Subjective Equilibria under Beliefs of Exogenous Uncertainty in Stochastic Dynamic Games
Bibliographic record
Abstract
We consider a non-cooperative multi-stage game with discrete-time dynamics. The salient aspect of our model is that it includes `environment' variables which influence the cost as well as the state dynamics of each player. The `environment variables' are identical for all players and are determined by the decisions of all players. We provide a stochastic and dynamic generalization of what is known as the price-taking behavior in the economics literature in which each player chooses its decisions optimally under the (incorrect) belief that the environment variables are generated by an independent and exogenous stochastic process. In our setup, players observe only the past realizations of the environment variables in addition to their own state realizations and their own past decisions. At an equilibrium, referred to as a \textit{subjective equilibrium}, if players are given the full distribution of the stochastic environment process as if it is an exogenous process, they would have no incentive to unilaterally deviate from their equilibrium strategies. We establish the existence of subjective equilibria in mixed strategies for general compact metric space models. We study various structural properties of such equilibria in two different cases where the state, control, disturbance, and environment variables belong to (i) finite sets or (ii) finite dimensional Euclidean spaces. In either case, the time-horizon can be finite as well as infinite. We establish the near person-by-person optimality of a subjective equilibrium (which constitutes an approximate Nash equilibrium) when there are large number of players and the environment variables are generated either by the empirical distributions of the decisions in the first case or by the average decisions in the second case. This result on near person-by-person optimality is also extended to pure strategies under additional assumptions.
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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 | 0.004 | 0.016 |
| 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 | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".