To Wait or Not to Wait? A Trade-off Between Population Externality and Signal Quality (Lan-Yi Liu, National Taiwan University)

Abstract: Transparency is vital for efficiency in social systems, yet individuals with critical information often strategically postpone disclosure, even when required, to benefit themselves.
To study this behavior, we introduce a multi-stage Chinese restaurant game with incomplete information that features system-recommended action rules and varying levels of player foresight. In our model, players initially receive a suggestion to join a queueing group based on their private signal, but can choose to switch groups. Following this, players sequentially select a final resource, balancing the desire to avoid congested externalities with the need to acquire more information.
We prove a closed-form solution for the players’ pure-strategy Nash equilibrium. Our key finding is that players with high-quality signals have no incentive to reveal their information to those with low-quality signals. This suggests that allowing players to strategically determine their decision timing, without further system design, leads to an inefficient equilibrium allocation.
Our results on congested externalities and system suggestions help explain the inherent trade-off between information quality and decision timing in various real-world scenarios, such as the challenges of vaccine distribution during a pandemic, the strategic crowding of factory location selection, and the decision-making faced by political candidates positioning themselves on the spectrum.