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Konrad (2007) - Strategy In Contests-An Introduction (view source)
Revision as of 18:35, 25 April 2010
, 18:35, 25 April 2010→All-pay auctions
:<math>\mathbb{E}x_1 = \frac{v_2}{2}\,</math> and <math>\mathbb{E}x_2=\frac{v_2^2}{2v_1}\,</math>
Furthermore, we note that:
:<math>\mathbb{E}x_1 + \mathbb{E}x_2 = \frac{v_1 v_2 + v_2^2}{2v_1}\,</math>
which under the assumption that <math>v_1 \ge v_2\,</math>, we have <math>\mathbb{E}x_1 + \mathbb{E}x_2 \le v_2\,</math>.
So not only is the auction in efficient in that it doesn't extract the value of the second highest player, but it is also inefficient in the sense that it does not necessarily allocate the good to the individual with the highest valuation.
