# Competitive outcomes and the inner core of NTU market games

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## Abstract

We consider the inner core as a solution concept for cooperative games with non-transferable utility (NTU) and its relationship to payoffs of competitive equilibria of *markets* that are induced by NTU games. An NTU game is an NTU market game if there exists a market such that the set of utility allocations a coalition can achieve in the market coincides with the set of utility allocations the coalition can achieve in the game. In this paper, we introduce a new construction of a market based on a closed subset of the inner core which satisfies a *strict positive separability*. We show that the constructed market represents the NTU game and, further, has the given closed set as the set of payoff vectors of competitive equilibria. It turns out that this market is not uniquely determined, and thus, we obtain a class of markets. Our results generalize those relating to competitive outcomes of NTU market games in the literature.

## Keywords

Market games NTU games Competitive payoffs Inner core## JEL Classification

C71 D51## Notes

### Acknowledgments

We are grateful for numerous interesting discussions with and comments from Jean-Marc Bonnisseau and Walter Trockel. Moreover, we would like to thank Herbert Dawid, Gaël Giraud, Claus-Jochen Haake, Carlos Hervés-Beloso, Tomoki Inoue, Enrico Minelli, Hans Peters and two anonymous referees for their suggestions and comments. Financial support through the International Research Training Group EBIM, the Institute of Mathematical Economics, the German Academic Exchange Service (DAAD) and the Franco-German University (DFH – UFA) is gratefully acknowledged. This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901). This research was mainly carried out at the Institute of Mathematical Economics, Bielefeld University, and the Centre d’Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, while being members of the International Research Training Group “Economic Behavior and Interaction Models” (EBIM) financed by the German Research Foundation (DFG) under contract GRK 1134/2. An earlier version has been part of the dissertation Brangewitz (2012) and Gamp (2012)

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