Here a game is a two player, alternating turn where the loser is the first player to have no moves. Also suppose that we have a notion of consecutive moves, where it is possible for a player to continue playing the game if their opponent passes (basically all board games satisfy these requirements)
Then we have a notion of the disjoin sum of two games. Basically imagine having two boards and players take turns playing on one board at a time, their choice of which board. The loser is the first with no moves on any board.
What is known about the value/solution of such a game in terms of the component games? I know the answer is quite complicated, even for simple games, but what work has been done?