论文标题
一阶平均场类型差异游戏的晶格近似
Lattice approximations of the first-order mean field type differential games
论文作者
论文摘要
一阶平均场类型差异游戏的理论研究了通过某些外部媒体相互作用的许多相同的代理的系统，假设每个代理都由两个玩家控制。我们使用模型有限维差异游戏的解决方案来研究一阶平均场类型差异游戏的价值函数的近似值。模型游戏是一种平均场类型连续时间马尔可夫游戏，即，游戏理论问题是无限的许多代理和动态的每个代理的动态，由受控的有限状态非线性马尔可夫链确定。鉴于模型游戏的汉密尔顿 - 雅各比方程的超级分析（分别订阅），我们构建了第一名（分别为第二）玩家的次优策略，并使用奖励功能的连续性和原始游戏和模型游戏之间的距离的模量值来评估近似准确性。这给出了通过有限维差分游戏的值，这给出了平均场类型差异游戏的价值函数。此外，我们介绍了构建有限维差异游戏的方法，该游戏以给定的精度近似原始游戏。
The theory of first-order mean field type differential games examines the systems of infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study the approximations of the value function of the first-order mean field type differential game using solutions of model finite-dimensional differential games. The model game appears as a mean field type continuous time Markov game, i.e., the game theoretical problem with the infinitely many agents and dynamics of each agent determined by a controlled finite state nonlinear Markov chain. Given a supersolution (resp. subsolution) of the Hamilton-Jacobi equation for the model game, we construct a suboptimal strategy of the first (resp. second) player and evaluate the approximation accuracy using the modulus of continuity of the reward function and the distance between the original and model games. This gives the approximations of the value function of the mean field type differential game by values of the finite-dimensional differential games. Furthermore, we present the way to build a finite-dimensional differential game that approximates the original game with a given accuracy.
