Basic concepts of game theory
Bibliographic record
Abstract
This chapter introduces those concepts in static and dynamic game theory that are particularly relevant for the study of differential games, the theory of which will be presented in chapters 4 to 8. In this chapter we proceed in a somewhat informal way and do not attempt to render a precise mathematical representation of each and every concept. The main idea is to provide an understanding of what game theory is about, and we have chosen not to complicate matters by insisting on mathematical rigour. Those wishing to study more precise accounts of game theory should consult the references mentioned in section 2.4. We start by discussing the distinction between noncooperative and cooperative games and offer some comments on game theoretic modelling. The chapter proceeds by presenting the two types of game theoretic models: the strategic form (or normal form) and the extensive form. We introduce fundamental concepts such as a player's strategy, the Nash equilibrium, the role of the information available to the players, and the concept of subgame perfectness. Finally, a brief presentation of a standard differential game model is given, postponing the detailed description to chapter 4. Axioms of game theory Game theory is concerned with the study of situations involving two or more decision makers (individuals, organizations, or governments). Decision makers are designated as players. The players often have partly conflicting interests and make individual or collective 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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.022 | 0.009 |
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".