Eficiency of Competitive Stock Markets Where Trades have Diverse Information 579 h(yy|P1)=(2丌) /n1/n PI 1/n)|y-P1 -1八(1n1n)(p (27) [=[-P)(-P(y-P (P1-y)p-P)+n(-P1)] 2n-1 g2(y, Pi=exp( 2n [2P1-P2+n(-P)2 (19) Then h(y,列|P1)=g1(y,)g2(元,P1.QED We use Lemma I to prove Lemma 2 below. Lemma 2 states that if a trader is given y, then yi provides no additional information about P, over that provided LEMMA 2. Let m(PI ly) be the density of P, conditional on y. Let m(Pi,yi)be the density of PI conditional on y and y, Then m(P,lD)=m(Pily, y)and hence E[P1列=E[P1 P B (P)=一8(P)(FP g(Pih, o P) where g(Pi) is the marginal density of P 病(P1)=8( Pig yi,y)g(PD g(P1)g2(,P1) g(P)g1(y,y)g2(,P1) g(P1)(, P)dP