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This paper introduces a novel contextual bandit algorithm for personalizedpricing under utility fairness constraints in scenarios with uncertain demand,achieving an optimal regret upper bound. Our approach, which incorporatesdynamic pricing and demand learning, addresses the critical challenge offairness in pricing strategies. We first delve into the static full-informationsetting to formulate an optimal pricing policy as a constrained optimizationproblem. Here, we propose an approximation algorithm for efficiently andapproximately computing the ideal policy.  We also use mathematical analysis and computational studies to characterizethe structures of optimal contextual pricing policies subject to fairnessconstraints, deriving simplified policies which lays the foundations of morein-depth research and extensions.  Further, we extend our study to dynamic pricing problems with demandlearning, establishing a non-standard regret lower bound that highlights thecomplexity added by fairness constraints. Our research offers a comprehensiveanalysis of the cost of fairness and its impact on the balance between utilityand revenue maximization. This work represents a step towards integratingethical considerations into algorithmic efficiency in data-driven dynamicpricing.

Utility Fairness in Contextual Dynamic Pricing with Demand Learning