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.

翻译：纳什均衡是扩展式博弈中的一个基本解概念，但其高效计算仍远非直接。本文考虑有限$n$玩家完美回忆扩展式博弈，采用序列形式表示。与主要将序列形式视为紧凑计算重构的现有方法不同，我们发展了纳什均衡的直接序列形式定义。在此基础上，通过混合策略纳什均衡的等价性证明，严格建立了关联的序列形式纳什均衡系统。基于此，我们提出了一种用于均衡计算的单阶段内点可微路径跟踪方法。该方法利用对数障碍正则化在实现计划空间内部生成可微均衡路径，从而具有良好的数值稳定性和收敛性能。数值结果显示，所提方法有效且计算高效。