发表机构
The Chinese University of Hong Kong（香港中文大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对类型分布未知的贝叶斯博弈，提出风险规避贝叶斯学习者的两种均衡模型，证明其存在唯一性及向真实均衡的收敛速率，并应用于价格竞争问题。
AI 中文摘要
经典贝叶斯博弈假设博弈参与者的类型联合分布是共同知识，但这一假设在实际应用中很少成立。我们通过研究一组短视参与者在贝叶斯纳什猜想下重复互动，并在贝叶斯学习框架内从随时间观测到的类型剖面中学习参数化联合类型分布，来解决这一问题。参与者可能持有异质先验，并可能对关于分布参数的认识论不确定性和对手类型中的随机不确定性均表现出风险规避。我们提出了两个模型：风险规避贝叶斯学习者之间的贝叶斯纳什均衡（BNE-RABL），其中认识论风险和随机风险被分别评估；以及基于贝叶斯预测分布的贝叶斯纳什均衡（BNE-BPD），其中两种不确定性来源被整合到贝叶斯预测分布中，并通过单一风险度量进行评估。在适当条件下，我们建立了两种均衡的存在性和唯一性，并推导了随着博弈重复进行和更多类型剖面被观测，均衡序列向真实类型分布下相应神谕贝叶斯纳什均衡收敛的非渐近收敛速率。这些结果进一步表明，随着样本量的增长，BNE-RABL和BNE-BPD策略之间的差异消失，这说明这两个模型可以被视为彼此的有效近似。我们将所提出的模型应用于价格竞争问题，并对理论结果进行了数值说明。
英文摘要
Classical Bayesian games assume that the joint distribution of players' types is common knowledge, an assumption that rarely holds in practical applications. We address this issue by studying a group of myopic players who repeatedly interact under the Bayesian Nash conjecture and learn a parametric joint type distribution from type profiles observed over time within a Bayesian learning framework. Players may hold heterogeneous priors and may be risk averse toward both epistemic uncertainty about the distributional parameter and aleatoric uncertainty in their rivals' types. We propose two models: a Bayesian Nash equilibrium among risk-averse Bayesian learners (BNE-RABL), in which epistemic and aleatoric risks are evaluated separately, and a BNE based on Bayesian predictive distributions (BNE-BPD), in which the two sources of uncertainty are integrated into a Bayesian predictive distribution and evaluated through a single risk measure. Under suitable conditions, we establish the existence and uniqueness of both equilibria, and derive non-asymptotic convergence rates of the equilibrium sequences toward the corresponding oracle BNE under the true type distribution as the game is repeatedly played and more type profiles are observed. These results further show that the discrepancy between the BNE-RABL and BNE-BPD strategies vanishes as the sample size grows, which illustrates that the two models can be regarded as effective approximations to each other. We apply the proposed models to a price competition problem and numerically illustrate the theoretical results.
