Markov perfect equilibria in non-stationary mean-field games
It provides a novel computational method for mean-field games with non-stationary dynamics, relevant for economists and engineers modeling large populations with strategic interactions.
This paper develops a backward recursive algorithm for computing Markov perfect equilibria in non-stationary mean-field games, applied to a cybersecurity vaccination problem. The algorithm handles dynamic population states, enabling equilibrium computation in settings where previous methods assumed stationarity.
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.