If you've ever watched a starcraft match, you'll notice they nearly never play to the complete destruction of the other team. This is because of a simple thing, the concession of defeat by the defeated when it's obvious that they have lost. Here, we're facing a similar thing with demigod. People leaving the game once it becomes obvious to them they have lost, giving a concessing 'gg' is nothing terrible. You've won by concession. There is a problem in that right now in that it is a team game, and having one person speak for everyone else is unreasonable, and not fair to the team, because it leaves them with an AI in place of a real player.
So what we need is probably the ability to vote to concess. It's boring to stick around a game that you've obviously lost, being a substantial level below other players, being outgunned in resources, greater troops by the enemy making it impossible to stage a comeback, all of this stuff can add up to a lousy time for the losing team. Playing the whole thing out isn't neccesary. A day ago, I played a game on Crucible that we certainly lost. We were, 6 levels lower in total, had our towers, fortresses and archer towers destroyed (the first set, closest to the neutral center line of the map), were unable to hold any of the neutral flags, and they had purchased catapultsaurs against our priests. At this point I decided it was time to go, gave the enemy a gg, since I didn't want to go through a length loss fraught with long respawn times I couldn't afford to shorten because our income was low, and there were more pressing concerns.
This was met with...some sort of negative reaction by the enemy team. I get that they still wanted to play, but I didn't think it was necessary, a concession is enough in that or worse situations, I don't think we need to play the whole thing out if you're not having fun with it anymore, or it's obvious that you're going to lose. If you're having fun, if you're learning from your mistakes and consider it worthwile to play out every iota of the game, by all means do so, but I think a mechanism needs to be in place to allow concessions of defeat, and right now there is none.
I'm not sure how this should be implemented, right now I'm thinking a vote, but maybe there is a better way. As it stands right now, you're leaving the situation open to people quitting without any way to leave in a dignified manner, and we need that. It is a game, remember.