Inference in Games Without Equilibrium Restriction: An Application to Restaurant Competition in Opening Hours
Bibliographic record
Abstract
Erhao Xie*Bank of Canada, Ottawa, CanadaSupplementary materials for this article are available online. Please go to www.tandfonline.com/UBES.CONTACT Erhao Xie erhaoxie@bankofcanada.ca Bank of Canada, 234 Wellington St W, Ottawa, Ontario, Canada K1A 0G9.AbstractThis article relaxes the Bayesian Nash equilibrium assumption in the estimation of discrete choice games with incomplete information. Instead of assuming unbiased/correct expectations, the model specifies a player’s belief about the behaviors of other players as an unrestricted unknown function. I then study the joint identification of belief and payoff functions in a game where players have different numbers of actions (e.g., 3 × 2 game). This asymmetry in action sets partially identifies the payoff function of the player with more actions. Moreover, if usual exclusion restrictions are satisfied, the payoff and belief functions are point identified up to a scale, and the restriction of equilibrium beliefs is testable. Finally, under a multiplicative separability condition on payoffs, the above identification results are extended to the player with fewer actions and to games with symmetric action sets. I apply this model and its identification results to study the store hours competition between McDonald’s and Kentucky Fried Chicken in China. The null hypothesis of unbiased beliefs is rejected. If researchers incorrectly impose the equilibrium assumption, then the estimated interactive effect would be biased downward by more than 50%.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.021 | 0.118 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.005 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".