Characterization of pure strategy equilibria in uniform price IPO auctions

We characterize pure strategy equilibria of common value multi-unit uniform price auctions under the framework of initial public offerings, where bidders have incomplete private information regarding the value of shares and submit discrete demand schedules. We show that there exists a continuum of equilibria where investors with a higher expectation about the value of shares bid for higher quantities at higher prices, and as a result the market price increases with the market value. The collusive equilibria, in which investors place bids regardless of their expectation about the value, are obtained under stricter conditions than in the continuous price case.