Do buyer-size discounts depend on the curvature of the surplus function? Experimental tests of bargaining models

A number of recent theoretical papers have shown that, for buyer-size discounts to emerge in a bargaining model, the total surplus function over which parties bargain must have certain nonlinearities. We test the theory in an experimental setting in which a seller bargains with a number of buyers of different sizes. Nonlinearities in the surplus function are generated by varying the shape of the seller's cost function. Consistent with the theory, we find that quantity discounts emerge only in the case of increasing marginal cost, corresponding to a concave surplus function. We provide additional structural estimates to help identify the source of remaining discrepancies between experimental behavior and theoretical predictions (whether due to preferences for fairness or other factors such as computation errors).