# Markov perfect equilibria in non-stationary mean-field games

## TL;DR

This paper develops a backward recursive algorithm to compute Markov perfect equilibria in non-stationary mean-field games, accounting for dynamic population states and private types, with applications to cyber-physical security.

## Contribution

It introduces a novel method for analyzing non-stationary mean-field games with private types, extending previous models that assumed stationary population dynamics.

## Key findings

- Algorithm successfully computes MPE in non-stationary settings
- Application to cyber-physical security demonstrates practical relevance
- Numerical results illustrate strategic vaccination decisions

## Abstract

In this paper, we consider both finite and infinite horizon discounted dynamic mean-field games where there is a large population of homogeneous players sequentially making strategic decisions and each player is affected by other players through an aggregate population state. Each player has a private type that only she observes. Such games have been studied in the literature under simplifying assumption that population state dynamics are stationary. In this paper, we consider non-stationary population state dynamics and present a novel backward recursive algorithm to compute Markov perfect equilibrium (MPE) that depend on both, a player's private type, and current (dynamic) population state. Using this algorithm, we study a security problem in cyberphysical system where infected nodes put negative externality on the system, and each node makes a decision to get vaccinated. We numerically compute MPE of the game.