An equilibrium occurred when there were no more gains from trade available, and where nobody could make a better offer to prevent the actual trades from occurring.

This outcome was "stable" because if the kids began going down this path, there would be no reason for the kids to stray from it.

The textbook was not saying that real-world children would necessarily trade their candy according to such an equilibrium, because (for example) the kids might make mistakes in their negotiation strategies, and end up having someone "call their bluff."

Sample Partial Credit Answer

An equilibrium occurred after all the trades were made.