Information Revelation and Strategic Delay in a Model of Investment
We model investment as an $N$-player game with a pure informational externality. Each player's payoff depends only on his own action and the state of nature. However, because a player's action reveals his private information, players wait to see what other players will do. Equilibrium is inefficient because delay is costly and information is imperfectly revealed. We characterize the unique symmetric perfect Bayesian equilibrium and study the robustness of delay, which turns out to be sensitive to the reaction speed and the number of players. We establish the following results. (i) When the period length is very short, the game ends very quickly and there is a form of herding or informational cascade which results in a collapse of investment. (ii) As the period length increases, the possibility of herding disappears. (iii) As the number of players increases, the rate of investment and the information flow are eventually independent of the number of players; adding more players simply increases the number who delay. (iv) In the limit, the time-profile of investment is extreme, a period of low investment followed either by an investment surge or a collapse.