The Simple Algebra of Surplus in Open, Private Values Auctions : A Nested Logit Merger Model

In a private values, open auction, we show that bidder surplus can be expressed as a simple difference between unconditional moments of order statistics. The strength of the result is its simplicity and generality, as we dispense with the typical assumptions of independence and/or symmetry. We show how to use the expression to derive closed-form expressions for the effects of a merger among bidders for any joint value distribution, and illustrate its use by simulating the effects of the 2016 proposed Anthem-Cigna merger using a nested logit specification