June  2012, 7(2): i-ii. doi: 10.3934/nhm.2012.7.2i

Preface

1. 

"Sapienza", Università di Roma, Dipartimento di Scienze di Base e Applicate per l'Ingegneria, 00161 Roma

2. 

Dipartimento di Matematica, Istituto "Guido Castelnuovo", Sapienza Università di Roma, Piazzale Aldo Moro, 2 I-00185 Roma

Published  June 2012

The theory of Mean Field Games (MFG, in short) is a branch of the theory of Differential Games which aims at modeling and analyzing complex decision processes involving a large number of indistinguishable rational agents who have individually a very small influence on the overall system and are, on the other hand, influenced by the mass of the other agents. The name comes from particle physics where it is common to consider interactions among particles as an external mean field which influences the particles. In spite of the optimization made by rational agents, playing the role of particles in such models, appropriate mean field equations can be derived to replace the many particles interactions by a single problem with an appropriately chosen external mean field which takes into account the global behavior of the individuals.

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