34 BIAIS AND FAUGERON-CROUZET The retail investors <strong>and</strong> the informed investor with a bad signal obtain 0-expected gains in equilibrium <strong>and</strong> it is straightforward to see that they cannot obtain positive profits by deviating. Proof of Proposition 5. Consider a c<strong>and</strong>idate equilibrium, whereby tacit collusion would prevail, <strong>and</strong> in which the <strong>IPO</strong> price would always equal v0. In such an equilibrium the investors would bid as much as possible while not pushing the price above v0 <strong>and</strong> still deterring the other investor from competing away market shares. To avoid pushing the price above v0, they place bids for (slightly less than) S N shares at pN <strong>and</strong> for S(1 − 1/N) atv0. The expected profit from such tacit collusion after observing a good signal is S [E(v | g) − v0]. N + 1 − k If, she expects the others to follow this strategy, the informed investor placing a bid for S shares at p1 = v1 expects to gain S[E(v | g) − v1]. Hence, she prefers to follow that strategy rather than to implicitly collude if E(v | g) − v1 > 1 [E(v | g) − v0]. N + 1 − k REFERENCES Allen, F., <strong>and</strong> Faulhaber, G. (1989). Signaling by underpricing in the <strong>IPO</strong> market, J. Finan. Econ. 23, 303–323. Beatty, R. P., <strong>and</strong> Ritter, J. (1986). Investment banking, reputation <strong>and</strong> the underpricing of initial public offerings, J. Finan. Econ. 15, 213–232. Belletante, B., <strong>and</strong> Paliard, R. (1993). Does knowing who sells matter in <strong>IPO</strong> pricing: The <strong>French</strong> Second Market Experience, Cah. Lyon. Rech. Gestion 14, 42–74. Benveniste, L., <strong>and</strong> Spindt, P. (1989). How investment bankers determine the offer price <strong>and</strong> allocation of new issues, J. Finan. Econ. 24, 343–361. Benveniste, L., <strong>and</strong> Wilhelm, W. (1990). A comparative analysis of <strong>IPO</strong> proceeds under alternative regulatory environments, J. Finan. Econ. 28, 173–207. Benveniste, L., <strong>and</strong> Wilhelm, W. (1997). Initial public offerings: Going by the boook, J. Appl. Corp. Finan., Spring. Biais, B., Bossaerts, P., <strong>and</strong> Rochet, J. C. (2002). An optimal <strong>IPO</strong> mechanism, Rev. Econ. Stud., forthcoming. Brennan, M., <strong>and</strong> Franks, J. (1995). Underpricing, ownership <strong>and</strong> control in <strong>IPO</strong> of equity securities in the UK, mimeo, London Business School. Chemmanur, T. (1993). The pricing of <strong>IPO</strong>s: A dynamic model with information production, J. Finance 48(1), 285–304.
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