Linear Mean-Field Games with Discounted Cost
Naci Saldi

TL;DR
This paper introduces linear mean-field games with discounted costs, analyzing their equilibrium properties and proposing an algorithm for computing equilibria with convergence guarantees in large populations.
Contribution
It formulates linear mean-field games with discounted costs, establishes their approximate Nash equilibrium properties, and develops a convergent algorithm for equilibrium computation.
Findings
Infinite population equilibrium is approximately Nash for large N.
Explicit error bounds for finite N are derived.
A convergent algorithm for computing equilibria is proposed.
Abstract
In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly coupled with another agent via their dynamics and one-stage cost function, where this randomization is generated via the empirical distribution of their states (i.e., the mean-field term). Therefore, the transition probability and the one-stage cost function of each agent depend linearly on the mean-field term, which is the key distinction between classical mean-field games and linear mean-field games. Under mild assumptions, we show that the policy obtained from infinite population equilibrium is -Nash when the number of agents is sufficiently large, where is an explicit function of . Then, using the linear…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGame Theory and Applications · Experimental Behavioral Economics Studies · Auction Theory and Applications
