Selecting Normal-Form Nash Equilibria in Extensive-Form Games via a Sequence-Form Variant of Logit Quantal Response Equilibrium

TL;DR

This paper introduces a sequence-form approach to compute logit QRE in extensive-form games efficiently, enabling equilibrium selection and convergence to Nash equilibria without exponential strategy space growth.

Contribution

It develops a novel sequence-form formulation of logit QRE and a differentiable path-following method for efficient equilibrium computation in extensive-form games.

Findings

Sequence-form logit QRE avoids exponential strategy space growth.

The path-following method converges to Nash equilibria.

Numerical experiments validate the approach's effectiveness.

Abstract

Although logit quantal response equilibrium (logit QRE) offers a natural equilibrium selection mechanism and converges to Nash equilibrium as the rationality parameter tends to infinity, its computation in extensive-form games is generally intractable when based on the normal-form representation, due to the exponential growth of the strategy space. To address this difficulty, this paper develops a sequence-form formulation of logit QRE for finite n-player extensive-form games with perfect recall, which avoids explicit construction of the normal form and enables compact computation. Based on this formulation, we further develop a differentiable path-following method starting from an arbitrary initial point, such that each point on the path corresponds to a logit QRE associated with a particular value of the rationality parameter, and the limiting point yields a Nash equilibrium. In this way, the proposed method provides an efficient computational framework for exploiting the equilibrium selection property of logit QRE in extensive-form games. The effectiveness of the proposed method is validated by theoretical analysis and numerical experiments.