Realistically, they'd use multiple factors. Deriving location from multiple independent sources is always better than any single solution however neat.
Practically free, so there is absolutely no reason to use it.
Celltowers and Wifi
Gives independent verification that the phone is in the area reported by the GPS.
The player devices can probably connect to each other. This is a useful addition since the players move. This means the set of connections a cheater needs to spoof is constantly changing and it would be difficult to control which devices are close to you reliably.
AR devices need to see the environment. This includes other players. This means the game will get a constant stream of random identity and position checks. This would make cheating risky unless you can control all the players in the area.
Cities are filled with surveillance cameras. If the game can hook into this system it can see all players in many areas. And the game will know in advance where it can observe the players. By putting all critical targets in areas that the game can see or that require players to move thru areas the game can see, the difficulty of cheating goes up drastically.
The game can require players to perform verification actions. AR devices are likely to have some biometric verification capability at least as good as with smartphones. The game can require actions that the surveillance cameras ot other players can see and verify. A player observing an action by another player acts as a verification on both players.
The game can recognize what the players see and verify it matches what other players and cameras have seen. This can include changing elements such as cars, people, or weather which can be difficult to spoof over time, if the game has independent data sources.
Behauvior modelling The game can build models of how players act. This allows it to spot player characteristic actions to support positive identification and suspicious actions or patterns that trigger added verification by the system.
By combining these and other data the game should be able to verify player location and identity with high confidence. More importantly, the more factors the game uses the more difficult the system will be reliably to spoof. If your GPS says you are in a location where a surveillance camera sees nothing, the game will not be fooled by your GPS. If your location data suggests you can teleport or walk thru the walls the system will not trust it. If you see a red car when other players see an empty parking lot the system will not trust your video.