Academic Journal
Linear Mean-Field Games with Discounted Cost.
| Τίτλος: | Linear Mean-Field Games with Discounted Cost. |
|---|---|
| Συγγραφείς: | Saldi, Naci1 (AUTHOR) naci.saldi@bilkent.edu.tr |
| Πηγή: | Mathematics of Operations Research (INFORMS). Feb2026, Vol. 51 Issue 1, p358-397. 40p. |
| Θεματικοί όροι: | *Nash equilibrium, *Markov processes, *Distribution (Probability theory), *Cost |
| People: | Nash, John F., 1928-2015 |
| Περίληψη: | In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. 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 ε(N) -Nash when the number of agents N is sufficiently large, where ε(N) is an explicit function of N. Then, using the linear programming formulation of Markov decision processes (MDPs) and the linearity of the transition probability in the mean-field term, we formulate the game in the infinite population limit as a generalized Nash equilibrium problem (GNEP) and establish an algorithm for computing equilibrium with a convergence guarantee. [ABSTRACT FROM AUTHOR] |
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