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An example of multiple mean field limits in ergodic differential games

Cardaliaguet, Pierre; Rainer, Catherine (2020), An example of multiple mean field limits in ergodic differential games, NoDEA. Nonlinear Differential Equations and Applications, 27, p. 1-19. 10.1007/s00030-020-00628-w

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Article accepté pour publication ou publié
Date
2020
Journal name
NoDEA. Nonlinear Differential Equations and Applications
Volume
27
Publisher
Springer
Pages
1-19
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Author(s)
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Rainer, Catherine
Laboratoire de Mathématiques de Bretagne Atlantique [LMBA]
Abstract (EN)
We present an example of symmetric ergodic N-players differential games, played in memory strategies on the position of the players, for which the limit set, as N→+∞, of Nash equilibrium payoffs is large, although the game has a single mean field game equilibrium. This example is in sharp contrast with a result by Lacker for finite horizon problems.
Subjects / Keywords
Mean field games; Differential games; Ergodic control; Folk Theorem