Value in mixed strategies for zero-sum stochastic differential games without Isaacs condition

DOI10.1214/13-AOP849zbMath1296.49034arXiv1407.7326MaRDI QIDQ400582

Rainer Buckdahn, Marc Quincampoix, Juan Li

Publication date: 22 August 2014

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.7326

zbMATH Keywords

viscosity solutionbackward stochastic differential equationsvalue functionIsaacs conditiondynamic programming principle2-person zero-sum stochastic differential gamerandomized controls

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Dynamic programming in optimal control and differential games (49L20) Differential games and control (49N70) 2-person games (91A05) Differential games (aspects of game theory) (91A23) Stochastic games, stochastic differential games (91A15) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (12)

Differential games with incomplete information on a continuum of initial positions and without Isaacs condition ⋮ Dynamic Set Values for Nonzero-Sum Games with Multiple Equilibriums ⋮ Zero-Sum Stochastic Differential Games Without the Isaacs Condition: Random Rules of Priority and Intermediate Hamiltonians ⋮ Zero-sum path-dependent stochastic differential games in weak formulation ⋮ Nash equilibrium payoffs for non-zero-sum stochastic differential games without Isaacs condition ⋮ Differential Games ⋮ Differential games with asymmetric information and without Isaacs' condition ⋮ Nash equilibria for nonzero-sum ergodic stochastic differential games ⋮ Two-player zero-sum stochastic differential games with random horizon ⋮ Contract Theory in a VUCA World ⋮ Asymptotic Perron's Method and Simple Markov Strategies in Stochastic Games and Control ⋮ Zero-sum risk-sensitive stochastic differential games with reflecting diffusions in the orthant

Cites Work

• Value function of differential games without Isaacs conditions. An approach with nonanticipative mixed strategies
• Some recent aspects of differential game theory
• Adapted solution of a backward stochastic differential equation
• Exponentially growing solutions of parabolic Isaacs' equations
• Another approach to the existence of value functions of stochastic differential games
• Backward Stochastic Differential Equations Driven By Càdlàg Martingales
• Stochastic Differential Games and Viscosity Solutions of Hamilton–Jacobi–Bellman–Isaacs Equations
• User’s guide to viscosity solutions of second order partial differential equations
• Nash Equilibrium Payoffs for Nonzero-Sum Stochastic Differential Games
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