Related papers: Stochastic differential games with inside informat…
In this paper we study zero-sum two-player stochastic differential games with jumps with the help of theory of Backward Stochastic Differential Equations (BSDEs). We generalize the results of Fleming and Souganidis [10] and those by Biswas…
In this paper, we study the following nonlinear backward stochastic integral partial differential equation with jumps \begin{equation*} \left\{ \begin{split} -d V(t,x) =&\displaystyle\inf_{u\in U}\bigg\{H(t,x,u, DV(t,x),D \Phi(t,x), D^2…
In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…
We discuss stochastic dynamics of finite populations of individuals playing games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of…
We investigate the set of Nash equilibrium payoffs for two person differential games. The main result of the paper is the characterization of the set of Nash equilibrium payoffs in the terms of nonsmooth analysis. Also we obtain the…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
This paper studies a two-player nonzero-sum stochastic differential game governed by a controlled convection-diffusion stochastic partial differential equation (SPDE) with spatially heterogeneous coefficients. The diffusion and transport…
We study stochastic effects on the lagging anchor dynamics, a reinforcement learning algorithm used to learn successful strategies in iterated games, which is known to converge to Nash points in the absence of noise. The dynamics is…
This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
Recent extensions to dynamic games of the well-known fictitious play learning procedure in static games were proved to globally converge to stationary Nash equilibria in two important classes of dynamic games (zero-sum and…
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…
We discuss similarities and differencies between systems of many interacting players maximizing their individual payoffs and particles minimizing their interaction energy. We analyze long-run behavior of stochastic dynamics of many…
Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…
Decentralized optimization of distributed stochastic differential systems has been an active area of research for over half a century. Its formulation utilizing static team and person-by-person optimality criteria is well investigated.…
Distributed power control for parallel Gaussian interference channels recently draws great interests. However, all existing works only studied this problem under deterministic communication channels and required certain perfect information…
This paper tackles the problem of solving stochastic optimization problems with a decision-dependent distribution in the setting of stochastic strongly-monotone games and when the distributional dependence is unknown. A two-stage approach…
This paper presents a pioneering investigation into discrete-time two-person non-zero-sum linear quadratic (LQ) stochastic games with random coefficients. We derive necessary and sufficient conditions for the existence of open-loop Nash…
Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space…
We analyze a class of stochastic dynamic games among teams with asymmetric information, where members of a team share their observations internally with a delay of $d$. Each team is associated with a controlled Markov Chain, whose dynamics…