428 / 2024-04-25 09:46:17

Robust dynamic pricing under minimax regret with demand uncertainty

dynamic pricing,minimax regret,demand uncertainty

We consider a monopoly firm that dynamically sets prices for a new product under incomplete information. At the beginning of the selling season, the firm only knows the support of customers' valuation but has no information about the distribution of their valuation. To model this situation, we design a robust dynamic pricing scheme whose objective is to minimize the worst-case regret. By observing customers' purchase actions, the firm learns customers' valuations continuously and updates their pricing decisions dynamically. We consider two distinct kinds of customers: homogeneous customers and heterogeneous customers. We design an optimal pricing policy for homogeneous customers concerning the minimax total period regret rule for each possible scenario. We show that the minimax regret is identical in any price path and prove that the T-period minimax regret is bounded by O(log T). For heterogeneous customers, given information on historical prices, we propose a forward algorithm for calculating optimal prices under minimax regret. Furthermore, numerical experiments show that the algorithm can accurately learn the optimal price and performs better than traditional methods.