We are a Senior Research Affiliate at the Karlsruhe Institute of Technology (KIT), and we have authored contributions in environmental economics, resource management, cooperative game theory, and algorithmic game theory. In total, we authored or contributed to over 64 publications, including chapter counts (see ResearchGate), with significant works on the pre-kernel, and related solutions like the pre-nucleolus, modiclus, or on game classes like convex and permutation games.  Herein, we have designed several algorithms to efficiently calculate a pre-kernel point (cf. Meinhardt, 2013) and a method of replicating a pre-kernel element of a cooperative game by creating related games (cf. Meinhardt, 2024) relying on the Fenchel-Moreau conjugation from convex analysis. Though the Fenchel-Moreau conjugation-based approach is a specialized and highly optimized algorithm for the pre-kernel, it assures a runtime complexity of O(n^3) for computing the pre-nucleolus whenever the pre-kernel is a single point. In addition, we provided several new axiomatic characterizations of the modiclus and coincident results of it with the anti-pre-nucleolus. In this context, we developed software tools under Mathematica and MATLAB for efficient computation of other game-theoretic solutions, leveraging vectorized, parallel, and GPU computing.