Optimal Policies for Online Markets with Social Signals

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Replicates the MusicLab setup and models sampling with a generalized multinomial logit where visibility, appeal, quality and a popularity exponent r govern sampling; computing the best ranking reduces to a linear fractional assignment solvable in strongly polynomial time; stochastic dynamics map to a Robbins–Monro ODE so r ≤ 1 yields a unique interior equilibrium with market shares proportional to quality and fast convergence, while r > 1 produces unstable equilibria, monopolies and unpredictability; segmentation restores efficiency; heterogeneous-class global optimization is NP‑hard.

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" chapters (22)

1. 0:00Start
2. 5:12Popularity Signals
3. 5:28Some Informal Results (Watts, 2013) M
4. 7:14Generalized Multinomial Logit M
5. 7:45The Objective
6. 8:33Estimating Quality
7. 9:10Marketing Optimization
8. 9:39Expected Performance
9. 10:14Quality and Market Share (1)
10. 12:52Outline
11. 13:47Benefits of Social Influence
12. 15:35Mixed Multinomial Logic Model
13. 16:32Average Quality Ranking
14. 17:44Market Segmentation Policy
15. 18:51How the market share evolves
16. 20:27The ODE Method to RMA
17. 21:23Convergence
18. 23:16Expected Purchases
19. 24:52What theory says
20. 25:36The Music Lab Revisited
21. 25:59Open Issues
22. 27:15Questions?