Identification of games of incomplete information with multiple equilibria and unobserved heterogeneity
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Bibliographic record
Abstract
This paper deals with identification of discrete games of incomplete information when we allow for three types of unobservables: payoff‐relevant variables, both players' private information and common knowledge, and nonpayoff‐relevant variables that determine the selection between multiple equilibria. The specification of the payoff function and the distributions of the common knowledge unobservables is nonparametric with finite support (i.e., finite mixture model). We provide necessary and sufficient conditions for the identification of all the primitives of the model. Two types of conditions play a key role in our identification results: independence between players' private information, and an exclusion restriction in the payoff function. When using a sequential identification approach, we find that the up‐to‐label‐swapping identification of the finite mixture model in the first step creates a problem in the identification of the payoff function in the second step: unobserved types have to be correctly matched across different values of observable explanatory variables. We show that this matching‐type problem appears in the sequential estimation of other structural models with nonparametric finite mixtures. We derive necessary and sufficient conditions for identification, and show that additive separability of unobserved heterogeneity in the payoff function is a sufficient condition to deal with this problem. We also compare sequential and joint identification approaches.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it