Geodesic
Von Neumann--Morgernstern modified generalized Raiffa solution and its application
Contributions to game theory and management, Tome 7 (2014), pp. 393-403.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we would like to discuss one of the possible modifications of Raiffa's unique point solution which has applications in the analysis of social networks associated with investing in social position and creating the structures based on mutual covering of violations of the generally accepted principles. These structures are formed on the base of games of Tragedy of commons type when one player detects breaking the rules by another player. Hence the first player begins bribing the other player and simultaneously covering his back, one player is rejudiced in favour of another player. This gives a rise to social networks that significantly affect the formation of coalitions in various areas of the social system, including institutions whose mission is to protect society against violations of the generally accepted principles. We also consider an original theoretical concept. We show that this concept can be used to implement the NM-modified Raiffa's solution for $n = 3$.
Keywords: three-person game, bribing, Nash bargaining problem; NM-modified Raiffa sequential solution; redistribution system; social networks based on mutual covering violate the generally accepted principles. 
@article{CGTM_2014_7_a34,
     author = {Radim Valen\v{c}{\'\i}k and Ond\v{r}ej \v{C}ern{\'\i}k},
     title = {Von {Neumann--Morgernstern} modified generalized {Raiffa} solution and its application},
     journal = {Contributions to game theory and management},
     pages = {393--403},
     publisher = {mathdoc},
     volume = {7},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2014_7_a34/}
}
TY  - JOUR
AU  - Radim Valenčík
AU  - Ondřej Černík
TI  - Von Neumann--Morgernstern modified generalized Raiffa solution and its application
JO  - Contributions to game theory and management
PY  - 2014
SP  - 393
EP  - 403
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2014_7_a34/
LA  - en
ID  - CGTM_2014_7_a34
ER  - 
%0 Journal Article
%A Radim Valenčík
%A Ondřej Černík
%T Von Neumann--Morgernstern modified generalized Raiffa solution and its application
%J Contributions to game theory and management
%D 2014
%P 393-403
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2014_7_a34/
%G en
%F CGTM_2014_7_a34
Radim Valenčík; Ondřej Černík. Von Neumann--Morgernstern modified generalized Raiffa solution and its application. Contributions to game theory and management, Tome 7 (2014), pp. 393-403. http://geodesic.mathdoc.fr/item/CGTM_2014_7_a34/

[1] Becker G. S., Stigler G. J., “Law Enforcement, Malfeasance, and Compensation of Enforcers”, Journal of Legal Studies, 3:1 (1974), 1–18 | DOI

[2] Benson B. L., Baden J., “The Political Economy of Governmental Corruption: The Logic of Underground Government”, Journal of Legal Studies, 14:2 (1985), 391–410 | DOI

[3] Brousseau E., Glachant J.-M. (eds.), New Institutional Economics — a Guidebook, Cambridge University Press, Cambridge, USA, 2008

[4] Colombatto E., Why is corruption tolerated?, Review of Austrian Economics, 16:4 (2003), 367–379 | DOI

[5] David T., Mach A., “Institutions and Economic Growth: the Successful Experience of Switzerland”, Institutional Change and Economic Development, ed. Chang H.-J., United Nations University Press, New York, 2007

[6] Diskin A., Koppel M., Samet D., “Generalized Raiffa Solutions”, Games and Economic Behavior, 73 (2011), 452–458 | DOI | MR | Zbl

[7] Hardin G., “The Tragedy of the Commons”, Science, 162:3859 (1968), 1243–1248 | DOI

[8] Kalai E., “Proportional Solutions of Bargaining Situations: Interpersonal Utility Comparisons”, Econometria, 45:7 (1977), 1623–1630 | DOI | MR | Zbl

[9] Kalai E., Smorodinsky M., “Other Solutions to Nash's Bargaining Problem”, Econometrica, 43:3 (1975), 513–518 | DOI | MR | Zbl

[10] Klitgaard R. E., Controlling Corruption, University of California Press, Berkeley–Los Angeles, 1991

[11] Lukašíková M., Otáhal T., “Vývoj vnímané korupce v zemích Visegrádské čtyřky a v Číně”, Scientia et Societas, 8:1 (2012), 36–47

[12] Menard C., Shirley M. (eds.), Handbook of New Institutional Economics, Springer, Berlin, 2008

[13] Nash J. F., “The Bargaining Problem”, Econometrica, 18:2 (1950), 155–162 | DOI | MR | Zbl

[14] Neumann J., Morgenstern O., Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1953 | Zbl

[15] North D. C., The Role of Institutions in Economic Development, UNECE Discussion Paper Series, October 2003, No 2, 2003

[16] North D. C., Understanding the Process of Economic Change, Princeton University Press, Princeton, NJ, 2005

[17] Ostrom E., “The Challenge of Common-Pool Resources”, Environment, 50:4 (2008), 8–20 | DOI

[18] Ostrom E., Andersson K. P., “Decentralized Resource Regimes from a Polycentric Perspective”, Policy Science, 41 (2008), 71–93 | DOI

[19] Otáhal T., Grochová L., “Corruption, Rule of Law, and Economic Efficiency: Virginia vs. Chicago Public Choice Theories”, ACTA VŠFS, 6:2 (2012), 136–154

[20] Platje J., “Institutional Capital as a Factor of Sustainable Development: the importance of an Institutional Equilibrium”, Baltic Journal on Sustainability, 14:2 (2008), 144–150

[21] Raiffa H., “Arbitration Schemes for Generalized Two Person Games”, Contributions to the Theory of Games, v. II, eds. H. W. Kuhn, A. W. Trucker, Princeton Univeristy Press, Princeton, 1953 | MR

[22] Trockel W., An Axiomatization of the Sequential Raiffa Solution, Working Papper, Institute of Mathematical Economics (IMW), Bielefeld University, 2009