Mergers, concurrent marketing mechanisms and the performance of sequential auctions

The allocation efficiency is maintained because the object is still won by the bidder with the highest valuation, but the expected price is lower because of the impact of the smaller number of bidders on the probability of winning. [...] Starting at the bottom of the tree in Figure 1, we can see that the vector of gross payoffs when bidder A wins both objects is (17; 0; 0), which is simply the sum of the valuations for the objects won by the bidders. [...] The price trend is constant, p = p = 6 , and the allocation is efficient since 1 2 the objects end up in the hands of the bidders with the highest valuations. [...] Hence, the seller’s revenue is R S = 101 2 7 If 2 + 2V V < 2 1V and 2 + 2V V < 2 1V the post merger price of the second object is lower than A B B A C C the pre merger price of the second object ( 2 2V < V ) while the post merger price of the first object B C is lower than the pre merger price of the first object if and only if 2 − 2 > 1 − 1VB V. [...] The weakly higher prices under the merger generate higher gains for the merged firm relative to the gains of firms A and B prior to the merger because the gains under the merger are computed using the three highest valuations, 1 , 2V V , 3V , as opposed A A A to 1 1V ,V , 2V under the pre-merger equilibrium.