A Characterization of vNM-Stable Sets for Linear Production Games

We discuss linear production games or market games with a continuum of players which are represented as minima of finitely many nonatomic measures. Within this contex we consider vNM-Stable Sets according to von Neumann and Morgenstern. It is shown that we can classify or characterize all solutions of this type which are convex polyhedra, i.e., which are the convex hull of finitely many measures. We also compare this with the case of a finite game. For certain classes of glove games we optain a characterization also in the finite case using the results from the continuum.

Formation of cartels in glove markets and the modiclus

cartels;game theory

The endogenous formation of cartels

games;production;cartels

Stable cores in information graph games

In an information graph situation, a finite set of agents and a source are the set of nodes of an undirected graph with the property that two adjacent nodes can share information at no cost. The source has some information (or technology), and agents in the same component as the source can reach this information for free. In other components, some agent must pay a unitary cost to obtain the information. We prove that the core of the derived information graph game is a von Neumann-Morgenstern stable set if and only if the information graph is cycle-complete, or equivalently if the game is concave. Otherwise, whether there always exists a stable set is an open question. If the information graph consists of a ring that contains the source, a stable set always exists and it is the core of a related situation where one edge has been deleted.Xunta de Galicia | Ref. ED431B 2019/34Generalitat de Catalunya | Ref. 2017SGR778Agencia Estatal de Investigación | Ref. ECO2017-82241-RAgencia Estatal de Investigación | Ref. PID2020-113110GB-I0

A characterization of vNM-stable sets for linear production games

Rosenmüller J, Shitovitz B. A characterization of vNM-stable sets for linear production games. INTERNATIONAL JOURNAL OF GAME THEORY. 2000;29(1):39-61.We discuss linear production games or market games with a continuum of players which are represented as minima of finitely many nonatomic measures. Within this context we consider vNM-Stable Sets according to von Neumann and Morgenstern. We classify or characterize all solutions of this type which are convex polyhedra, i.e., which are the convex hull of finitely many imputations. Specifically, in each convex polyhedral vNM-Stable Set (and not only in the symmetric ones), the different types of traders must organize themselves into cartels. The vNM-Stable Set is then the convex hull of the utility distributions of the cartels. Using the results from the continuum, we obtain a similar characterization also for finite glove market games

A characterization of vNM stable sets for linear production games

Rosenmüller J, Shitovitz B. A characterization of vNM stable sets for linear production games. Working Papers. Institute of Mathematical Economics. Vol 302. Bielefeld: Center for Mathematical Economics; 1998

A characterization of vNM-stable sets for linear production games

We discuss linear production games or market games with a continuum of players which are represented as minima of finitely many nonatomic measures. Within this context we consider vNM-Stable Sets according to von Neumann and Morgenstern. We classify or characterize all solutions of this type which are convex polyhedra, i.e., which are the convex hull of finitely many imputations. Specifically, in each convex polyhedral vNM-Stable Set (and not only in the symmetric ones), the different types of traders must organize themselves into cartels. The vNM-Stable Set is then the convex hull of the utility distributions of the cartels. Using the results from the continuum, we obtain a similar characterization also for finite glove market games.Nonatomic games, linear production games, vNM-stable sets, formation of cartels