Two Sequence-Form Interior-Point Differentiable Path-Following Method to Compute Nash Equilibria

TL;DR

This paper introduces a novel interior-point path-following method for computing Nash equilibria in extensive-form games using a direct sequence-form approach, improving stability and efficiency.

Contribution

It develops a direct sequence-form definition of Nash equilibrium and proposes a differentiable path-following method with logarithmic-barrier regularization.

Findings

Method demonstrates favorable numerical stability.

Algorithm achieves efficient convergence.

Numerical results confirm effectiveness.

Abstract

Nash equilibrium is a fundamental solution concept in extensive-form games, while its efficient computation is still far from straightforward. This paper considers finite $n$-player extensive-form games with perfect recall under the sequence-form representation. Unlike existing approaches, which mainly treat the sequence form as a compact computational reformulation, we develop a direct sequence-form definition of Nash equilibrium. Building on this, we rigorously establish the associated sequence-form Nash equilibrium system through an equivalence proof with mixed-strategy Nash equilibrium. On this basis, we propose a single-stage interior-point differentiable path-following method for equilibrium computation. The method uses logarithmic-barrier regularization to generate a differentiable equilibrium path in the interior of the realization-plan space, leading to favorable numerical stability and convergence properties. Numerical results show that the proposed method is effective and computationally efficient.