Zero-Sum Stochastic Differential Games Without the Isaacs Condition: Random Rules of Priority and Intermediate Hamiltonians
Zero-Sum Stochastic Differential Games Without the Isaacs Condition: Random Rules of Priority and Intermediate Hamiltonians
复制标题
无艾萨克斯条件的零和随机微分博弈：优先级和中间哈密顿量的随机规则
DOI：
10.1137/17m1128976
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Mihai Sîrbu
中科院分区：
文献类型：
--
作者：
Daniel Hernández;Mihai Sîrbu
对于不满足Isaacs条件的零和随机对策，给出了哈密顿量介于上下哈密顿量之间的Isaacs型方程的值函数表示，即两者的凸组合。对于一般情况（即凸组合依赖于时间和状态），我们的表示相当于游戏规则的随机改变，允许每个玩家在任何时刻看到其他玩家的行动，根据PDE中出现的凸组合给出的正面和反面概率投掷硬币。如果组合是状态独立的，那么就可以以确定性的方式提前设置所有规则。这意味着在游戏中投掷硬币，或者在游戏开始时反复投掷硬币都会得到相同的值。表示是渐近的，随时间离散化。空间离散化也是可能的，导致类似的结果。
For a zero-sum stochastic game which does not satisfy the Isaacs condition, we provide a value function representation for an Isaacs-type equation whose Hamiltonian lies in between the lower and upper Hamiltonians, as a convex combination of the two. For the general case (i.e. the convex combination is time and state dependent) our representation amounts to a random change of the rules of the game, to allow each player at any moment to see the other player's action or not, according to a coin toss with probabilities of heads and tails given by the convex combination appearing in the PDE. If the combination is state independent, then the rules can be set all in advance, in a deterministic way. This means that tossing the coin along the game, or tossing it repeatedly right at the beginning leads to the same value. The representations are asymptotic, over time discretizations. Space discretization is possible as well, leading to similar results.
inf-sup型微分博弈与Isaacs方程
DOI：
--
发表时间：
2005
期刊：
Appl. Math. Optimization Vol. 52
影响因子：
--
作者：
H.Kaise;S.-J.Sheu
通讯作者：
S.-J.Sheu