A Partially Defined Game with Payments
Abstract: The present study explores an original problem that can be resolved by employing the notion of a PDG, yet cannot by using a restricted game. The following situation is considered: First, it is assumed that the worth of the grand and singleton coalitions are known. It takes some amount of costs to obtain worth of larger coalitions. If it is performed, then the worth of the grand coalition is decreased by the value of a cost function. The problem of a partially defined game with payments is finding the solution of partially defined games at each point and the best exiting rule of examinations of coalitional worth.
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