Inference in Games Without Nash Equilibrium: An Application to Restaurants’ Competition in Opening Hours
Bibliographic record
Abstract
This paper relaxes the Bayesian Nash equilibrium (BNE) assumption commonly imposed in empirical discrete choice games with incomplete information. Instead of assuming that players have unbiased/correct expectations, my model treats a player’s belief about the behavior of other players as an unrestricted unknown function. I study the joint identification of belief and payoff functions. I show that in games where one player has more actions than the other player, the payoff function is partially identified with neither equilibrium restrictions nor the usual exclusion restrictions. Furthermore, if the cardinality of players’ action sets varies across games, then the payoff and belief functions are point identified up to scale normalizations and the restriction of equilibrium beliefs is testable. For games where action sets are constant across players and observations, I obtain very similar identification results without imposing restrictions on beliefs, as long as the payoff function satisfies a condition of multiplicative separability. I apply this model and its identification results to study the store hours competition between McDonald’s and Kentucky Fried Chicken (KFC) in China. The null hypothesis that KFC has unbiased beliefs is rejected. Failing to account for KFC’s biased beliefs generates an attenuation bias on estimated strategic effects. Finally, the estimation results of the payoff functions indicate that the decision about store hours is a type of vertical differentiation. By operating through the night, a firm not only attracts night-time consumers but also can steal competitors’ day-time customers. This result has implications on the optimal regulation of stores’ opening hours.
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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 | 0.019 | 0.107 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.005 | 0.004 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.007 | 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".