Solving the semismooth equivalence problem

This paper presents a special semismooth system of equations and a suitable theoretical and numerical approach for its solution. Exploiting the combinatorial structure of max-type functions and by the introduction of index-sets we can state that a solution can be gained by Newton methods. The problem bases on an economic background which expresses itself in the game-theoretic description of the feasible sets. Especially, for 1-convex and quasibalanced games we regard the core as a feasible set and treat a special bargaining solution as a control parameter of a time-discrete system.