The DEA Game Cross-Efficiency Model and Its Nash Equilibrium
Bibliographic record
Abstract
In this paper, we examine the cross-efficiency concept in data envelopment analysis (DEA). Cross efficiency links one decision-making unit's (DMU) performance with others and has the appeal that scores arise from peer evaluation. However, a number of the current cross-efficiency approaches are flawed because they use scores that are arbitrary in that they depend on a particular set of optimal DEA weights generated by the computer code in use at the time. One set of optimal DEA weights (possibly out of many alternate optima) may improve the cross efficiency of some DMUs, but at the expense of others. While models have been developed that incorporate secondary goals aimed at being more selective in the choice of optimal multipliers, the alternate optima issue remains. In cases where there is competition among DMUs, this situation may be seen as undesirable and unfair. To address this issue, this paper generalizes the original DEA cross-efficiency concept to game cross efficiency. Specifically, each DMU is viewed as a player that seeks to maximize its own efficiency, under the condition that the cross efficiency of each of the other DMUs does not deteriorate. The average game cross-efficiency score is obtained when the DMU's own maximized efficiency scores are averaged. To implement the DEA game cross-efficiency model, an algorithm for deriving the best (game cross-efficiency) scores is presented. We show that the optimal game cross-efficiency scores constitute a Nash equilibrium point.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
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".