Bibliographic record
Abstract
We consider the ultimate game where the first player offers the second player a number in the closed interval [0,1], while the second player accepts that offer if is at least the number prechosen by the second player. In case the second player accepts the offer the first player's payoff is . If the second player declines the offer the payoff for both players is . We characterize the Nash equilibrium for this game with mixed strategies. Here by a mixed strategy we mean a Borel probability on the interval [0,1]. Upon generalizing the above game, we formulate an -person game where each player can use a mixed strategy from a compact Hausdorff topological space. Again here by a mixed strategy we mean a regular Borel probability on the topological space. We then, by using a locally convex topological vector space version of Kakutani's fixed point theorem for upper semi-continuous convex compact valued set function, show that this generalized game has a Nash equilibrium. As a corollary to our result we obtain, in the special finite dimensional case, Rosen's theorem, which, in its turn, generalizes Nash's theorem. References [1] J. P. Aubin, Mathematical methods of games and economic theory, North-Holland, 1982. [2] Jonathan M. Borwein, Convex analysis and nonlinear optimization, Canadian Mathematical Society, 2000. [3] Vasile I. Istratescu, Fixed point theory, D. Reidel Publishing Company, 1981. [4] John L. Kelley, General Topology, Springer-Verlag, 1955. [5] J. Nash, Equilibrium points in -person games, Proc. Nat. Acad. Sci. U.S.A. 36, 48-49, 1950. [6]J. B. Rosen, Existence and uniqueness of equilibrium points for concave -person games, Econometrica, Vol. 33, 520-534, 1965. Dept. of Data Information, Korea Maritime University, jgbae@hhu.ac.kr GIFTED, KAIST, cschoi@kaist.ac.kr
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".