De-synchornized Clocks in Preemption Games with Risky Prospects

We study an optimal timing decision problem where an agent endowed with a risky investment opportunity trades the benefits of waiting for additional information against a potential loss in first-mover advantage. The players' clocks are de-synchronized in that they learn of the investment opportunity at different times. Previous literature has uncovered an inverted-U shaped relationship between a player's equilibrium expected expenditures and the measure of his competitors. This result no longer holds when the increase in the measure of players leads to a decrease in the degree of clock synchronization in the game. We show that the result reemerges if information arrives only at discrete times, and thus, a player's strategic beliefs are updated between decision times in a measurably meaningful way.