Convexification Numerical Method for the Retrospective Problem of Mean Field Games

TL;DR

This paper introduces a convexification numerical method with proven global convergence for solving the retrospective problem in second-order Mean Field Games, enabling effective analysis of complex game scenarios with additional terminal conditions.

Contribution

The paper develops a novel convexification approach with rigorous convergence proof for the retrospective Mean Field Games system, incorporating an extra terminal condition.

Findings

Method demonstrates good performance on complex functions

Numerical experiments validate the approach's effectiveness

Applicable to coefficient inverse problems in game theory

Abstract

The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game of infinitely many rational players. In addition to traditional initial and terminal conditions, one extra terminal condition is assumed to be known. Carleman estimates and a Carleman Weight Function play the key role. Numerical experiments demonstrate a good performance for complicated functions. Various versions of the convexification have been actively used by this research team for a number of years to numerically solve coefficient inverse problems.