In Tuesday’s post, I talked about how Farmer Joe and Rancher Bob could specialize and trade, resulting in both of them being better off. Rationally, they should both participate, since specialization and trade will make them both better off. But if there’s no way to equitably split the economic profit, they may end up “irrationally” sticking with their current lot in life.
There’s a game theory experiment (along the lines of the Prisoner’s Dilemma) called The Ultimatum Game. It’s a two-player game, with a Divider and a Decider. A lump sum of money is given to the players—the Divider must decide how much money goes to each player, then the Decider chooses whether to accept the division or not. If the Decider does not accept, neither player gets anything.
So, for example, given $100, I might split it so that $10 goes to you and $90 goes to me. If you accept, you are $10 richer and I am $90 richer. If you decline, we both go home empty-handed.
From a rational, game theory perspective, assuming the game is played only once and anonymously (so reciprocation is not an issue), the logical behavior (and the Nash equilibrium) is for the Divider to offer the other player the smallest sub-amount possible (e.g. one cent), and for the Decider to accept.
Well, turns out that even when played under these conditions, people did not do the rational thing. According to Wikipedia, 50/50 divisions are common, and offers of less than 20% are usually rejected by the Decider. This is true even when played with relatively high stakes. (Wikipedia cites a study in Indonesia, where offers of $30 out of a total $100 were rejected, even though this is equivalent to about two weeks’ wages there.)
Obviously this leads to some interesting questioning about the definition of “rationality” in this situation, and much speculation on why humans would be so irrational. The Wikipedia article talks more about that, but I’m more interested in trying to find the “right” answer to the puzzle. What is “fair”? Can it be mathematically determined? Or is it just a fuzzy concept implemented only in our fleshy brains?
I’m not sure a mathematical equation can be found even if the numbers are known. But reality, of course, is even more complex than that. If I’m haggling with a vendor over the price of a tourist souvenir, I may not know exactly the intrinsic value I place on the item, and the vendor may not know exactly the cost to him (including opportunity costs) for the trinket. And we certainly don’t know each other’s number! But the difference between the two is that “economic profit” to be split fairly.
In fact, we’ll probably engage in various different tricks in order to sniff out the other person’s number and try to arrive at an equitable share of that economic profit. I might name a price obviously too low and try, by gauging his response, to guess his true costs. He, on the other hand, will likely start with a price obviously much too high and, by examining my own reactions, try to figure out what the item is really worth to me. And, much like the Ultimatum Game, either of us may walk away from the transaction unfulfilled even though a price was suggested that is both above his cost and below what I value it as, simply because of the perception that one or the other of us would be gobbling up more than his fair share of those tasty economic profits.
Rational or irrational? I’m not sure either way. But it certainly makes for an interesting game.
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