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A new solution using coalitional theory for superadditive TU n-person games.
by
Mike Ball
Department of Mathematical Sciences, University og Liverpool, U.K.
Arguments are presented for coalitional theory, in which coalitions have the structure of a rooted tree. The preference rule requires the tree to be full binary. Reversible moves and transitions between trees are defined. Bargaining equilibrium requires the set of trees to be as large as possible and for the trees to be connected by reversible transitions. The resulting conditions on the payoffs allow them to be calculated, provided the gains at the root of each tree are known (the root allocation). If this is done by splitting the difference (s.t.d.) the payoff averaged over all full binary trees is the Shapley value. Coalitional theory provides a statistical solution, i.e. each tree providing a possible set of suitable payoffs. Sometimes the s.t.d. allocation of gains at the root violates the preference rule. A N-trio is defined as the set of 3 disjoint coalitions at the root in 3 trees such that reversible moves can be made from one tree to another. A core-like N-trio is one where each coalition gets the same payoff in each tree. The root allocations are altered to avoid violation by ensuring a core-like N-trio. When all N-trios are core-like the resulting solution is in the core but is unique and in general not the Shapley value.
Date received: June 9, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafi-34.