Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDifferential games with asymmetric information and without Isaacs condition
313
0
0.0
(
0
)
Authors
Rainer Buckdahn
Ask ChatGPT about the research
No Arabic abstract
We investigate a two-player zero-sum differential game with asymmetric information on the payoff and without Isaacs condition. The dynamics is an ordinary differential equation parametrised by two controls chosen by the players. Each player has a private information on the payoff of the game, while his opponent knows only the probability distribution on the information of the other player. We show that a suitable definition of random strategies allows to prove the existence of a value in mixed strategies. Moreover, the value function can be characterised in term of the unique viscosity solution in some dual sense of a Hamilton-Jacobi-Isaacs equation. Here we do not suppose the Isaacs condition which is usually assumed in differential games.
rate research
Read More
We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noise, Hida-Malliavin calculus, forward integrals and the Donsker delta functional. We obtain a characterization of Nash equilibria of such games in terms of the corresponding Hamiltonians. This is used to study applications to insider games in finance, specifically optimal insider consumption and optimal insider portfolio under model uncertainty.
We investigate a two-player zero-sum stochastic differential game problem with the state process being constrained in a connected bounded closed domain, and the cost functional described by the solution of a generalized backward stochastic differential equation (GBSDE for short). We show that the value functions enjoy a (strong) dynamic programming principle, and are the unique viscosity solution of the associated Hamilton-Jacobi-Bellman-Isaacs equations with nonlinear Neumann boundary problems. To obtain the existence for viscosity solutions, we provide a new approach utilizing the representation theorem for generators of the GBSDE, which is proved by a random time change method and is a novel result in its own right.
We consider an example of stochastic games with partial, asymmetric and non-classical information. We obtain relevant equilibrium policies using a new approach which allows managing the belief updates in a structured manner. Agents have access only to partial information updates, and our approach is to consider optimal open loop control until the information update. The agents continuously control the rates of their Poisson search clocks to acquire the locks, the agent to get all the locks before others would get reward one. However, the agents have no information about the acquisition status of others and will incur a cost proportional to their rate process. We solved the problem for the case with two agents and two locks and conjectured the results for $N$-agents. We showed that a pair of (partial) state-dependent time-threshold policies form a Nash equilibrium.
We study a two-player, zero-sum, stochastic game with incomplete information on one side in which the players are allowed to play more and more frequently. The informed player observes the realization of a Markov chain on which the payoffs depend, while the non-informed player only observes his opponents actions. We show the existence of a limit value as the time span between two consecutive stages vanishes; this value is characterized through an auxiliary optimization problem and as the solution of an Hamilton-Jacobi equation.
A two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the maximizing player is allowed to take continuous and switching controls. By taking strategies in the sense of Elliott--Kalton, we prove the existence of value and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
