Relative Value Iteration for Stochastic Differential Games

Policy iteration algorithm for zero-sum multichain stochastic games with mean payoff and perfect information

We consider zero-sum stochastic games with finite state and action spaces, perfect information, mean payoff criteria, without any irreducibility assumption on the Markov chains associated to strategies (multichain games). The value of such a game can be characterized by a system of nonlinear equations, involving the mean payoff vector and an auxiliary vector (relative value or bias). We develop...

The variational iteration method for a class of tenth-order boundary value differential equations

Fast Planning in Stochastic Games

Stochastic games generalize Markov decision processes (MDPs) to a multiagent setting by allowing the state transitions to depend jointly on all player actions, and having rewards determined by multiplayer matrix games at each state. We consider the problem of computing Nash equilibria in stochastic games, the analogue of planning in MDPs. We begin by providing a generalization of nite-horizon v...

Stochastic Shortest Path Games and Q-Learning

We consider a class of two-player zero-sum stochastic games with finite state and compact control spaces, which we call stochastic shortest path (SSP) games. They are total cost stochastic dynamic games that have a cost-free termination state. Based on their close connection to singleplayer SSP problems, we introduce model conditions that characterize a general subclass of these games that have...

Stochastic multi-player pursuit–evasion differential games

Autonomous aerial vehicles play an important role in military applications such as in search, surveillance and reconnaissance. Multi-player stochastic pursuit–evasion (PE) differential game is a natural model for such operations involving intelligent moving targets with uncertainties. In this paper, some fundamental issues of stochastic PE games are addressed. We first model a general stochasti...