A fundamental study for partially defined cooperative games
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The payoff of each coalition has been assumed to be known precisely in the conventional cooperative games. However, we may come across situations where some coalitional values remain unknown. This paper treats cooperative games whose coalitional values are not known completely. In the cooperative games it is assumed that some of coalitional values are known precisely but others remain unknown. Some complete games associated with such incomplete games are proposed. Solution concepts are studied in a special case where only values of the grand coalition and singleton coalitions are known. Through the investigations of solutions of complete games associated with the given incomplete game, we show a focal point solution suggested commonly from different viewpoints.
KeywordsCooperative game Lower game Upper game Reference point game Shapley value Nucleolus
- Kopelowitz, A. (1967). Computation of the kernels of simple games and the nucleolus of cooperative games as locuses in the strong \(\epsilon \)-core. Research Memo. 31. Jerusalem: Department of Mathematics, Hebrew University.Google Scholar
- Shapley, L. S. (1953). A value for \(n\)-person games. In H. Kuhn & A. Tucker (Eds.), Contributions to the theory of games II (pp. 307–317). Princeton: Princeton University Press.Google Scholar
- Tanino, T. (2006). On dividends for cooperative games. RIMS Kôkyûroku, 1484, 5–15.Google Scholar