A Sequence-Form Formulation of Logistic Quantal Response Equilibrium in Extensive-Form Games for Selecting Nash Equilibria

Abstract

For an extensive-form game, logistic quantal response equilibrium (QRE) is defined with respect to its associated normal form and provides a natural equilibrium-selection mechanism as the rationality parameter tends to infinity. However, direct computation of logistic QRE in the normal form is generally impractical because the strategy space grows exponentially in the number of information sets. To address this difficulty, we construct a dilated-entropy-barrier artificial game in the sequence form and prove that its Nash equilibria characterize the corresponding logistic QREs. Building on this characterization, we further develop a sequence-form formulation of logistic QRE relative to a totally mixed strategy profile. This formulation gives rise to a differentiable path-following method for tracing the associated logit-QRE path, and we establish the existence of the corresponding smooth path. By recasting the dilated-entropy terms as the standard entropy terms, we additionally derive an equivalent smooth path. Numerical experiments illustrate the equilibrium-selection process of the proposed methods and evaluate their computational performance.