Competing for Consumer's Attention
Bibliographic record
Abstract
We consider an infinite-horizon differential game played by two direct marketers. Each player controls the number of emails sent to potential customers at each moment in time. There is a cost associated to the messages sent, as well as a potential reward. The latter is assumed to depend on the state variable defined as the level of the representative consumer's attention. Two features are included in the model, namely, marginal decreasing returns and bounded rationality. By the latter, we mean that the representative consumer has a limited capacity for processing the information received. The evolution of this capacity depends on its level, as well as on the emails sent by both players. This provides environmental flavour where, usually, one player's pollution emissions (here emails) also affect the payoff of the other player by damaging the common environment (here, the stock of consumer attention).We characterize competitive equilibria for different scenarios based on each player's type, i.e., whether the player is a spammer or not. We define a spammer as a myopic player, i.e., a player who cares only about short-term payoff and ignores the impact of her action on the state dynamics. In all scenarios, the game turns out to be of the linear-quadratic variety. Feedback Nash equilibria for the different scenarios are characterized and the equilibrium strategies and outcomes are compared.Finally, we analyze the game in normal form, where each player has the option of choosing between being a spammer or not, and we characterize Nash equilibria
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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 | 0.006 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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".