This paper studies whether two profit-seeking firms will slow down dangerous technological progress on their own, or race ahead and raise the chance of a shared catastrophe. The authors build a model where each firm chooses a development speed between 0 (pause) and 1 (full racing). A separate “safety threshold” moves forward at a fixed rate. If the leading firm’s capability passes this safety line, the chance of a disaster that ends both firms’ future profit rises with how far ahead the leader is.

In the model, each firm’s capability is the time integral of its past speeds, and the capability frontier is the higher of the two firms’ capabilities. The disaster hazard is a nondecreasing, concave function of the frontier’s distance above the safety threshold; it can jump at the moment the frontier crosses safety. Before any disaster, a firm’s flow profit rises with its own capability and falls with its rival’s. There is no direct monetary cost to developing in the model, and disaster simply terminates future profits.

The authors characterize equilibrium behavior in two formal senses. In Markov perfect equilibria (MPE) — strategies that depend only on the current state — they find three regimes. When the disaster hazard is low, only “racing” is an MPE: both firms always develop at full speed. When hazard is intermediate, both racing and a “pacing” pattern can be equilibria. Pacing means the leader pauses after reaching a chosen lead above safety while the follower continues to catch up. When hazard is high, only pacing survives as an MPE. Looking across all subgame-perfect equilibria (SPE), low risk tends to produce perpetual racing while high risk rules it out, and the authors provide bounds on the probability of disaster at any finite time across all SPE.

The paper also studies how parameters change the balance between racing and pacing. Faster progress of the safety threshold, a higher hazard function, and greater patience by firms (a lower discount rate) each make pacing more likely in equilibrium. Under a particular linear form for the hazard, the thresholds separating the three regimes depend strictly on safety speed and patience. Notably, even if safety advances almost as fast as development, the racing equilibrium can still persist. The authors further show that when firms’ internal, undeployed capabilities are hidden for a fixed delay, sustaining pacing becomes harder — a finding that points to the practical importance of transparency about internal capabilities.