Targeting customers under response-dependent costs

Abstract: This study provides a formal analysis of the customer targeting problem when the cost for a marketing action depends on the customer response and proposes a framework to estimate the decision variables for campaign profit optimization. Targeting a customer is profitable if the impact and associated profit of the marketing treatment are higher than its cost. Despite the growing literature on uplift models to identify the strongest treatment-responders, no research has investigated optimal targeting when the costs of the treatment are unknown at the time of the targeting decision. Stochastic costs are ubiquitous in direct marketing and customer retention campaigns because marketing incentives are conditioned on a positive customer response. This study makes two contributions to the literature, which are evaluated on an e-commerce coupon targeting campaign. First, we formally analyze the targeting decision problem under response-dependent costs. Profit-optimal targeting requires an estimate of the treatment effect on the customer and an estimate of the customer response probability under treatment. The empirical results demonstrate that the consideration of treatment cost substantially increases campaign profit when used for customer targeting in combination with an estimate of the average or customer-level treatment effect. Second, we propose a framework to jointly estimate the treatment effect and the response probability by combining methods for causal inference with a hurdle mixture model. The proposed causal hurdle model achieves competitive campaign profit while streamlining model building. Code is available at https://github.com/Humboldt-WI/response-dependent-costs.