We formulate the model based on an extension of infinite population game theory called Mean Field Games. The proposed dynamical system has two sets of equations: conservation equations for the traffic flow dyna
In this work we investigate the existence of solutions to the following system arising in the theory of viscous ergodic Mean Field Games, with Neumann boundary conditions and local coupling {−Δu+H(∇u)+λ=f(x,m(x))on Ω−Δm−div(m∇H(∇u))=0on Ω∂u∂n=0, ∂m...
1 Introduction to Mean Field Games Mean field game theory is a branch of game theory. It is therefore a set of concepts, mathematical tools, theorems, simulation methods and algorithms, which like all game theory, is intended to help specialists model situations where agents make decisions str...
In the appropriate mean field version of the game the representative player knows the distributionof the time horizon, but the actual time horizon arrives unpredicted. The threshold describing the equilibrium control strongly depends on the distribution. For the cases whereis an exponential distribution ...
infinite dimensional optimization and control theory, vol. 54. cambridge university press, london (1999). https://doi.org/10.1017/cbo9780511574795 book math google scholar gomes, d.a., pimentel, e.a., voskanyan, v.: regularity theory for mean-field game systems. springer, ...
‘social norms’ of the society. This game represents a rare example of an exactly solvable model. In particular, it reveals explicitly the non-uniqueness of solutions which is widely discussed in the general mean-field-game theory. On the other hand, we hope this example can serve as a ...
In this paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The m
Cardaliaguet, P.: Notes on mean-field games. From P.-L. Lions’ Lectures at the College de France. Available at https://www.ceremade.dauphine.fr/~cardaliaguet/MFG20130420.pdf (2011) Cardaliaguet, P., Porretta, A.: An Introduction to Mean Field Game Theory. Mean Field Games, Cetraro...
Game Theory Model Theory Partial Differential Equations Stochastic Differential Equations Agent-based Economics References Achdou Y (2013) Finite difference methods for mean field games. In: Hamilton–Jacobi equations: approximations, numerical analysis and applications. Springer, Berlin, pp 1–47 ...
First-order Mean Field Game First-order Mean Field Equilibrium Second-order Mean Field Game Variance Linearly Dependent on the State Constant Variance Numerical Experiment Conclusion Availability of Data and Materials Code Availability References Author information Ethics declarations Additional information Rights...