在线性-二次-高斯博弈中通过信息设计最大化社会福利与一致性
Maximizing Social Welfare and Agreement via Information Design in Linear-Quadratic-Gaussian Games
AI总结：
该研究针对LQG博弈的信息设计问题，推导了最大化社会福利、减少行动分歧及二者加权目标的解析与数值结果，明确了不同场景下完全信息披露或隐藏信息的最优条件。
摘要：
我们研究线性-二次-高斯（LQG）博弈：参与者的收益为依赖自身行动和未知收益相关状态的二次函数，且关于状态的信号在给定状态实现值时服从高斯分布。信息设计者决定向参与者披露信息的保真度，以最大化参与者的社会福利或减少参与者行动间的分歧。利用信息设计问题的半正定性，我们推导了特定LQG博弈下这些目标的解析解。我们证明，当存在共同的收益相关状态、参与者行动存在策略替代性或信号为公开信号时，完全信息披露可最大化社会福利。数值结果表明，随着策略替代性增强，信息披露的价值随之提升。当目标是促使参与者行动保持一致时，隐藏信息是最优策略。最后，我们研究了由社会福利与参与者行动凝聚力加权组合而成的信息设计目标。对于具有策略替代性的公开信号博弈，我们得到了完全信息披露为最优策略的权重区间。数值解显示，随着替代性增强，完全信息披露最优的实际区间会趋近于所得的解析区间。
英文摘要：
We consider linear-quadratic Gaussian (LQG) games in which players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution conditional on the state realization. An information designer decides the fidelity of information revealed to the players in order to maximize the social welfare of the players or reduce the disagreement among players' actions. Leveraging the semi-definiteness of the information design problem, we derive analytical solutions for these objectives under specific LQG games. We show that full information disclosure maximizes social welfare when there is a common payoff-relevant state, when there is strategic substitutability in the actions of players, or when the signals are public. Numerical results show that as strategic substitution increases, the value of the information disclosure increases. When the objective is to induce conformity among players' actions, hiding information is optimal. Lastly, we consider the information design objective that is a weighted combination of social welfare and cohesiveness of players' actions. We obtain an interval for the weights where full information disclosure is optimal under public signals for games with strategic substitutability. Numerical solutions show that the actual interval where full information disclosure is optimal gets close to the analytical interval obtained as substitution increases.
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