Optimal Pricing In Black Box Producer-Consumer Stackelberg Games Using Revealed Preference Feedback

This paper considers an optimal pricing problem for the black box producer-consumer Stackelberg game. A producer sets price over a set of goods to maximize his profit (the difference in revenue and cost function). The consumer buys quantity to maximize his utility function. The utility function of the consumer and the cost function of the producer are ‘black box’ functions (unknown functions with limited evaluations). Using a Gaussian process framework we derive a Bayesian algorithm for learning the optimal price. Numerical results illustrate the efficacy of our approach compared to existing literature.