Related papers: Dynkin games in a general framework
The traditional difficulty about stochastic singular control is to characterize the regularities of the value function and the optimal control policy. In this paper, a multi-dimensional singular control problem is considered. We found the…
A new class of multi-player competitive stochastic games in discrete-time with an affine specification of the redistribution of payoffs at exercise is proposed and examined. Our games cover as a very special case the classic two-person…
A multi-player competitive Dynkin stopping game is constructed. Each player can either exit the game for a fixed payoff, determined a priori, or stay and receive an adjusted payoff depending on the decision of other players. The single…
We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with…
The paper solves constrained Dynkin games with risk-sensitive criteria, where two players are allowed to stop at two independent Poisson random intervention times, via the theory of backward stochastic differential equations. This…
In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that…
We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…
In optimal stopping problems, a Markov structure guarantees Markovian optimal stopping times (first exit times). Surprisingly, there is no analogous result for Markovian stopping games once randomization is required. This paper addresses…
A Dynkin game is a zero-sum, stochastic stopping game between two players where either player can stop the game at any time for an observable payoff. Typically the payoff process of the max-player is assumed to be smaller than the payoff…
We introduce a setup of model uncertainty in discrete time. In this setup we derive dual expressions for the super--replication prices of game options with upper semicontinuous payoffs. We show that the super--replication price is equal to…
We study a Stackelberg variant of the classical discrete-time Dynkin game, in which Player 1 (the leader) commits to a stopping strategy first and Player 2 (the follower) responds optimally. This leader-follower structure induces an optimal…
In this paper we consider Dynkin's games with payoffs which are functions of an underlying process. Assuming extended weak convergence of underlying processes $\{S^{(n)}\}_{n=0}^{\infty}$ to a limit process $S$ we prove convergence Dynkin's…
The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity. We prove existence and uniqueness of classical solutions…
We offer some theorems, mainly of finiteness, for certain patterns in elliptical billiards, related to periodic trajectories. For instance, if two players hit a ball at a given position and with directions forming a fixed angle in…
We consider reflected backward stochastic differential equations with two optional barriers of class (D) satisfying Mokobodzki's separation condition and coefficient which is only continuous and non-increasing. We assume that data are…
We study the existence of classical solutions to a broad class of local, first order, forward-backward Extended Mean Field Games systems, that includes standard Mean Field Games, Mean Field Games with congestion, and mean field type control…
Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility,…
This work establishes sufficient conditions for existence of saddle points in discrete Markov games. The result reveals the relation between dynamic games and static games using dynamic programming equations. This result enables us to prove…
We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise when agents control their acceleration. Such systems include independent variables representing the spatial position as well as velocity. We consider…
In this paper, we consider mean-field games where the interaction of each player with the mean-field takes into account not only the states of the players but also their collective behavior, To do so, we develop a random variable framework…