Negative and positive effects of competition in a preemption game

Agents compete to acquire a limited economic opportunity of uncertain profitability. Each agent decides how much he acquires public signals before making investment under fear of preemption. I show that equilibria have various levels of efficiency under mild competition. The effect of competition on the equilibrium strategy is different depending on which class of equilibrium we focus on. However, when competitive pressure is sufficiently high, there exists a unique equilibrium. Finally, I show that the effect of competition on efficiency is different between the common value and the private value setting. Strong competition leads to the least efficient equilibrium for the common value setting but efficiency can be improved by competition in the private value setting.