3,004 research outputs found
Markov Perfect Nash Equilibrium in stochastic differential games as solution of a generalized Euler Equations System
This paper gives a new method to characterize Markov Perfect Nash Equilibrium in stochastic
differential games by means of a set of Generalized Euler Equations. Necessary and sufficient
conditions are given
Mean field games with controlled jump-diffusion dynamics: Existence results and an illiquid interbank market model
We study a family of mean field games with a state variable evolving as a
multivariate jump diffusion process. The jump component is driven by a Poisson
process with a time-dependent intensity function. All coefficients, i.e. drift,
volatility and jump size, are controlled. Under fairly general conditions, we
establish existence of a solution in a relaxed version of the mean field game
and give conditions under which the optimal strategies are in fact Markovian,
hence extending to a jump-diffusion setting previous results established in
[30]. The proofs rely upon the notions of relaxed controls and martingale
problems. Finally, to complement the abstract existence results, we study a
simple illiquid inter-bank market model, where the banks can change their
reserves only at the jump times of some exogenous Poisson processes with a
common constant intensity, and provide some numerical results.Comment: 37 pages, 6 figure
Efficient Communication for Pursuit-Evasion Games with Asymmetric Information
We consider a class of pursuit-evasion differential games in which the evader
has continuous access to the pursuer's location, but not vice-versa. There is
an immobile sensor (e.g., a ground radar station) that can sense the evader's
location and communicate that information intermittently to the pursuer.
Transmitting the information from the sensor to the pursuer is costly and only
a finite number of transmissions can happen throughout the entire game. The
outcome of the game is determined by the control strategies of the players and
the communication strategy between the sensor and the pursuer. We obtain the
(Nash) equilibrium control strategies for both the players as well as the
optimal communication strategy between the static sensor and the pursuer. We
discuss a dilemma for the evader that emerges in this game. We also discuss the
emergence of implicit communication where the absence of communication from the
sensor can also convey some actionable information to the pursuer
- …