Mean Field Games
Mean Field Game (MFG) theory studies the existence of Nash equilibria, together with the individual strategies which generate them, in games involving a large number of agents modeled by controlled stochastic dynamical systems. This is achieved by exploiting the relationship between the finite and corresponding infinite limit population problems. The solution of the infinite population problem is given by the fundamental MFG Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations which are linked by the state distribution of a generic agent, otherwise known as the system’s mean field.
Large-population, dynamical, multi-agent, competitive, and cooperative phenomena occur in a wide range of designed and natural settings such as communication, environmental, epidemiological, transportation, and energy systems, and they underlie much economic and financial behavior. Analysis of such systems is intractable using the finite population game theoretic...
KeywordsNash Equilibrium Stochastic Differential Equation Finite Population Infinite Population Infinite Time Horizon
- Altman E, Basar T, Srikant R (2002) Nash equilibria for combined flow control and routing in networks: asymptotic behavior for a large number of users. IEEE Trans Autom Control 47(6):917–930. Special issue on Control Issues in Telecommunication NetworksGoogle Scholar
- Bergin J, Bernhardt D (1992) Anonymous sequential games with aggregate uncertainty. J Math Econ 21:543–562. North-HollandGoogle Scholar
- Cardaliaguet P (2012) Notes on mean field games. Collège de FranceGoogle Scholar
- Correa JR, Stier-Moses NE (2010) In: Cochran JJ (ed) Wardrop equilibria. Wiley encyclopedia of operations research and management science. Jhon Wiley & Sons, Chichester, UKGoogle Scholar
- Ho YC (1980) Team decision theory and information structures. Proc IEEE 68(6):15–22Google Scholar
- Huang MY, Caines PE, Malhamé RP (2003) Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions. In: IEEE conference on decision and control, Maui, pp 98–103Google Scholar
- Jovanovic B, Rosenthal RW (1988) Anonymous sequential games. J Math Econ 17(1):77–87. ElsevierGoogle Scholar
- Neyman A (2002) Values of games with infinitely many players. In: Aumann RJ, Hart S (eds) Handbook of game theory, vol 3. North Holland, Amsterdam, pp 2121–2167Google Scholar
- Tembine H, Zhu Q, Basar T (2012) Risk-sensitive mean field games. arXiv:1210.2806Google Scholar
- Wardrop JG (1952) Some theoretical aspects of road traffic research. In: Proceedings of the institute of civil engineers, London, part II, vol 1, pp 325–378Google Scholar
- Weintraub GY, Benkard C, Van Roy B (2005) Oblivious equilibrium: a mean field approximation for large-scale dynamic games. In: Advances in neural information processing systems. MIT, CambridgeGoogle Scholar