选择偏好理论中的持久混合世界观
Persistent mixed worldviews in the theory of chosen preferences
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中文总结 AI 辅助
本文证明选择偏好理论中混合世界观在平稳均衡中可持久存在，并给出收敛到纯粹世界观的条件及均衡存在性刻画。
中文摘要 AI 辅助
Bernheim、Braghieri、Martínez-Marquina 和 Zuckerman（2021年，《美国经济评论》）发展了一种选择偏好理论，并推测在低思维灵活性下会收敛到纯粹世界观。我们证明（原始的）推测不成立：即使有任意多的世界观，当所有纯粹世界观都是吸收态时，从一个相对开放的世界观初始集合出发，在每个平稳均衡中，一个共同价值行动仍能维持混合世界观。然而，有限线性规划刻画了一个充分的持久性条件。相反，混合累积点要求共享价值最大化。如果每个可实施行动都有唯一的评估者最大化者，那么每个现有的平稳均衡在内部灵活性和贴现参数下都会收敛到纯粹性。经验效用收敛不需要唯一性。在现有均衡中，小的收益扰动以高概率在固定时间范围内保持妥协。严格定制的世界观在足够低的思维灵活性下产生存在性和一步均衡刻画；弱实施可能阻碍平稳纯策略的存在性。持久性和收敛性结果扩展到平稳随机化。
英文摘要
Bernheim, Braghieri, Martínez-Marquina, and Zuckerman (2021, American Economic Review) develop a theory of chosen preferences and conjecture convergence to pure worldviews at low mindset flexibility. We show that the (original) conjecture fails: with arbitrarily many worldviews, a common-value action sustains mixed worldviews in every stationary equilibrium from a relatively open set of initial worldviews, even when all pure worldviews are absorbing. However, finite linear programs characterize a sufficient persistence condition. Conversely, mixed accumulation points require shared valuation maxima. If each implementable action has a unique maximizing evaluator, every existing stationary equilibrium converges to purity for all interior flexibility and discount parameters. Experienced utility converges without uniqueness. In existing equilibria, small payoff perturbations preserve compromise over fixed horizons with high probability. Strictly tailored worldviews yield existence and a one-step equilibrium characterization at sufficiently low mindset flexibility; weak implementation can preclude stationary pure-strategy existence. The persistence and convergence results extend to stationary randomization.
发表机构
- Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）
- Research Institute of Intelligent Complex Systems, Fudan University（复旦大学智能复杂系统研究院）
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