Auctions With Resale Markets a Model of Treasury Bill Auctions

Sushil Bikhchandani

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, ' \ + / u;f {i, x, y; Xo)/*(y|a;;xo)<^y. i'jt(i|i;ioJ Jx (10) where /t(y|x;xo) denotes the conditional density of Yk given Xi = x and Xq = Xq. In addition, the boundary condition 6(x; Xq) = u;''(i, x, x; Xq) must be satisfied. The solution to (10) with this boundary condition is — r*^ r^ hftl' Xr\) b{x;xo) = w'^{x, x, x;xo) - L{u\x;xo)dt(u;xo) +, . , ,' rdL(u|x;xo), (11) Jx Jx /t(u|u;xoj where L(ulx;xo) = exp|-y^^r(^j^^rf^|, f(u;xo) = iy''(u, u, u;xo), /■u /i(u;xo) = / u;f(u, u, y;xo)/t(y|u;xo)rfy. •'I Next, we define conditional information complements. Definition 2 Random variables, [Zi, . . . , Zm), are said to be information comple- ments conditional on random variable Y with respect to random variable T if OZiOZj where 4>{zi, ... , Zm, y) = E f Zi ^ Zi, . . . , Zm = Zm, Y = yj . If {Xi, X2, ... , Xn, P) are information complements conditional on Xq with re- spect to V, then a proof identical to that of Theorem 1 shows that b defined in (11) is a symmetric equilibrium strategy.

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