AI 中文总结
该研究构建了量子贝叶斯相关均衡理论，证明量子信息结构的顺从性等价于算子的Loewner序关系，其均衡集合可计算，经典结构可嵌入，且更多量子信息会缩小均衡集合。
AI 中文摘要
Bergemann和Morris（2016）证明，当且仅当某一信息结构在所有博弈中诱导出更小的贝叶斯相关均衡结果集合时，该信息结构比另一信息结构更具信息性。我们构建其量子对应形式：信息结构成为由收益状态索引的密度算子族，由中介观测。我们证明，顺从性等价于某一参与者子系统上算子的Loewner序关系；均衡集合为非空紧谱面体，可通过半定规划计算；经典结构可精确嵌入；在量子个体充分性条件下，更多信息会缩小所有博弈中的均衡集合。
英文摘要
Bergemann and Morris (2016) show that one information structure is more informative than another exactly when it induces a smaller set of Bayes correlated equilibrium outcomes in every game. We build the quantum analogue. An information structure becomes a family of density operators indexed by the payoff state, which the mediator observes. We show that obedience is equivalent to a Loewner domination between operators on one player's subsystem. The equilibrium set is then a nonempty compact spectrahedron computable by semidefinite programming, classical structures embed exactly, and under quantum individual sufficiency more information shrinks the equilibrium set in every game.
Comments24 pages, 1 figure
