Strategic decision in a two-period game using a multi-leader-follower approach. Part 1 – General setting and weighted Nash equilibrium
Bibliographic record
Abstract
In the situation where a new player wants to join a group of players, which is interacting in a non-cooperative way through a generalized Nash game, this new player can face three different situations: playing together with the other players in a generalized Nash game, playing first and waiting for the response of the opponent group, or letting the group play first and act then as a follower. This two-period game can thus lead to a generalized Nash game, a single-leader-multi-follower game, or a multi-leader-single-follower game. Our aim in this couple of papers is to elaborate a decision-making strategy to help this new player when choosing the most beneficial game, beside the fact that he does not know what game the group of other players would like to select. This work, composed of a couple of papers, extends to n + 1 players the previous research of B. von Stengel (Games and Economic Behaviour -2010) done for a two-player symmetric duopoly game. In this first part, we present the main concepts, introduce in particular the new notion of weighted Nash equilibrium, and provide an adapted analysis in the case of a specific model. In the companion second part, the decision-making policy is developed and numerical simulations are conducted.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".