离散选择LQG平均场博弈中的对称性破缺
Symmetry-breaking in a discrete-choice LQG mean field game
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中文总结 AI 辅助
本文研究双选择LQG平均场博弈中的对称性破缺，证明随着社会不从众惩罚增加，对称均衡失稳并出现共识型不对称均衡。
中文摘要 AI 辅助
平均场博弈为建模大规模、相互作用的非合作智能体群体的动力学提供了一个连续统框架。本文研究了一个有限时域、双选择最小LQG平均场博弈中的对称性破缺，其中具有线性随机动力学的相同智能体在两个同等理想的终端目的地之间进行选择，同时权衡控制努力与从众的社会压力。该模型在两个目的地之间具有奇对称性，因此始终存在一个对称的动态纳什均衡，其中群体在两个目的地之间均匀分配，在最终时刻产生僵局集体状态。数值研究表明，随着社会不从众惩罚的增加，该对称均衡作为相关的标量自洽映射的不动点会失去稳定性，并出现不对称的共识纳什均衡，其中大多数智能体选择相同的目的地。通过标量映射表示分析线性化的前向-后向偏微分方程组，我们提供了对称均衡稳定性丧失的证明。结合映射的奇对称性，这暗示了对应于任一目的地共识的对称性破缺平均场博弈均衡的存在。
英文摘要
Mean-field games provide a continuum framework for modeling the dynamics of large, interacting populations of non-cooperative agents. This paper studies symmetry-breaking in a finite-horizon, two-choice min-LQG mean-field game in which identical agents with linear stochastic dynamics choose one of two equally desirable terminal destinations, while trading off control effort against social pressure to conform. The model has an odd symmetry between the two destinations and therefore always admits a symmetric, dynamic Nash equilibrium in which the population splits evenly between them, producing a deadlock collective state at final time. Numerical studies have suggested that, as the penalty for social nonconformity increases, this symmetric equilibrium loses stability as a fixed point of an associated scalar, self-consistency map, and asymmetric consensus Nash equilibria emerge, where most agents select the same destination. By analyzing the linearized forward-backward PDE system through the scalar map representation, we provide a proof of this loss of stability of the symmetric equilibrium. Together with the odd symmetry of the map, this implies the existence of symmetry-broken mean-field game equilibria corresponding to consensus on either destination.
发表机构
- University of Nebraska–Lincoln（内布拉斯加大学林肯分校）
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