Since there is no cost involved in starting a game with another player, and the fact that the winner earn some MGP, a forfeit button in a Player VS Player TT game could be easily exploitable.
Plus, if you remove the MGP in case of a forfeited game, the looser can easily deny a potential well-deserved victory from the winner by pressing the button just before losing.
So, in case of Player VS Player games, the forfeit button would need quite a bunch of restrictions. Either a number of uses per day, or a removal of the forfeit button after a set number of turns, a MGP penalty for the player to forfeit, etc.