scholarly journals Selection by vanishing common noise for potential finite state mean field games

2021 ◽  
pp. 1-76
Author(s):  
Alekos Cecchin ◽  
François Delarue
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Common Noise ◽  
Finite State

scholarly journals Finite state mean field games with Wright–Fisher common noise

2021 ◽  
Vol 147 ◽  
pp. 98-162
Author(s):  
Erhan Bayraktar ◽  
Alekos Cecchin ◽  
Asaf Cohen ◽  
François Delarue
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Common Noise ◽  
Finite State

scholarly journals On mean field games with common noise and McKean-Vlasov SPDEs

2019 ◽  
Vol 37 (4) ◽  
pp. 522-549 ◽  
Author(s):  
Vassili N. Kolokoltsov ◽  
Marianna Troeva
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Common Noise

scholarly journals Socio-economic applications of finite state mean field games

2014 ◽  
Vol 372 (2028) ◽  
pp. 20130405 ◽  
Author(s):  
Diogo Gomes ◽  
Roberto M. Velho ◽  
Marie-Therese Wolfram
Keyword(s):  
Consumer Choice ◽  
Numerical Experiments ◽  
Free Market ◽  
Hyperbolic Systems ◽  
Mean Field ◽  
Mean Field Games ◽  
Paradigm Shifts ◽  
Choice Behaviour ◽  
Mean Field Game ◽  
Finite State

In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.

Mean Field Game System with a Common Noise

2019 ◽  
pp. 85-127
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Existence And Uniqueness ◽  
Mean Field ◽  
Mean Field Games ◽  
Random Functions ◽  
Common Noise ◽  
The Common ◽  
The Mean ◽  
Random Flow ◽  
Uniqueness Of A Solution ◽  
Classical Strategy

This chapter talks about the unique solvability of the mean field games (MFGs) system with common noise. In terms of a game with a finite number of players, the common noise describes some noise that affects all the players in the same way, so that the dynamics of one given particle reads a certain master equation. It explains the use of the standard convention from the theory of stochastic processes that consists in indicating the time parameter as an index in random functions. Using a continuation like argument instead of the classical strategy based on the Schauder fixed-point theorem, this chapter investigates the existence and uniqueness of a solution. It discusses the effect of the common noise in randomizing the MFG equilibria so that it becomes a random flow of measures.

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