Strategic behavior in acquiring and revealing costly private information

- This paper studies an agent's strategic behavior in acquiring and revealing costly private information in the presence of the payoff externality.
- If the penalty for an incorrect forecast is greater than the reward for being right, the forecast cannot be informative because there is no investment in a costly private information.
- The payoff structure under which the reward is greater than the penalty is necessary for acquiring a costly private information. The acquisition of a costly signal is not monotone with respect to the information quality: it happens as long as the public information is moderately accurate.
- The acquired costly information is always revealed truthfully without herding or anti-herding. The introduction of endogenous costly information raises the issue of “free-riding” rather than the issue of “herding” or “anti-herding”.

When an agent has the opportunity to access public information, whether or not to acquire costly private information is a strategic decision. In this case, to study the informativeness of the revealed information, it is essential to consider the processes of both information acquisition and revelation together. Using a model in which two agents sequentially forecast the true state of a forthcoming period, this paper studies an agent's strategic behavior in acquiring and revealing costly private information in the presence of the payoff externality due to their competition. If the penalty for an incorrect forecast is greater than the reward for being right, the forecast cannot be informative because there is no investment in private information. Otherwise, costly private information is acquired as long as the information quality is moderate. Hence, the payoff structure under which the reward is greater than the penalty is a necessary condition for the investment in costly private information. Moreover, the acquired information is always revealed truthfully without herding or anti-herding. That is, the introduction of endogenous costly information raises the issue of “free-riding” rather than the issue of “herding or anti-herding”.