Predicting Transaction Outcomes Under Customized Pricing with Discretion : A Structural Estimation Approach

We consider a company selling heterogeneous products with prices customized for each customer and the final price is set by negotiations between sales agents and customers. This type of pricing modality is referred to as customized pricing with discretion and commonly used in insurance, consumer loans, mortgages, and many business-to-business markets. We assume that each sales agent has a minimum reserve price (RP) and each customer has a maximum willingness-to-pay (WTP) and, if the deal occurs, they agree on a price between these two values, which are not directly observable. Given the outcomes of a series of negotiations, our goal is to estimate the underlying joint distribution of WTP and RP and predict the outcomes of future transactions. We assume that the price that prevails as the outcome of the negotiation can be represented as a generalized Nash bargaining equilibrium. We develop a structural estimation method based on the expectation-maximization algorithm that allows for the WTP and RP distributions to depend on an arbitrary set of covariates. Using both simulated and a real-world data set, we show that our proposed method improves the predictive accuracy of the deals’ final prices by 6.8% and the customers' decision to accept the deal by around 2% compared to standard regression-based approaches. These results are robust to assumptions on the distribution of bargaining power between the two parties in the negotiation. We also show that the estimated distributions can be used to optimize controls on negotiated prices that can significantly increase revenues relative to both unconstrained negotiations and centrally-optimized fixed prices