On martingale problems with continuous-time mixing and values of zero-sum games without Isaacs condition

2013/07/17 by Mihai Sîrbu, Sîrbu, Mihai
Mathematics · #60G46 #60H10 #91A05 #91A15 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:60G46 #msc:60H10 #msc:91A05 #msc:91A15

paper · pdf · doi:10.48550/arxiv.1307.4686

references and comments added, revised description of the literature

arxiv created 2014/04/15 · arxiv updated 2014/04/16

Abstract

We consider a zero-sum stochastic differential game over elementary mixed feed-back strategies. These are strategies based only on the knowledge of the past state, randomized continuously in time from a sampling distribution which is kept constant in between some stopping rules. Once both players choose such strategies, the state equation admits a unique solution in the sense of the martingale problem of Stroock and Varadhan. We show that the game defined over martingale solutions has a value, which is the unique continuous viscosity solution of the randomized Isaacs equation.

Related

• A probabilistic representation for the value of zero-sum differential games with incomplete information on both sides
• Zero-sum stochastic differential games without the Isaacs condition:\n random rules of priority and intermediate Hamiltonians
• Stochastic differential games with state constraints and Isaacs equations with nonlinear Neumann problems
• Stochastic Perron's method and elementary strategies for zero-sum differential games
• Value Function of Differential Games without Isaacs Conditions. An Approach with Non-Anticipative Mixed Strategies