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Coalitional interval games for strategic games in which players cooperate. (English) Zbl 1162.91309
Summary: We propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. Associating with a strategic game a coalitional interval game we avoid having to take either a pessimistic or an optimistic approach to the problem. The paper makes two contributions to the literature: It provides a theoretical foundation for the study of coalitional interval games and it also provides, studies, and characterizes a natural method of associating coalitional interval games with strategic games.

91A12 Cooperative games
Full Text: DOI
[1] Bergantiños G., García-Jurado I. (1995), Estudio comparativo de diversas funciones características asociadas a un juego en forma normal. Investigaciones Económicas 19:127–138
[2] Branzei R., Dimitrov D., Pickl S., Tijs S. (2004), How to cope with division problems under interval uncertainty of claims? International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 12:191–200 · Zbl 1101.91055 · doi:10.1142/S021848850400276X
[3] Branzei R., Dimitrov D., Tijs S. (2003) Shapley-like values for interval bankruptcy games. Economics Bulletin 3:1–8
[4] Carpente L., Casas-Méndez B., García-Jurado I., van den Nouweland A. (2005) Values for strategic games in which players cooperate. International Journal of Game Theory 33:397–419 · Zbl 1076.91003 · doi:10.1007/s001820400176
[5] Demange, G. and Wooders, M. (2005), Group Formation in Economics; Networks, Clubs, and Coalitions, Cambridge University Press.
[6] Gerber, A. (2003), Coalition formation. in General NTU Games, in Dutta, B. and Jackson, M. (eds). Networks and Groups; Models of Strategic Formation. Springer-Verlag, 285–311.
[7] Harsanyi J.C. (1963) A simplified bargaining model for the n-person cooperative game. International Economic Review 4:194–220 · Zbl 0118.15103 · doi:10.2307/2525487
[8] Myerson, R.B. (1991), Game Theory, Analysis of Conflict, Harvard University Press. · Zbl 0729.90092
[9] Ray D., Vohra R. (1999) A theory of endogenous coalition structures. Games and Economic Behavior 26:286–336 · Zbl 0918.90146 · doi:10.1006/game.1998.0648
[10] Von Neumann, J. and Morgenstern, O. (1944), Theory of games and economic behavior, Princeton University Press. · Zbl 0063.05930
[11] Yi S. (1997) Stable coalition structures with externalities. Games and Economic Behavior 20:201–237 · Zbl 0894.90186 · doi:10.1006/game.1997.0567
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