Domain Shrinkage: A Constant-Memory (O(1)) Algorithm for Mixed Nash Equilibrium Computation via Coupled Interval Contraction

Domain Shrinkage is a constant-memory (O(1)) algorithm for computing mixed-strategy Nash equilibria in finite 2×2 bimatrix games. Unlike fictitious play and replicator dynamics, which accumulate a belief history that grows with the number of iterations, Domain Shrinkage keeps only a bounded, non-accumulating record and converges by iteratively contracting a shared feasible-strategy corridor based solely on the players' current best responses. The paper analyzes convergence (linear in the number of contraction cycles), characterizes the running time as O(1/δ) for step floor δ, and presents an interactive 3D visualization of the expected-payoff surfaces that animates the shrinkage process in real time.

This record contains the paper (PDF and LaTeX source), the figures, and a screen-recorded demo of the interactive visualization.

Source code: https://github.com/daluan217/3D-Nash-Equilibrium
Live interactive demo: https://nash-equilibrium-simulator.com

Please email me with any questions, comments, or feedback: daluan217@g.ucla.edu