Testing Collusion and Cooperation in Binary Choice Games
Bibliographic record
Abstract
This paper studies the testable implication of players’ collusive or cooperative behaviours in a binary choice game with complete information. In this paper, these behaviours are defined as players coordinating their actions to maximize the weighted sum of their payoffs. I show that this collusive model is observationally equivalent to an equilibrium model that imposes two restrictions. The first restriction is on each player’s strategic effect and the second one requires a particular equilibrium selection mechanism. Under the equilibrium condition, these joint restrictions are simple to test using tools in the literature on empirical games. This test, as suggested by the observational equivalence result, is the same as testing collusive and cooperative behaviours. I illustrate the implementation of this test by revisiting the entry game between Walmart and Kmart studied by Jia (2008). Under the equilibrium condition, Jia’s original estimates are consistent with the first restriction on the strategic effects, serving as a warning sign of potential collusion. This paper tests and rejects the second restriction on the equilibrium selection mechanism. Thus, the empirical evidence suggests that Walmart and Kmart did not collude on their entry decisions.
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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 | 0.031 | 0.179 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| 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".