How damaging is shouting "Fire" in a crowded theatre?

Abstract

The canonical example of unprotected speech-falsely shouting "fire" in a crowded theatre-presumes such an act inevitably causes harmful panic. This paper challenges that presumption through a game-theoretic analysis of evacuation dynamics. I model a theatre as an N ×M grid where rational patrons navigate spatial constraints while evacuating. Strategic conflicts arise only when patrons are equidistant from exits, creating localized "clash games" that admit multiple equilibria, including numerous pure-strategy equilibria that achieve zero-collision evacuations. Using global games methodology, I show that strategic uncertainty uniquely selects an equilibrium, where those entering from rows have precedence over those already in aisles. However, introducing a panic mechanism based on accumulated waiting time reveals a tension: the strategically optimal East-priority equilibrium proves most vulnerable to behavioral breakdown, while the alternating equilibrium exhibits superior robustness to panic. These findings suggest that whether false alarms cause harmful disorder depends critically on the interaction between spatial geometry, strategic behavior, and psychological limits-not merely on the alarm itself.

Keywords: evacuation, coordination games, global games, crowd dynamics, free speech, panic behavior