Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

From First-Order to Second-Order Rationality: Advancing Game Convergence with Dynamic Weighted Fictitious Play

Qi Ju, Falin Hei, Yuxuan Liu, Zhemei Fang, Yunfeng Luo

TL;DR

A novel perspective is introduced, positing that the key to accelerating convergence in game theory is rationality, and a Dynamic Weighted Fictitious Play (DW-FP) algorithm is proposed, which can converge to a NE and exhibits a convergence rate of O(T^{-1})$ in experimental evaluations.

Abstract

Constructing effective algorithms to converge to Nash Equilibrium (NE) is an important problem in algorithmic game theory. Prior research generally posits that the upper bound on the convergence rate for games is $O\left(T^{-1/2}\right)$. This paper introduces a novel perspective, positing that the key to accelerating convergence in game theory is rationality. Based on this concept, we propose a Dynamic Weighted Fictitious Play (DW-FP) algorithm. We demonstrate that this algorithm can converge to a NE and exhibits a convergence rate of $O(T^{-1})$ in experimental evaluations.

From First-Order to Second-Order Rationality: Advancing Game Convergence with Dynamic Weighted Fictitious Play

TL;DR

A novel perspective is introduced, positing that the key to accelerating convergence in game theory is rationality, and a Dynamic Weighted Fictitious Play (DW-FP) algorithm is proposed, which can converge to a NE and exhibits a convergence rate of O(T^{-1})$ in experimental evaluations.

Abstract

Constructing effective algorithms to converge to Nash Equilibrium (NE) is an important problem in algorithmic game theory. Prior research generally posits that the upper bound on the convergence rate for games is . This paper introduces a novel perspective, positing that the key to accelerating convergence in game theory is rationality. Based on this concept, we propose a Dynamic Weighted Fictitious Play (DW-FP) algorithm. We demonstrate that this algorithm can converge to a NE and exhibits a convergence rate of in experimental evaluations.
Paper Structure (13 sections, 3 equations, 2 figures, 3 algorithms)

This paper contains 13 sections, 3 equations, 2 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Notation and Preliminaries
  3. Game Theory
  4. Normal-Form Games
  5. NE and $\epsilon$-NE
  6. Regret Minimization and Greedy Regret Minimization
  7. Fictitious Play
  8. Method
  9. Dynamic Weighted Fictitious Play
  10. Experimental Results
  11. Two-Player Zero-Sum Normal-Form Games
  12. The Convergence Rate of DW-FP
  13. Conclusions and Future Work

Figures (2)

  • Figure 1: The figure illustrates the performance of various algorithms on 30 randomly generated two-player zero-sum games, with matrix payoff entries drawn from a standard normal Gaussian distribution $N(0,1)$. The shaded regions around each line represent the 95% confidence interval. This setting will also be used in subsequent experiments.
  • Figure 2: This figure indicates how many iterations of the original FP correspond to the iteration of DW-FP.