vNM–Stable Sets for Totally Balanced Games

Rosenmüller J (2018) Center for Mathematical Economics Working Papers; 581, aktual. Ausg.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
This paper continues the treatise of vNM Stable Sets for totally balanced (cooperative) games with a continuum of players. We generalize and extend the results obtained by a series of presentations of this topic (Part I,II,III,IV see [5], [6], [7], [8], [9]).

Thus, the coalitional function is generated by r "production factors" (non atomic measures). Some *q < r* factors are normalized (i.e. "probabilities") establishing the core of the game. The remaining factors are represented by non-normalized non atomic measures. Hence, these factors are available in excess and the representing measure is not in the core of the game. As previously, we switch freely between interpretatins, e.g., the defining measures can also be seen asl initial distributions in a pure exchange market ( a"glove game"").

The requirements maintained in our previous presentations, i.e., orthogonality and the existence of just one carrier 'across the corners' of the market, are completely dropped. All factors are being distributed all across the market and the core does not necessarily consist of orthogonal distributions. That is, no more can we distinguish well defined 'corners' of the market or production process. Nevertheless, we consider the regime of a production factor, i.e., the carrier, the coalitions with positive measure, the distribution of quantities of this factor as a 'cartel'; i.e., a large group of players commanding solely an indispensable domain of the market or production process.

Within this context we study 'standard' vNM Stable Sets. The result is an existence theorem of essentially the same nature as in the previous context: for each factor pick a specified imputation, absolutely continuous w.r.t. this factor with density bounded by 1, the the convex hull of these imputations constitutes a vNM Stable Set.

We interprete this as a solution concept which, other then the concepts of the 'equivalence theorems' (notably the core), establish an influence of cartels not only by their power to achieve certain gains but also by their ability to prevent others from achieving anything without cooperation.
Erscheinungsjahr
2018
Band
581
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2930698

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Rosenmüller J. vNM–Stable Sets for Totally Balanced Games. Center for Mathematical Economics Working Papers. Vol 581 aktual. Ausg. Bielefeld: Center for Mathematical Economics; 2018.
Rosenmüller, J. (2018). vNM–Stable Sets for Totally Balanced Games (Center for Mathematical Economics Working Papers, 581) aktual. Ausg. Bielefeld: Center for Mathematical Economics.
Rosenmüller, J. (2018). vNM–Stable Sets for Totally Balanced Games. Center for Mathematical Economics Working Papers, 581, aktual. Ausg. Bielefeld: Center for Mathematical Economics.
Rosenmüller, J., 2018. vNM–Stable Sets for Totally Balanced Games, Center for Mathematical Economics Working Papers, no.581, aktual. Ausg., Bielefeld: Center for Mathematical Economics.
J. Rosenmüller, vNM–Stable Sets for Totally Balanced Games, Center for Mathematical Economics Working Papers, vol. 581, aktual. Ausg., Bielefeld: Center for Mathematical Economics, 2018.
Rosenmüller, J.: vNM–Stable Sets for Totally Balanced Games. Center for Mathematical Economics Working Papers, 581, aktual. Ausg. Center for Mathematical Economics, Bielefeld (2018).
Rosenmüller, Joachim. vNM–Stable Sets for Totally Balanced Games. aktual. Ausg. Bielefeld: Center for Mathematical Economics, 2018. Center for Mathematical Economics Working Papers. 581.
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