Competition with high number of agents and a major one

Valeria De  Mattei

doi:10.3934/jdg.2016017

Article Contents

2016, Volume 3, Issue 4: 319-334. Doi: 10.3934/jdg.2016017

This issue Previous Article Network formation games with teams Next Article Interception in differential pursuit/evasion games

Competition with high number of agents and a major one

Valeria De Mattei^1,

1.
Dipartimento di Matematica, Largo Bruno Pontecorvo, Pisa

Received: June 2015

Revised: February 2016

Published: October 2016

Abstract / Introduction Related Papers Cited by

Abstract

In the framework of mean field game theory, a new optimization problem is presented by adding an additional player, called the principal. After introducing a proper payoff for the principal, continuity and existence of minimum is proved. Some considerations about uniqueness and possible ways of continuing the analysis of this problem are given.

Keywords:

Mathematics Subject Classification: Primary: 35Q91, 35Q70; Secondary: 91A13.

Citation:

Related Papers

Cited by

References

[1]	Y. Achdou, F. Camilli and I. Capuzzo-Dolcetta, Meand field games: Numerical methods for the planning problem, SIAM J. Control Optim., 50 (2012), 77-109.doi: 10.1137/100790069.
[2]	M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Systems and Control: Foundations and Applications. Birkhauser Boston Inc., Boston, MA, 1997.doi: 10.1007/978-0-8176-4755-1.
[3]	T. Borgers, An introduction to the Theory of Mechanism Design, 2015. doi: 10.1093/acprof:oso/9780199734023.001.0001.
[4]	P. Cardaliaguet, Notes on Mean Field Games, 2012.
[5]	H. Gintis, Game Theory Evolving, Princeton University Press, 2009.
[6]	O. Guéant, J. M. Lasry and P. L. Lions, Mean field games and applications, 2009.
[7]	M. Lasry and P. L. Lions, Jeux à champ moyen. I. Le cas stationaire, C. R. Math.Acad. Sci. Paris, 343 (2006), 619-625.doi: 10.1016/j.crma.2006.09.019.
[8]	M. Lasry and P. L. Lions, Jeux à champ moyen. II. Horizon fini et controle optimal, C. R. Math.Acad. Sci. Paris, 343 (2006), 679-684.doi: 10.1016/j.crma.2006.09.018.
[9]	J. M. Lasry and P. L. Lions, Mean field games, Japanese Journal of Mathematics, 2 (2007), 229-260.doi: 10.1007/s11537-007-0657-8.
[10]	J. M. Lasry and P. L. Lions, Cours du College de France, 2009.
[11]	S. Perkins and D. S. Leslie, Stochastic fictitious play with continuous action sets, Journal of Economic Theory, 152 (2014), 179-213.doi: 10.1016/j.jet.2014.04.008.
[12]	A. Porretta, Weak solutions to Fokker Planck equations and mean field games, Archive for Rational Mechanics and Analysis, 216 (2015), 1-62.doi: 10.1007/s00205-014-0799-9.
[13]	D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Springer Verlag, 1979.