On a games theory of random coalitions and on a coalition imputation

Oleg, Vorobyev and Ellen, Goldenok and Helena, Tyaglova (2002): On a games theory of random coalitions and on a coalition imputation. Published in: e-Notices of the FAM seminar, Krasnoyarsk: Inst. of Comp. Modeling of RAS (2002): pp. 99-110.

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
• Language: English
• Keywords: games theory, random coalition, coalition imputation
• 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

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, 317--343.

3. Aumann R.J., and L.S.Shapley (1974) Values of Non-Atomic 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) Set-summation. Novosibirsk: Nauka, 137 p., in Russian.