You are having dinner with your child in a restaurant. He has ordered chicken tenders with fries and you force him to have a small salad before the main course arrives. In a “When Harry met Sally” moment, you ask for the fries to be brought “on the side”, i.e. on another plate.
He has a small amount of the chicken and you give him a few fries as a reward. He then claims that he is full. Is he really?
There are two states of the world, full F and hungry H. The state is known to the agent/child but the principal/parent does not know the state. The agent has private information. How does the principal work out the true state? Offer the agent another french fry. If it is accepted, the true state is H – he is truly hungry and only pretending to be full. If he refuses, it is F and the chips he had earlier filled him up. Of course you have to know your kids to determine which food product separates or screens the two states.
The first few times you try this trick, you can go a bit further. Once he has accepted the fry, you point out he must really be in state H and make him have some more chicken. In the long run, he will work out that accepting the fry leads to more chicken. He will refuse the fry and you’ll never work out if the true state is F or H. Your solution depends on bounded rationality and if learning helps to eliminate it, you are powerless in the long run. Also, if you choose the wrong food group you won’t be able to screen the two states in the first place. In our case, ice cream is always acceptable in all states while more french fries are acceptable if and only if the true state is H.