Nonlinear Stability Framework for Computational Game Theory: Completing Nash’s Agency Formation Method

Nash’s agencies method for coalition formation suffers from a critical computational flaw: negative acceptance probabilities when coalition values are large relative to the rationality parameter. This breakdown has prevented practical implementation for over fifteen years. We resolve this instability by replacing linear utility calculations with squared payoffs, ensuring mathematical positivity while preserving the method’s core game-theoretic properties. Our approach guarantees 0