集体随机离散选择问题：一种Min-LQG博弈建模
Collective Stochastic Discrete Choice Problems: A Min-LQG Game Formulation
AI总结：
本文研究了具有社会互动的动态集体选择模型，通过Min-LQG博弈框架分析离散选择问题，提出基于均场博弈的去中心化控制策略，证明其收敛于纳什均衡。
摘要：
我们考虑了一类具有社会互动的动态集体选择模型，其中大量非均匀智能体必须在多个离散替代选项中做出选择，其选择的相关性持续受到噪声和群体行为的影响。此类问题被建模为所谓的Min-LQG博弈，即线性二次高斯动态非合作博弈，其中包含一个终端成本中的最小化项。该最小化项对于强制每个智能体做出特定的离散选择至关重要。均场博弈理论被用来生成一组去中心化的智能体反馈控制策略，然后显示当玩家数量增加到无穷大时，这些策略收敛到博弈的精确纳什均衡。我们方法的关键构建块是显式求解计算通用智能体对任意设定的平滑均场轨迹的最佳响应的问题。最终，智能体面临一个不断修订的离散选择问题，其中由当前条件决定的贪婪选择必须不断与未来过程噪声可能破坏此类决策的风险平衡。尽管智能体最终选择的替代品是随机的，由其整个噪声历史和初始状态决定，但极限无限人口的宏观行为仍可以预测。证明了任何博弈的纳什均衡由一个可以预先计算的概率矩阵定义，该矩阵描述了智能体人口最终在可用替代品中分裂的方式。
英文摘要：
We consider a class of dynamic collective choice models with social interactions, whereby a large number of non-uniform agents have to individually settle on one of multiple discrete alternative choices, with the relevance of their would-be choices continuously impacted by noise and the unfolding group behavior. This class of problems is modeled here as a so-called Min-LQG game, i.e., a linear quadratic Gaussian dynamic and non-cooperative game, with an additional combinatorial aspect in that it includes a final choice-related minimization in its terminal cost. The presence of this minimization term is key to enforcing some specific discrete choice by each individual agent. The theory of mean field games is invoked to generate a class of decentralized agent feedback control strategies which are then shown to converge to an exact Nash equilibrium of the game as the number of players increases to infinity. A key building block in our approach is an explicit solution to the problem of computing the best response of a generic agent to some arbitrarily posited smooth mean field trajectory. Ultimately, an agent is shown to face a continuously revised discrete choice problem, where greedy choices dictated by current conditions must be constantly balanced against the risk of the future process noise upsetting the wisdom of such decisions.Even though an agent's ultimately chosen alternative is random and dictated by its entire noise history and initial state, the limiting infinite population macroscopic behavior can still be predicted. It is shown that any Nash equilibrium of the game is defined by an a priori computable probability matrix characterizing the manner in which the agent population ultimately splits among the available alternatives.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
