It’s Sunday morning.  You are reading the Week in Review section of the New York Times and realize piracy still exists in the twenty-first century.  Who would have thought it? The Travel Section leaves you a bit wistful as you realize how many interesting places in the world you’ll never visit. Now you pack like a small army because you have two young children.  You wish you had done the Inca Trail in 1987 when you went to Peru.  That might have invited a kidnapping at the hands of the Sendero Luminoso, but maybe that’s better than grad school?

You hear the sound of Lego and see your kids building the John Hancock Building out of Lego.  You smile, thinking, “The Inca Trail can never compare to the joy I just felt seeing the kids playing together so happily.”  You turn to the crossword puzzle.  Your reverie comes to a screaming end as a fight breaks out behind you.  Who got one of diagonal bits that criss-cross the Hancock a bit wonky?  You will never know but each kid blames the other.

What to do?

The situation reminds you of the famous Moral Hazard in Teams paper by Bengt Holmstrom.  Someone clearly did not exert the cooperative effort level. But you cannot tell who it was as there is no kid-specific signal, just the aggregate signal of the building falling over and the fight.  First, you think that you should be fair and punish a child if and only if the weight of evidence is high. You realize you’re screwed as you never have that level of evidence.  You could ask the children what happened and cross-check what one did against the other.  In fact, this would give an opportunity to apply your own research and you’re excited about that.  It dawns on you that the 8 year old can always out-lie the 4 year old.   And the volume of the four year old’s cries is measured on the Richter scale.  Your research obviously did not take account of these practical matters.

Incentive theory gives the obvious answer: punish them both.  This works very well if there is nothing random that can cause the building to fall over.  Then, each child knows they get punished if they start fighting so no-one fights as long as the punishment is big enough.  If a fight can start randomly – and we parents know this can happen – sometimes you’ll punish them even though nothing truly bad happened.  This is unfair and inefficient but what can you do?  This second-best solution is still better than no incentives at all.

Briefly, you think about the theory of repeated games which claims to get cooperation even when the game is quite noisy and there is lots of private information about who did what to whom.  You  remember that Jeff has made important contributions to this theory.  You use your common sense and decide that using his research might take the application of game theory to family life a little bit too far.  You get up, confiscate the Lego and send the kids to their room to get out of their pajamas and put clothes on.  The ultimate punishment.  The lovely mother of your lovely children has solved the crossword puzzle by the time you’re done. Bugger.

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