Before revision:  If there are no search frictions, then the problem reduces to the one examined in Hulko and Whitmeyer (2017). On the other hand, with search frictions,  if the expected value of the prize is sufficiently high, there is a symmetric equilibrium in pure strategies ;
After revision:  If there are no search frictions, there is a unique symmetric equilibrium in pure strategies; and for any finite number of firms, the signals are not fully informative. If there are search frictions, if the expected value of the prize is sufficiently high, there is a symmetric equilibrium in pure strategies ;