Simplicial algorithm for computing a core element in a balanced game

This paper proposes a simplicial algorithm to find a core element for balanced games without side payments. The algorithm subdivides an appropriate simplex into smaller simplices and generates from an arbitrarily chosen point a sequence of adjacent simplices of variable dimension. Within a finite number of iterations the algorithm finds a simplex yielding an approximating core element. If the accuracy of approximation is not satisfactory, the algorithm can be restarted with a smaller mesh size in order to improve the accuracy.