Algorithms for Computing the Pre-Kernel

From the dual characterization of the pre-kernel based on a generalized conjugation theory several methods can be alluded to iteratively solve a system of quadratic minimization problems. In this regard, it is proved that under a regime of orthogonal projections the sequence of payoff vectors generated by each one of the proposed computation methods is cycle-free. The generated cycle-free sequence induces a filtration on the vector space of unbalanced excesses. The filtration of this vector space allows us to give a first result on the maximum number of iteration steps required to successfully carry out the computational pre-kernel search process.