Does an API-based gaming platform wich take care of game execution exists?

I'm looking for some platforms that are "reachable" through APIs and support a decent set of multiplayer games. Such platform should take care of the game execution and management (e.g. synchronization between players, turn-taking).

I need it to develop a web application (and hopefully a mobile version if supported by those platforms) in which (at some point), the user can take a game against one or more other players.

The game will ideally be "set-up" from the application side (e.g. partecipants and any other configuration if the game requires it), the execution will then be delegated to the platform and, at the end of the game, I will only know statistics about it, in order to proceed with my flow. Classical games could be enough but, of course, a more complete list of possibility would be better.

I'm sorry if I couldn't explain what I'm looking for in an efficient way, I hope that my needs are clear. I will answer any question if some clarifications are needed. Thanks