OddThinking

Recently the urban-legend debunking web-site, Snopes discussed the etymology of the word handicap, particularly in reference to disabled people.

Along the way, they included a description of a bartering “game” called “hand-in-cap”. I had never heard of it before. I found the brief description a little cryptic. (I include it below, and try to explain it better with an example.) When I figured it out, I found it fascinating – but I’m not sure anyone else will, so it’s perfect fodder for a lapsing blog.

Here is how the Snopes description starts:

To play hand-in-cap required three people; two players and a referee. The game began with all three putting forfeit money into a cap, with ownership of this kitty to be decided by the outcome of the game. Each of the two players would then offer up an item he thought the other guy might want. The referee would inspect the items and assign a monetary value to the difference between the worth of the two things, thereby more or less equalizing the transaction. He who offered the lesser-valued item also had to pony up with the amount decreed by the referee.

It is probably easier to understand as a story:

Once upon a now, Alice has a dozen chickens she wants to barter away, and Bob has a second-hand Canon 1D MkII N camera body he wants to barter away.

Alice wants a camera. Bob wants some chickens. Time to make a deal.

But a camera is worth more than a dozen chickens, so Alice is going to have to fork over some money for the difference. How much money? No-one wants to be ripped off, so they bring in Charlie to help broker the deal. Charlie is an expert at evaluating chickens and cameras. But Charlie is a busy man, so they decide to pay Charlie an brokerage fee – but only if he does a good job. If he does a bad job, they want him to pay a forfeit.

So, all three put $20 into a cap. (Actually, Charlie could pay a different amount to Alice and Bob, but let’s keep it simple.)

Charlie considers how much chickens are worth, and how much a camera is worth, (I imagine there is a bit of lobbying done here) and decides that a camera is worth $600 more. The proposed deal is now a dozen chickens plus $600 for a camera.

Once this appraisal was completed, the two players would reach into their pockets to either draw out loose change or not, depending on whether they were happy with the proposed swap. (This change did not become part of the transaction over and above the appraisal fee; it was merely symbolic, representing a visual proof of the intent to “purchase” the other’s goods.) If both drew out coins, the exchange was effected, and the referee took the forfeit money for himself. If neither drew out coins, the referee again took the forfeit money, though the exchange was not made. But if only one drew out coins, he was entitled to the forfeit money, even though again the exchange was not made.

The coins are a furphy. Ignore those. What matters is who is happy with the proposed deal.

So, the ideal situation is that Charlie has done a good job. Both sides are happy with the price. Alice gets the camera and is happy. Bob gets the chickens and the $600 and is happy. Charlie gets the $60 in the hat ($40 profit = brokerage fee) and is happy.

If both sides are unhappy with the price, then Charlie hasn’t done a bad job. If Charlie over-estimated the value of the chickens Alice would have been happy. If Charlie over-estimated the value of the camera, Bob would have been happy. If neither side wants the deal, then Charlie has done his job but there is no deal to be made – both parties are happier with what they have than the other person’s item. So, no deal, but Charlie still gets his $40 brokerage fee.

If one side is happy but the other is unhappy then Charlie has done a bad job – he’s not found the right price to make the deal. Charlie forfeits his money! (As described, he actually loses out of the deal, although in practice his contribution to the hat could be negligible.) WARNING: MISTAKE FOLLOWS Strangely, the person who got the favourable estimation also forfeits his money. That provides an incentive against lobbying Charlie too strongly to estimate your items worth too highly, to the point that the deal is broken. The person whose goods were undervalued walks away with a $40 profit, and no deal. Actually the Snopes description says the the person who got the favourable estimation TAKES the money.

This is more than just a game – it provides a way to determining a fair price for bartering. I was impressed that the system provided an incentive for both of the parties to ask for a fair price for their goods.

That applies to Charlie too. Charlie has to be careful that the brokerage fee isn’t too high. If the brokerage fee becomes high enough, Alice (and Bob) face the Prisoner’s Dilemma: If Alice says Yes and Bob says Yes (i.e. the prisoners stay silent), they both suffer slightly (they make a deal that is unprofitable after brokerage). If Alice says Yes and Bob says No (i.e. one prisoner blames the other), Alice loses. If Alice says No and Bobe says Yes, Alice wins. If Alice says No and Bob says No, they both lose.

So, whatever Bob says, Alice would be better off saying No, and vice versa – but if they both say No, they both lose. That’s the Prisoner’s Dilemma.

When the fee is low, the prize for reaching a deal is high enough to break the dilemma.

So far, it sounds like a pretty good negotiating strategy.

However, it suffers from being fixed with secret cartels.

If Alice and Bob meet beforehand, and Alice pays Bob $30 for playing the game and always saying No Yes, while always saying Yes No herself, they each make a $10 profit from poor Charlie.

Alternatively, if Alice and Charlie meet beforehand, and agree that Alice will always say No, and to split the profit, they will each make a $10 profit from poor Bob.

Anyway, I found the game an interesting one to explore misread.