Discounted robust stochastic games with applications to homeland security and flow control

Restricted until 26 June 2009. This dissertation presents a distribution-free, robust optimization model for n-person finite state/action discounted stochastic games with incomplete information. We consider n-player, non-zero sum discounted stochastic games in which none of the players knows the true data of the game and each player considers a distribution-free incomplete information stochastic game to be played using robust optimization. We call such games discounted robust stochastic games. Discounted robust stochastic games allow us to use simple uncertainty sets for the unknown data of the game, and to eliminate the former approaches' requirements on defining prior probability distributions over a set of games. We prove the existence of equilibrium points when the payoffs of the game belong to a bounded set and the transition data is ambiguious. Unlike the prior work on incomplete information stochastic games, our approach lends itself to an explicit mathematical programming formulation for an equilibrium calculation. We illustrate the use of discounted robust stochastic games in a security related decision problem, followed by a control problem in a single server queuing system.本数据集的公开权限受限至2009年6月26日。本文针对具有不完全信息的n人有限状态/行动折扣随机博弈，提出了一种无分布依赖（distribution-free）的鲁棒优化（robust optimization）模型。本文所研究的对象为n人非零和折扣随机博弈，所有参与方均无法获知博弈的真实数据，且各参与方均采用鲁棒优化方法处理该无分布依赖的不完全信息随机博弈，我们将此类博弈命名为折扣鲁棒随机博弈。折扣鲁棒随机博弈允许我们为博弈的未知数据采用简洁的不确定性集合，同时无需沿用此前研究中需为博弈集合定义先验概率分布的要求。我们证明了当博弈收益属于有界集合且转移数据存在歧义时，均衡点的存在性。与此前针对不完全信息随机博弈的研究不同，我们的方法可直接用于构建均衡计算的显式数学规划模型。我们首先通过一个安防相关决策问题阐释了折扣鲁棒随机博弈的应用场景，随后又通过单服务器排队系统中的控制问题进一步展示其具体应用。