Oleg, Vorobyev and Ellen, Goldenok and Helena, Tyaglova (2002): On a games theory of random coalitions and on a coalition imputation. Published in: eNotices of the FAM seminar, Krasnoyarsk: Inst. of Comp. Modeling of RAS (2002): pp. 99110.

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Abstract
The main theorem of the games theory of random coalitions is reformulated in the random set language which generalizes the classical maximin theorem but unlike it defines a coalition imputation also.
The theorem about maximin random coalitions has been introduced as a random set form of classical maximin theorem. This interpretation of the maximin theorem indicate the characteristic function of the game and its close connection with optimal random coalitions. So we can write the apparent natural formula of coalition imputation generalizing the strained formulas of imputation have been in the game theory till now. Those formulas of imputation we call the strained formulas because it is unknown from where the characteristic function of the game appears and because it is necessary to make additional suppositions about a type of distributions of random coalitions. The reformulated maximin theorem has both as its corollaries. The main outputs are two results of the games theory were united and the type of characteristic function of game defined by the game matrix was discovered.
Item Type:  MPRA Paper 

Original Title:  On a games theory of random coalitions and on a coalition imputation 
Language:  English 
Keywords:  games theory, random coalition, coalition imputation, random set 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory 
Item ID:  16983 
Depositing User:  Oleg Vorobyev 
Date Deposited:  28. Aug 2009 01:01 
Last Modified:  16. Mar 2015 23:56 
References:  1. von Neumann J., and O.Morgenstern (1947) Theory of games and economic behaviour, 2nd ed., Princeton: Princeton Univ. Press. 2. Banzhaf J.F. (1965) Weighted voting doesn't work: a mathematical analysis. Rutgers Law Rev., Vol. 19, 317343. 3. Aumann R.J., and L.S.Shapley (1974) Values of NonAtomic Games. Princeton, New Jersey: Princeton University Press. 4. Moulin H. (1981) Theorie des Jeux Pour L'Economie et la Politique. Paris: Hermann. 5. Vilkas E.J. (1990) Optimality in games and decisions. Moscow: Nauka, 256 p., in Russian. 6. Vorobyev O.Yu. (1984) Average measure modeling. Moscow: Nauka, 133 p., in Russian. 7. Vorobyev O.Yu.} (1993) Setsummation. Novosibirsk: Nauka, 137 p., in Russian. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/16983 