MArcomage

true but if they both play for 100 rounds and are bored because there isnt much progress then they can agree who will surrender e.g

Sounds like not the likeliest situation, but for these situation I suggest something else known from many mindgames:
The option to offer a draw.

"Offer surrender" or "Attempt to surrender" would work better linguistically than "Request." Request sounds like you're asking your opponent to surrender to you. Thinking of it, though, just leaving the first step as "Surrender" makes the most sense. In war, you can certainly surrender without your opponent acknowledging the action.