Game, set and match

Free exchange: Game, set and match | The Economist

This is another example of a stable I-O market where one side uses chaos and hidden information while the other uses openness and randomness. The schools act as Iv making offers and giving options, then the Bi doctors can look at the previously secret information more openly. However this only works as long as the system is policed well, for example an Iv school might make an offer and then renege if it can get a better doctor instead.

For example Uni A wants Alice or Bob as doctors, but prefers Alice. Alice wants to go to Uni B and rejects A so A offers a post to Bob who accepts. However if Alice changes her mind then Uni A can dump Bob if he has no way to sue them.

The games then imply not only neutral I-O police but ones biased towards Bi, a doctor has a better chance of getting a Uni that usually would not want him with this game. For example Uni A might have gotten Alice at the beginning if it could have demanded she agree immediately. Because only one side can say maybe then those taking options have an advantage in some markets just as on the futures market. This is then a Buyer's Market instead of a Seller's market.

For example in the marriage game the husbands might make an offer which women have to say yes or no to, but the men only offer maybe. They are now selling themselves and can get an advantage if some are allowed to move first. Now the men might negotiate the options they have for their profit, the ugliest men might pick the best women first so they can trade them for profit or keep them. The women often have to take the bad husband or perhaps end up with someone worse.

For example Bob might take a uni he doesn't want because it is better for someone else, he can then make a deal to drop them in exchange for a fee. He has a valuable option, players would then often be better off taking the best options they can and then trading them for profit which is what happens in a real futures market.

It is the same in the marriage game, a woman might take an offer and hold a man to it unless she gets something of value for dropping him. She then exercises this option when it is most profitable.  

A Roy game has to minimize losses because of scarcity, the men might not be of high quality as husbands and so the women must minimize their chances of getting a bad one. She then holds onto a bad husband in the hopes a less bad one will propose.



In the 1940s the competition for new doctors sometimes saw hospitals making offers to students years before they graduated and thus before their qualifications were truly known. The National Resident Matching Programme was devised to match doctors to hospitals in a way that maximised their satisfaction. This programme, Mr Roth noted in a 1984 paper, was a real-life example of the “deferred-acceptance” algorithm of Messrs Gale and Shapley. The tests of a well-designed market are that participants are satisfied enough that they don’t go around it, and that there is little incentive to game the system—by, for example, lying about their preferences. This was true of the resident-matching programme, Mr Roth said.
Other systems worked far less well. Both the New York and Boston public-school systems used to assign students according to their preferred choices, but students often had to decide before knowing all their options. Thousands ended up at schools for which they had expressed no preference. Mr Roth helped both design algorithms that significantly reduced these mismatches.