Level 88
Something like this should put you in the right direction
$gameActivities = GameActivity::select([
'*',
\DB::raw('(select ga.score FROM game_activities AS ga WHERE ga.creator_id = game_activities.creator_id AND ga.type = 0 AND ga.game_id = game_activities.game_id) as start_score')
])
->where('type', 2)
->where('game_id', 37)
->groupBy('creator_id')
->get();