  We construct explicitly a bridge process whose distribution, in its own
filtration, is the same as the difference of two independent Poisson processes
with the same intensity and its time 1 value satisfies a specific constraint.
This construction allows us to show the existence of Glosten-Milgrom
equilibrium and its associated optimal trading strategy for the insider. In the
equilibrium the insider employs a mixed strategy to randomly submit two types
of orders: one type trades in the same direction as noise trades while the
other cancels some of the noise trades by submitting opposite orders when noise
trades arrive. The construction also allows us to prove that Glosten-Milgrom
equilibria converge weakly to Kyle-Back equilibrium, without the additional
assumptions imposed in \textit{K. Back and S. Baruch, Econometrica, 72 (2004),
pp. 433-465}, when the common intensity of the Poisson processes tends to
infinity.
