More on homotopy continuation method and discounted zero-sum stochastic game with ARAT structure

TL;DR

This paper develops a modified homotopy continuation method with higher convergence order to solve two-person zero-sum discounted stochastic ARAT games, demonstrating its effectiveness through numerical examples.

Contribution

It introduces a new homotopy function and algorithm specifically designed for solving stochastic ARAT games with improved convergence properties.

Findings

The algorithm has higher order of convergence.

The homotopy path is smooth and bounded.

Numerical examples confirm effectiveness.

Abstract

In this paper, we introduce a homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of two-person zero-sum discounted stochastic ARAT game. We show that the algorithm has the higher order of convergence. For the proposed algorithm, the homotopy path approaching the solution is smooth and bounded. Two numerical examples are illustrated to show the effectiveness of the proposed algorithm.