Non-Linear Strategies in a Linear Quadratic Differential Game
Non-Linear Strategies in a Linear Quadratic Differential Game
复制标题
线性二次微分博弈中的非线性策略
DOI：
10.2139/ssrn.658061
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
C. Rowat
中科院分区：
文献类型：
--
作者：
C. Rowat
研究了两智能体线性二次微分对策中的非线性马尔可夫完全均衡问题。与Tsutsui和Mino(1990)的文献不同，我们没有将状态空间的内生子集与候选解联系起来。取而代之的是，我们利用“追赶最优性”标准来解决无限水平上的无界低于值函数的问题。基于Dockner，Jorgenson，Long和Sorger(2000)的结果，我们给出了存在的充分条件。将这些应用到我们的模型中，得到了熟悉的线性解以及存在非线性解的连续体的条件。当代理人更有耐心时，这一条件会放松，并允许更有效的稳定状态，这类似于微分对策的民间定理。这里给出的模型是一个大气污染模型；结果更普遍地适用于微分对策。
We study non-linear Markov perfect equilibria in a two agent linear quadratic differential game. In contrast to the literature owing to Tsutsui and Mino (1990), we do not associate endogenous subsets of the state space with candidate solutions. Instead, we address the problem of unbounded-below value functions over infinite horizons by use of the `catching up optimality' criterion. We present sufficiency conditions for existence based on results in Dockner, Jorgenson, Long and Sorger (2000). Applying these to our model yields the familiar linear solution as well as a condition under which a continuum of non-linear solutions exist. As this condition is relaxed when agents are more patient, and allows more efficient steady states, it resembles a Folk Theorem for differential games. The model presented here is one of atmospheric pollution; the results apply to differential games more generally.