Ergodic control of a heterogeneous population and application to electricity pricing - Q. Jacquet, W. van Ackooij, C. Alasseur & S. Gaubert

We consider a dynamic pricing model, in which a population of customers can change contracts at any time depending on pricing conditions and customer-specific characteristics such as inertia (propensity to stay with the same supplier). A supplier then seeks to maximise its average revenue per unit time, assuming that the population is of infinite size (the 'mean field' limit).
We present an application to energy pricing, and solve this problem by applying an iteration algorithm on relative values. When the inertia of some customers is sufficient, the optimal strategy leads to cyclical pricing policies, interpreted as occasional discounts.