginal worth vector is in the core, and any marginal contribution is increasing. Some economic examples satisfy this convexity. KeywordsCooperative game; Convex game; NTU game; Core; Supermodularity JEL classification codes: C62; D52; D53

Fractional Solutions for NTU-Games

In this paper we survey some applications of Scarf’s Lemma. First, we introduce the notion of fractional core for NTU-games, which is always nonempty by the Lemma. Stable allocation is a general solution concept for games where both the players and their possible cooperations can have capacities. We show that the problem of finding a stable allocation, given a finitely generated NTU-game with c...

An Axiomatization of the Inner Core Using Appropriate Reduced Games

I adapt a reduction process introduced by Serrano and Volij (1998) so that the reduced games of convex-valued games are convex-valued. I use the corresponding consistency property and its converse to axiomatize the inner core for games that are convex-valued, non-level and smooth.