FHI has released a new tech report:

Armstrong, Bostrom, and Shulman. Racing to the Precipice: a Model of Artificial Intelligence Development.

Abstract:

This paper presents a simple model of an AI arms race, where several development teams race to build the first AI. Under the assumption that the first AI will be very powerful and transformative, each team is incentivized to finish first — by skimping on safety precautions if need be. This paper presents the Nash equilibrium of this process, where each team takes the correct amount of safety precautions in the arms race. Having extra development teams and extra enmity between teams can increase the danger of an AI-disaster, especially if risk taking is more important than skill in developing the AI. Surprisingly, information also increases the risks: the more teams know about each others’ capabilities (and about their own), the more the danger increases.

The paper is short and readable; discuss it here!

But my main reason for posting is to ask this question: What is the most similar work that you know of? I'd expect people to do this kind of thing for modeling nuclear security risks, and maybe other things, but I don't happen to know of other analyses like this.