Estimating the Strategic Value of Long Term Forward Purchase Contracts Using Auc

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Estimating the Strategic Value of Long Term Forward Purchase Contracts Using Auc
John E Parsons
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= S^ = S„, > c 1 Q Q+1 r. S)| ]/| {S . | S . =S)|, i. E. The fractional share obtained by dividing the remaining capacity among the buyers with reservation values equal to Sq.
In environments similar to ours, when the range of possible reservation values Is continuous, and subject to the time consistency condition mentioned above this simple Vickrey auction is optimal for the seller — that is, among the class of feasible, incentive compatible, and time consistent mechanisms it maximizes revenue
.... However, for an environment such as ours with a discrete range of reservation values we must alter slightly the price rule in order to guarantee revenue maximization — the modification and the reason for it is discussed in Harris and Raviv (1981): Q+1 ^Q^'^h Sq^^. 5A(Q. 1) Sq >R^ ' Vl=^Q for a set of values (A, . . . A ) as defined in Appendix 2, A(j)=A. When S. =R. , and where R. =min{R . 1 R . >c} . This modified price function differs from the h j' J simple Vickrey auction price function defined in (4) in that whenever exactly Q buyers have valuations at least as high as a given price, S, and the valuation of the buyer with the Q^^lst highest valuation is below this level, 16 S„, k+v}, hf J J where k is the scalar parameter of the assumed constant marginal capital cost function and v is the scalar parameter of the assumed constant operating cost function.

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