So which of your kids will lay down arms first? You can try to initiate cooperation by taking turns with one child until a recalcitrant sibling jumps in. Or you might try the opposite strategy: You become the person who refuses to cooperate. It works like this: When the kids refuse to pick up the toys, you say you will step in and pick them up yourself. And neither of the kids will get ice cream. Often they quickly realize that they should cooperate before you clean up and they lose their reward.
Your efforts to harshly disrupt the game prompt your kids to cooperate. And remember the next time the situation arises, your children might very well decide to clean up the clutter before you can intervene, having learned that cooperation can be easier—and lead to more ice cream—than defecting.
I want to try this with adults all the time.