Bibliographic record
Abstract
Highlights • We analyze duopoly randomized pricing/lottery game with a potentially free product • Firm offering promotion with free products given behavioral bias zero price effect • We derive the equilibrium prices and optimal lottery parameters • Extensions: government certificate; symmetric game; binomial customer valuation; • Extensions: positive production cost; sequential market dynamics; partial market coverage This paper studies the design of probabilistic price promotions where consumers through a lottery are either offered one of many promotional prices, including zero, or offered, but not obligated, to purchase products at the a list price. Two behavioral biases are incorporated into the analysis: the cognitive bias zero-price effect , where consumers attach additional value to free products, and skepticism regarding the veracity of the lottery among a fraction of the consumers. The duopoly market consists of one firm operating the probabilistic price promotion and one firm operating a standard fixed price promotion. The equilibria regarding each firm’s optimal promotion parameters are derived. It is shown that a simple lottery, wherein consumers either receive the product for free or are offered to pay the fixed list price, is more profitable than a complex lottery with many promotional prices. Moreover, firms should only offer probabilistic price promotions when the zero-price effect is larger than a threshold, which decreases in the fraction of consumers who trust the promotions. This offers key managerial implications: firms with excellent reputations should offer the simple lottery to capitalize on the zero-price effect, while firms with mediocre reputations should prioritize fixed price promotions. Several robustness analyses and extensions to the base model are considered: symmetric promotion strategies; government lottery certification; sequential market dynamics; positive production cost; and heterogeneous consumer valuations.
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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 | 0.005 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".