Computing Nash equilibria for product design based on hierarchical Bayesian mixed logit models
基于层级贝叶斯混合 Logit 模型计算产品设计的纳什均衡AI 解读 ↓
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基于层级贝叶斯混合 Logit 模型计算产品设计的纳什均衡
- 研究问题
- 估计的混合 Logit 偏好模型能否恢复价格与产品设计竞争的真实纳什均衡，选择行为类型和贝叶斯不确定性如何影响恢复能力？
- 方法与思路
- 作者基于层级贝叶斯混合 Logit 模型模拟竞争，比较概率性与确定性选择规则，并分析大量采用真实价格和成本构造的均衡。
- 材料陈述的贡献
- 摘要称，均衡恢复主要取决于选择行为类型；真实行为确定时，采用确定性规则及纳入贝叶斯参数不确定性可提高恢复率。
- 阅读关注点
- 应核对真实均衡的定义与构造、数值精确性的标准、均衡多重性处理，以及偏好估计误差和参数不确定性如何传递至均衡。
- 阅读边界
- 这是 arXiv 预印本，同行评审或接收状态未核实；摘要未说明完整竞争模型和恢复率数值，结论不能直接推广至所有市场。
原文摘要
Despite a substantial body of theoretical and empirical research in the fields of conjoint and discrete choice analysis as well as product line optimization, relatively few papers focused on the simulation of subsequent competitive dynamics employing non-cooperative game theory. Only a fraction of the existing frameworks explored competition on both product price and design, none of which used fully Bayesian choice models for simulation. Most crucially, no one has yet assessed the choice models' ability to uncover the true equilibria, let alone under different types of choice behavior. Our analysis of thousands of Nash equilibria, derived in full and numerically exact on the basis of real prices and costs, provides evidence that the capability of state-of-the-art mixed logit models to reveal the true Nash equilibria seems to be primarily contingent upon the type of choice behavior (probabilistic versus deterministic), regardless of the number of competing firms, offered products and features in the market, as well as the degree of preference heterogeneity and disturbance. Generally, the highest equilibrium recovery is achieved when applying a deterministic choice rule to estimated preferences given deterministic choice behavior in reality. It is especially in the latter setting that incorporating Bayesian (hyper)parameter uncertainty further enhances the detection rate compared to posterior means. Additionally, we investigate the influence of the above factors on other equilibrium characteristics such as product (line) differentiation.