I knew that when 35mm film print was still playing in cinema,there were different optical tracks on the film for different sound format. But nowadays we all deliver wav to DCP. So how do cinemas decide when to playback in Dolby or DTS sound format?
My understanding is that the cinemas do not get to decide. They need to play whatever audio was mastered onto the DCP. That decision was made by whoever produced the DCP.
It was not quite the same with 35mm. At first, there was only an optical stereo track on the 35mm print. Then 70mm came along with 6-channel magnetic tracks, so Dolby, Sony and DTS came up with multi-channel formats for 35mm (which caused the death of 70mm). Since DTS would not fit on a 35mm print, they put an optical timing track on the 35mm print and put the audio on an optical disk. The old stereo analog tracks, Sony SDDS, Dolby Digital and the DTS timing track could all coexist on the 35mm print, so the theater would play whatever track their equipment was capable of decoding. Theaters weren't about to buy audio equipment for every screen for every format. At the same time, studios didn't like having to master for every format (and also pay royalties to both Dolby and DTS).
With digital projection a single audio decoder could handle all of the different audio formats, so the studios get to choose what goes on the DCP. They might master both a 5.1 and a 7.1 on the DCP, or they might just leave 7.1 off. If they master Atmos, they will likely also master an alternative format (likely another Dolby format). But it would be unusual for a DCP to contain both Dolby and DTS. Stereo is not supported by DCP, but three-channel (L, R, C) is.