2026-03-31

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杂记

今日感悟

The Revenue Equivalence Theorem simply says all the auctions we have the equivalent revenue. It’s only for expectation.

$$\sum _{i=1}^n{\int }_0^1{T}_i(v_i)dF(v_i)$$

在这里大家都 share 一个相同的 $F$

If you have a higher Virtual Valuation, you would have a higher probability. Since it is an increasing function, thus the good would be allocated to the person with highest valuation. But, if $F_1\ne F_2$ , thus ${\Psi }_1\ne {\Psi }_2$ , thus it’s possible that $\exists v_1{v}_2\text{s.t.}{v}_1>v_2$ .

$${\Psi }_1(v_1)<{\Psi }_2(v_2)$$

p24: Allocate to the “fake buyer” which is myself. The thing that changes is the $p$ .

今日杂谈