Algorithm

A

Our first offer calculator is based on over 25 million seller-buyer negotiations (see dataset for further details). The calculator can provide buyers with a recommended first offer, depending on which kind of product they want to buy (e.g., antiques, art, cell phones), the seller’s listing price (e.g., $400), and the buyer’s willingness to risk an impasse (e.g., max. 20% impasse risk). Our calculator suggests the first offer that minimizes the predicted final price whilst keeping the impasse risk level below the desired level.

Our calculator draws on three variables from the raw data: buyers’ first-offer magnitude, impasse risk, and sellers’ claimed value.

1Buyer’s first-offer magnitude: 
For buyers’ first-offer magnitude, we divided the absolute values of buyers’ first-offers (e.g., $100.00) by the absolute values of sellers’ asking prices (e.g., $400.00) to receive a relative measure of buyers’ first-offer magnitude (e.g., 25% of the seller’s asking price). We did this for each of the over 25 million negotiations in the data set. We then put each negotiation into one of 101 percentage-based subgroups depending on buyers’ first-offer magnitude (e.g., we grouped all negotiations with buyers’ first-offer magnitudes <0.5%, 0.50%-1.49%, 1.50%-2.49%, […] 97.50%-98.49%, 98.50%-99.49%, >99.50% into a percentage-based subgroup).

2. Impasse risk: 
For each of the buyers’ first-offer magnitude subgroups, we computed the impasse risk (i.e., the percentage of negotiations within this subgroup which ended in an impasse; e.g., 30 impasses / 100 negotiations = 30.00%).

3. Seller’s claimed value: 
For each of the buyers’ first-offer magnitude subgroups, we also computed the sellers’ claimed value (i.e., the mean final price of all negotiations within that subgroup that ended in a deal, as percentage of the seller’s asking price; e.g., for the 70 negotiations that ended with a deal, the mean final price was 80.00% of the sellers’ listing price). We then repeated this analysis separately for each product category, to provide first-offer recommendations tailored to each product category.

To provide customized first-offer recommendations for users’ unique negotiation situations, our calculator requires user input regarding the product category of the targeted item (e.g., antiques), the seller’s listing price for the item (e.g., $400.00), and the buyer’s willingness to risk an impasse in this negotiation (e.g., 20%). Based on this user input, our calculator identifies the first offer that is most favourable for the buyer’s specifications and returns a first-offer recommendation (e.g., $320.00, or 80% of the listing price), the accompanying impasse risk (e.g., 16.59%), and the predicted final price in case of a deal (e.g., $323.24). To convert the user input into first-offer recommendations, our algorithm goes through the following steps: 

Step 1) exclude all buyers’ first-offer magnitudes with an impasse risk that is higher than the buyer’s maximum willingness to reach an impasse,
Step 2) for the remaining data points, identify the first-offer magnitude that is associated with the lowest final price (i.e., lowest sellers’ claimed value),
Step 3) multiply the resulting first-offer magnitude with the seller’s listing price to provide the first-offer recommendation, and 
Step 4) multiply the sellers’ claimed value percentage with the seller’s listing price to provide the predicted final price.

In sum, our calculator provides buyers with a recommended first offer which minimizes the predicted final price, while considering the buyer’s risk preferences and the particular product category they’re interested in. You can try out the calculator and get negotiation advice based on over 25 million single negotiations for free.

Visit our OSF page here.