Price limits under incomplete preference information based on almost stochastic dominance

Abstract

We derive price limits as decision aids for identifying favorable and unfavorable contracts from the perspective of a selling firm in face of uncertain outcomes. The analysis is based on the concept of almost stochastic dominance to incorporate incomplete information about the decision-maker’s preferences. The main challenges to use this concept in practice are to define and limit the required preference information and to demonstrate the performance of the resulting price limits. We propose price limits that are suitable for a wide range of applications, in particular services. While their information requirements vary, all price limits refer to the same type of aggregate information about marginal utilities and risk aversion. In the scenario with the lowest requirements, the preference information shrinks to a single number which is easy to approximate and to communicate. A comprehensive numerical study featuring fixed-price contracts shows that the incomplete preference information may lead to substantial improvements of the price limits over the situation of no preference information. We also discuss determinants and caveats of these improvements. For instance, the improvements increase with decreases of the decision-maker’s risk sensitivity and may differ substantially in magnitude between the lower and the upper price limit.