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Is this a Game of Chance?

Sucker: Is this a Game of Change?
W.C. Fields: Not the way I play it.

W.C. Fields sums up my attitude to many claims made on behalf of rational choice theorists: game theory models offer unique prescriptive advice. Get the model right, and the correct thing to do is merely a matter of calculation.

No judgment is needed, after the theory has been constructed properly.

Models may be wrong, but if they are right or close to being correct, right action is merely a matter of calculation.

My own view, which I think or perhaps hope, is closer to Thomas Schelling's view. Game theory models of human interaction need to balanced by psychological insight. Following a model won't guarantee rationality, nor will deviating from it guarantee irrationality.

In a recent article, Michael Shermer has an interesting article about the Ultimatum Game called The Mind of the Market: Scientific American

"Behavioral economists employ an experimental procedure called the Ultimatum Game. It goes something like this. You are given $100 to split between yourself and your game partner. Whatever division of the money you propose, if your partner accepts it, you are both richer by that amount. How much should you offer? Why not suggest a $90–$10 split? If your game partner is a rational, self-interested money maximizer, he isn’t going to turn down a free 10 bucks, is he? He is. Research shows that proposals that deviate much beyond a $70–$30 split are usually rejected.

Why? Because they aren’t fair. Says who? Says the moral emotion of “reciprocal altruism,” which evolved over the Paleolithic eons to demand fairness on the part of our potential exchange partners. “I’ll scratch your back if you’ll scratch mine” only works if I know you will respond with something approaching parity. The moral sense of fairness is hardwired into our brains and is an emotion shared by most people and primates tested for it. Thousands of experimental trials with subjects from Western countries have consistently revealed a sense of injustice at low-ball offers. Further, we now have a sizable body of data from peoples in non-Western cultures around the world, including those living close to how our Paleolithic ancestors lived, and although their responses vary more than those of modern peoples living in market economies do, they still show a strong aversion to unfairness."

Here is a picture of the Ultimatum game, showing the difference between offering 50-50 and 80-20.

Proponent of rational choice, or in this case game theory, claim that if people are only maximizing money, then it is rational for player 1 to put forth a $99 - $1 and rational for player 2 to accept this.

The empirical evidence suggests, in the absence of these offers being accepted, that people are either irrational or not maximizing money, perhaps they are minimizing the difference between each player's outcome.

I have a different observation: I am not sure that even if the two players are only maximizing money, it is economically rational to a) put forth a $99-1 and b) to expect that on grounds of rationality player 2 will accept it, since $1 is better than nothing.

I can imagine a conversation going like this, with apologies to Plato.

Game Theorist: Michael, is something better than nothing?

Me: Why it is!

Game Theorist: So a $1 is better than nothing?

Me: Indeed and do you accept this, also?

Game Theorist: Yes, and you don't care about how much money I make?

Me: No indeed, and am I sure that you are equally unconcerned about my wealth.

Game Theorist: Correct. So if you accept my offer, you will get a $1 and you don't care that I get $99.

Me. Correct - just as I would be content with getting $99 and you having $1.

Game Theorist: So if I offer $99 - $1, then you will accept?

Me: Uh, well. Let's see. The game played this way appears to be worth $99 to you. So, I will play the game the way you wanted, but you will have to pay me $98 to play.

Game Theorist; But then I will only have $1 after the game!

Me: But, if you don't pay me, then you will get nothing. And a $1 is better than nothing.
So please pay me $98 and then we will play the game in the way you argued so ably was the rational way to play the game.

Game Theorist: But, what is to constrain you from demanding a bigger share after I pay you $98 to play the game?

Me: Ah, well that is a game for another day.

Full post as published by Misleading Advertising Law on February 03, 2008 (boomark / email).