We consider competition between two decentralized supply chains network under demand uncertainty. Each chain consists of one risk-averse manufacturer and a group of risk-averse retailers. These two chains present substitutable products to the geographical dispensed markets. The markets’ demands are contingent upon prices, service levels, and advertising efforts of two supply chains. We formulat...

In this paper, we initiate a study on optimal control problem for stochastic differential games under generalized expectation via backward stochastic differential equations and partial information. We first prove a sufficient maximum principle for zero-sum stochastic differential game problem. And then extend our approach to general stochastic differential games (nonzero–sum games), and obtain ...

We consider reinforcement learning algorithms in normal form games. Using two-timescales stochastic approximation, we introduce a modelfree algorithm which is asymptotically equivalent to the smooth fictitious play algorithm, in that both result in asymptotic pseudotrajectories to the flow defined by the smooth best response dynamics. Both of these algorithms are shown to converge almost surely...

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player’s controll...

We consider reinforcement learning algorithms in normal form games. Using two-time-scales stochastic approximation, we introduce a modelfree algorithm which is asymptotically equivalent to the smooth fictitious play algorithm, in that both result in asymptotic pseudotrajectories to the flow defined by the smooth best response dynamics. Both of these algorithms are shown to converge almost surel...

We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also inves...

Cognitive radio has been recently proposed as a promising technology to achieve efficient use of spectrum resources. In this paper, we consider spectrum sharing in a MIMO system where several secondary users (SUs) share spectrum with a primary user (PU). A leakage-based beamforming algorithm is proposed via game theory. The objective is to maximize the sum throughput of SUs subject to the signa...