Abstract
We define a duality of solutions in coalitional games that we call a twisted duality. This twisted duality extends the rule of self-duality in bankruptcy problems. After showing that the prekernel and prenucleolus exhibit twisted duality, we define a twisted reduced game property and characterize the prekernel and prenucleolus by axioms including this property. We note that the Shapley value satisfies twisted duality, and we define another twisted reduced game property by and characterize the Shapley value by axioms including this property.
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