The phrase recursive self-improvement (RSI) refers to the idea of an AI system designing and creating another, better AI system, which in turn designs and creates an even better one, and so on. While the idea has a long history, it has always been an abstract, futuristic idea -- until recently. Today's frontier AI has attained a set of abilities, including in programming, mathematics, research, tool use, and working coherently over extended periods of time, that make RSI seem plausible. AI companies are starting to pursue it, but many of the involved people are also expressing concerns, asking whether humanity should really set this in motion and under what conditions. I will discuss the situation, argue that we do not even have clear frameworks for thinking about the likely outcomes of RSI, and do a quick game-theoretic analysis of how to choose whether to initiate RSI when another party is making the same choice.

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