Inspection games in a mean field setting

TL;DR

This paper develops a mean field game model for inspection games involving one inspector and many inspectees, providing epsilon-equilibrium solutions and numerical approximation methods as the number of inspectees grows large.

Contribution

It introduces a dynamic mean field game framework for inspection games and derives epsilon-equilibrium solutions with a focus on numerical approximation techniques.

Findings

Epsilon goes to zero as the number of inspectees increases.

Smooth switching strategies approximate optimal strategies with error of order 1/N.

The model facilitates analysis of large-scale inspection scenarios.

Abstract

In this paper, we present a new development of inspection games in a mean field setting. In our dynamic version of an inspection game, there is one inspector and a large number N interacting inspectees with a finite state space. By applying the mean field game methodology, we present a solution as an epsilon-equilibrium to this type of inspection games, where epsilon goes to 0 as N tends to infinity. In order to facilitate numerical analysis of this new type inspection game, we conduct an approximation analysis, that is we approximate the optimal Lipschitz continuous switching strategies by smooth switching strategies. We show that any approximating smooth switching strategy is also an epsilon-equilibrium solution to the inspection game with a large and finite number N of inspectees with epsilon being of order 1/N.