Convergence Analysis of No-Regret Bidding Algorithms in Repeated Auctions
Bibliographic record
Abstract
The connection between games and no-regret algorithms has been widely studied in the literature. A fundamental result is that when all players play no-regret strategies, this produces a sequence of actions whose time-average is a coarse-correlated equilibrium of the game. However, much less is known about equilibrium selection in the case that multiple equilibria exist. In this work, we study the convergence of no-regret bidding algorithms in auctions. Besides being of theoretical interest, bidding dynamics in auctions is an important question from a practical viewpoint as well. We study the repeated game between bidders in which a single item is sold at each time step and the bidder's value is drawn from an unknown distribution. We show that if the bidders use any mean-based learning rule then the bidders converge with high probability to the truthful pure Nash Equilibrium in a second price auction, in VCG auction in the multi-slot setting and to the Bayesian Nash equilibrium in a first price auction. We note mean-based algorithms cover a wide variety of known no-regret algorithms such as Exp3, UCB, \epsilon-Greedy etc. Also, we analyze the convergence of the individual iterates produced by such learning algorithms, as opposed to the time-average of the sequence. Our experiments corroborate our theoretical findings and also find a similar convergence when we use other strategies such as Deep Q-Learning.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.008 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 teacher head, 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".