STRONGLY CONSISTENT SOLUTIONS TO BALANCED TU GAMES

Abstract

Consistency properties of game solutions connect between themselves the solution sets of games with different sets of players. In the paper, the strongly consistent solutions with respect to the Davis–Maschler definition of the reduced games to the class of balanced cooperative TU games with finite sets of players are considered. A cooperative game solution σ to a class [Formula: see text] of a TU cooperative game is called strongly consistent if for any [Formula: see text] and [Formula: see text] , where [Formula: see text] is the reduced game of Γ on the player set S and with respect to x. Evidently, all consistent single-valued solutions are strongly consistent. In the paper, we characterise anonymous, covariant bounded and strongly consistent to the class [Formula: see text] of balanced games. The core, its relative interior and the prenucleolus are among them. However, they are not unique solutions satisfying these axioms. Thus, more axioms are necessary in order to characterise these solutions with strong consistency. One of such axioms is the definition of a solution for the class of balanced two-person games. It is sufficient for the axiomatisation of the prenucleolus without the single-valuedness axiom. If we add the closed graph property of the solution correspondence to the given axioms, then the system characterises only the core. The two axiomatisations are the main result of the paper. An example of a strongly consistent solution different from the prenucleolus, the core and its relative interior is given.