A unified approach to restricted games. (English) Zbl 1039.91003

Literature on restricted games is available on two main lines. The first line was initiated by R. B. Myerson [Math. Oper. Res. 2, 225–229 (1977; Zbl 0402.90106)] where graph-restricted game was studied. This line of research was continued by G. Owen [SIAM J. Algebraic Discrete Methods 7, No. 2, 210–220 (1986; Zbl 0651.90109)] and many other researchers. The second line was started by U. Faigle [Z. Oper. Res. 33, No. 6, 405–422 (1989; Zbl 0685.90103)] who proposed a new model to analyze the partial cooperation by combinatorial methods. In this paper both models of partial cooperation are unified. The characterization of a partition system is given. The authors investigate the conditions under which the convexity is inherited from the underlying game to the restricted game.


91A12 Cooperative games
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