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Robust Competitive Ratio for Deterministic Monopoly Pricing
Tim S G van Eck1, Pieter Kleer1, Johan S H van Leeuwaarden1
1Department of Econometrics and Operations Research, Tilburg University, Tilburg, Netherlands.
Mathematical Methods of Operations Research (Heidelberg, Germany)
|July 25, 2026
Summary
This study introduces robust pricing strategies for sellers with limited market data. It finds that the worst-case market for competitive ratio (CR) also minimizes expected revenue, guiding optimal pricing decisions.
Area of Science:
- Economics
- Operations Research
- Game Theory
Background:
- Sellers often operate with incomplete market information, possessing only summary statistics of customer valuations.
- Deterministic monopoly pricing strategies need to account for this uncertainty to remain effective.
- Existing models may not adequately address pricing under partial knowledge of valuation distributions.
Purpose of the Study:
- To develop and analyze deterministic monopoly pricing strategies under partial market knowledge.
- To evaluate pricing strategies using the competitive ratio (CR) framework.
- To identify optimal pricing that minimizes the CR across various market scenarios.
Main Methods:
- Utilizing distributionally robust optimization and max-min analysis.
- Characterizing worst-case market scenarios consistent with available summary statistics (mean, dispersion, maximum value).
- Analyzing optimal pricing considering different measures of dispersion (variance, fractional moments).
Main Results:
- A complete solution for minimizing the competitive ratio (CR) is provided.
- The worst-case market scenario for CR was found to coincide with that for expected revenue.
- Dispersion and maximum valuation significantly influence optimal deterministic pricing strategies.
Conclusions:
- The study offers practical guidance for setting robust prices in markets with limited information.
- The findings provide a framework for optimizing pricing based on summary statistics.
- Understanding the interplay between CR, revenue, and market uncertainty is crucial for effective pricing.
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