1.A single AMD design difficulty is much lower. CPU+GPU+ bridge, Intel and NVIDIA can't do it all, one graphics card is too bad, one processor is too bad.
2. All use X86 architecture (NVIDIA's processor is not directly out of the X86), which is convenient for game developers to develop and low cross-platform cost. Because they are essentially a platform! Of course, "cross-platform low cost" is not a consideration for SONY and Microsoft, but the ease of game development should not be ignored, and the opinions of game developers should also be taken into account by SONY and Microsoft. Otherwise, where will exclusive games come from?
3.AMD has high comprehensive cost performance. In fact, the CPU+GPU on the host is also following AMD's desktop APU design pattern, which does not need special research and development. At most, a small amount of targeted design modification -- the research and development cost is relatively low. The manufacturing process is also based on the desktop APUS (e.g., Xiaomi's Thepaper.cn streamed 100 million at a time, continuous streaming failed until Xiaomi gave up treatment, that's the cost) -- and the manufacturing cost is relatively low. In terms of performance, AMD's CPU performance is already better than Intel's, and graphics cards can't beat NVIDIA's, but that's a tolerable disadvantage when the performance gap is small.
So: It makes sense that SONY and Microsoft both chose AMD