Simple Pricing Schemes for Consumers with Evolving Values
Talkat Optimization and Decision-Making Under Uncertainty (Simons Institute, September 2016) · 2016-09-19..09-23·
summary
Considers a buyer who repeatedly uses an app whose value evolves stochastically and compares a simple pricing to the omniscient benchmark that extracts the buyer’s cumulative value. Offers free trial then fixed price schedules announced up front and assumes a martingale with bounded step and minimum variance evolution (values in [0,1], absorption at zero). Shows constant-factor approximation for simple random walks and a bound that depends on the ratio epsilon/delta in the general case, robust to the buyer’s risk attitude and requiring only estimates of epsilon and delta.
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chapters (16)
- 0:00Intro
- 0:55Uncertainty drives mechanism design
- 5:30The app-store problem
- 6:59Formalism for one-shot mechanism design
- 8:28Formalism for dynamic mechanism design
- 11:13Dynamic MD: previous work
- 12:18Dynamic MD: desired properties
- 13:22App-store: martingale model
- 14:10"Pay per play" pricing and myopic buyers
- 15:42The competition
- 17:19An illustrative example
- 19:50Main result
- 25:42Proof intuition for simple random walk
- 28:23Proof: general version
- 28:59Proof sketch
- 30:34Summary
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