TY - JOUR
T1 - Policy Iteration Algorithms for Zero-Sum Stochastic Differential Games with Long-Run Average Payoff Criteria
AU - López-Barrientos, José Daniel
N1 - Publisher Copyright:
© 2014, Operations Research Society of China, Periodicals Agency of Shanghai University, and Springer-Verlag Berlin Heidelberg.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - This paper studies the policy iteration algorithm (PIA) for zero-sum stochastic differential games with the basic long-run average criterion, as well as with its more selective version, the so-called bias criterion. The system is assumed to be a nondegenerate diffusion. We use Lyapunov-like stability conditions that ensure the existence and boundedness of the solution to certain Poisson equation. We also ensure the convergence of a sequence of such solutions, of the corresponding sequence of policies, and, ultimately, of the PIA.
AB - This paper studies the policy iteration algorithm (PIA) for zero-sum stochastic differential games with the basic long-run average criterion, as well as with its more selective version, the so-called bias criterion. The system is assumed to be a nondegenerate diffusion. We use Lyapunov-like stability conditions that ensure the existence and boundedness of the solution to certain Poisson equation. We also ensure the convergence of a sequence of such solutions, of the corresponding sequence of policies, and, ultimately, of the PIA.
KW - Bias game
KW - Ergodic payoff criterion
KW - Nondegenerate diffusions
KW - Poisson equation
KW - Policy iteration algorithm
KW - Schäl convergence
KW - Zero-sum stochastic differential games
UR - http://www.scopus.com/inward/record.url?scp=84925938818&partnerID=8YFLogxK
U2 - 10.1007/s40305-014-0061-z
DO - 10.1007/s40305-014-0061-z
M3 - Artículo
AN - SCOPUS:84925938818
SN - 2194-668X
VL - 2
SP - 395
EP - 421
JO - Journal of the Operations Research Society of China
JF - Journal of the Operations Research Society of China
IS - 4
ER -