A fixed-point policy-iteration-type algorithm for symmetric nonzero-sum stochastic impulse games

09/09/2019
by   Diego Zabaljauregui, et al.
0

Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets and other areas, but the difficulty in solving such problems has hindered their proliferation. Semi-analytical approaches make strong assumptions pertaining very particular cases. To the author's best knowledge, the only numerical method in the literature is the heuristic one we put forward to solve an underlying system of quasi-variational inequalities. Focusing on symmetric games, this paper presents a simpler and more efficient fixed-point policy-iteration-type algorithm which removes the strong dependence on the initial guess and the relaxation scheme of the previous method. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. A provably convergent single-player impulse control solver, often outperforming classical policy iteration, is also provided. The main algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise too challenging problems, and even some for which results go beyond the scope of all the currently available theory.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/14/2020

Optimal market making under partial information and numerical methods for impulse control games with applications

The topics treated in this thesis are inherently two-fold. The first par...
research
08/15/2023

Near-Optimal Last-iterate Convergence of Policy Optimization in Zero-sum Polymatrix Markov games

Computing approximate Nash equilibria in multi-player general-sum Markov...
research
11/25/2022

Zero-Sum Stochastic Stackelberg Games

Zero-sum stochastic games have found important applications in a variety...
research
06/02/2021

Learn to Predict Equilibria via Fixed Point Networks

Systems of interacting agents can often be modeled as contextual games, ...
research
11/03/2018

Cooperative Search Games: Symmetric Equilibria, Robustness, and Price of Anarchy

Assume that a treasure is placed in one of M boxes according to a known ...
research
09/27/2019

A Generalized Training Approach for Multiagent Learning

This paper investigates a population-based training regime based on game...
research
03/31/2021

Distributed Picard Iteration

The Picard iteration is widely used to find fixed points of locally cont...

Please sign up or login with your details

Forgot password? Click here to reset