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We consider the profit-maximization problem solved by an electricity retailerwho aims at designing a menu of contracts. This is an extension of theunit-demand envy-free pricing problem: customers aim to choose a contractmaximizing their utility based on a reservation bill and multiple pricecoefficients (attributes). A basic approach supposes that the customers havedeterministic utilities; then, the response of each customer is highlysensitive to price since it concentrates on the best offer. A second classicalapproach is to consider logit model to add a probabilistic behavior in thecustomers' choices. To circumvent the intrinsic instability of the former andthe resolution difficulties of the latter, we introduce a quadraticallyregularized model of customer's response, which leads to a quadratic programunder complementarity constraints (QPCC). This allows to robustify thedeterministic model, while keeping a strong geometrical structure. Inparticular, we show that the customer's response is governed by a polyhedralcomplex, in which every polyhedral cell determines a set of contracts which iseffectively chosen. Moreover, the deterministic model is recovered as a limitcase of the regularized one. We exploit these geometrical properties to developa pivoting heuristic, which we compare with implicit or non-linear methods frombilevel programming, showing the effectiveness of the approach. Throughout thepaper, the electricity retailer problem is our guideline, and we present anumerical study on this application case.

Quadratic Regularization of Bilevel Pricing Problems and Application to Electricity Retail Markets