什么变体识别动态博弈中的收益？
What Variation Identifies Payoffs in a Dynamic Game?
- University of California, Riverside（加州大学河滨分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究探讨动态博弈中收益的识别问题，区分转移变化与策略变化的作用，提出秩识别条件，并在美国航空进入数据中验证了对手依赖对比的宽度。
AI中文摘要：
在动态博弈中，观察到的选择将当前利润与延续价值混合在一起。对手的存在增加了第二个问题：同样的比较平均了对手的均衡策略。改变原始转移过程会重写延续技术；在保持该定律不变的情况下，改变对手的马尔可夫策略，会重写对手条件收益上的混合。这两者不可相互替代。对于秩为$K$的对手特征收益，秩识别（至多差一个位置常数）需要$\u03c6=\lceil(MK-1)/(M-1)\rceil$个策略环境，当收益饱和时需要第二个核。秩仍可通过任意小的策略差异恢复。独立的私人冲击迫使混合对手行动可分解，因此依赖于$d$个对手的联合收益仅在接近共同内部基线的$\u03b7^{d}$阶上可见。要么秩失败，要么最小可识别奇异值至多为$\u03ba\u03b7^{\dPhi}$，与堆叠多少个核无关。在该方向上的Oracle-GLS方差仅在$n\u03b7^{2\dPhi}$发散时消失。一个在设计中携带第一阶段误差的Anderson-Rubin集在无消失风险条件下覆盖。在美国航空进入案例中，即使在秩识别方向上，最有利的对手依赖对比也比观察到的行为宽几倍。
英文摘要：
Observed choice in a dynamic game mixes current profit with continuation value. A rival adds a second problem: the same comparison averages over the rival's equilibrium policy. Changing the primitive transition rewrites continuation technology; changing the rival's Markov policy, holding that law fixed, rewrites the mixture over rival-contingent payoffs. The two are not substitutes. For a rival-feature payoff of rank $K$, rank identification up to location requires $\Ephi=\lceil(MK-1)/(M-1)\rceil$ policy environments, and a second kernel when payoffs are saturated. Rank can still be restored by arbitrarily small policy differences. Independent private shocks force mixed rival actions to factor, so a payoff that depends jointly on $d$ rivals is visible only at order $η^{d}$ near a common interior baseline. Either rank fails or the smallest identified singular value is at most $κη^{\dPhi}$, independently of how many kernels are stacked. Oracle-GLS variance in that direction vanishes only if $nη^{2\dPhi}$ diverges. An Anderson--Rubin set that carries first-stage error in the design matrix covers without a vanishing-risk condition. On U.S.\ airline entry, even among rank-identified directions, the most favorable rival-dependent contrast is several times wider than observed behavior.
