Haojie Liu, Zihan Lin
arXiv 12 Sep 2026 · Econometrics
arXiv:2609.14069 · PDF · Extracted main text
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.
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| Reference | Intensity | Mentions | Sections | Main text | |
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| 1 | Andrews, Donald W. K. and Guggenberger, Patrik (2017) Asymptotic Size of Kleibergen's LM and Conditional LR Tests for Moment Condition Models | 0.644 | 2 | 2 | 100% |
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| 3 | U.S. Department of Transportation, Bureau of Transportation Statistics (2014) T-100 Domestic Segment (U.S. Carriers) | 0.511 | 2 | 2 | 50% |
| 4 | Aguirregabiria, Victor and Magesan, Arvind (2020) Identification and Estimation of Dynamic Games When Players' Beliefs Are Not in Equilibrium | 0.405 | 1 | 1 | 100% |
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| 8 | Anderson, T. W. and Rubin, Herman (1949) Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations | 0.405 | 1 | 1 | 100% |
| 9 | Bajari, Patrick and Benkard, C. Lanier and Levin, Jonathan (2007) Estimating Dynamic Models of Imperfect Competition | 0.405 | 1 | 1 | 100% |
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