Implementing the Herings & Peeters Differentiable Homotopy in Gambit

The predictive power of game-theoretic analysis in n-person games is frequently undermined by the vast multiplicity of Nash equilibria. VISION: This project will implement the globally convergent, everywhere differentiable homotopy algorithm proposed by Herings & Peeters (2001) into the Gambit C++ core and expose it via the PyGambit API. It will be the first algorithm in Gambit repository that reaches a Nash Equilibrium taking into account a subjective Prior, which is critical for providing realistic context to game-theoretic models. DELIVERABLES: • Securing the Path-Tracking Foundation (Issue #492): Based on my mentor's feedback regarding my previous work on the logit_solve path-following methods, I will implement a configurable perturbation system, add a bifurcation logging mechanism. • Variable Transformation & System Definition. • Analytical Jacobian & Path Tracking Engine: I will abstract the existing Allgower-Georg path-tracking code to work with the H&P algorithm, ensuring that it can be easily substituted in the future by alternative solvers such as HOMPACK. I will also code the analytical Jacobian matrix. • PyGambit API Integration: I will write the necessary bindings to expose the C++ solver to Python. • Testing & Performance Benchmarking.