The game above is what game theorists call the centipede game:
One instance of the centipede game is as follows. A pile of $4 and a pile of $1 are lying on a table. Player I has two options, either to “stop” or to “continue.” If he stops, the game ends and he gets $4 while Player II gets the remaining dollar. If he continues, the two piles are doubled, to $8 and $2, and Player II is faced with a similar decision: either to take the larger pile ($8), thus ending the game and leaving the smaller pile ($2) for Player I, or to let the piles double again and let Player I decide. The game continues for at most six periods. If by then neither of the players have stopped, Player I gets $256 and Player II gets $64. Figure 1 depicts this situation. Although this game offers both players a very profitable opportunity, all standard game theoretic solution concepts predict that Player I will stop at the first opportunity, getting just $4.
The
Uncover Economist reports
on research by Ignacio Palacios-Huerta and Oscar Volij where skilled chess players were asked to play the game. With reference to Player I stopping at the first opportunity Tim Harford writes
... nobody really thinks this is the way players would behave in reality. The optimal strategy seems sociopathic; isn’t it worth playing cooperatively in the hope that the other player will do the same thing.
I not sure I get the "optimal strategy seems sociopathic" bit. The optimal strategy is the optimal strategy, counterintuitive it may be, but I don't see it as "sociopathic". Harford continues
They found that the chess players were far more likely to play optimally; grandmasters always played optimally and took the $4. Hyper-rationality can be a disadvantage. (Or did the experiment discover something else: that chess grandmasters are sociopaths?) Palacios-Huerta and Volij don’t speculate. My guess is that they have discovered something about the rationality rather than morality or empathy of chess players, but I may be wrong.
I'm not sure I would go for the "Hyper-rationality can be a disadvantage" bit either. If Player I doesn't go for the $4, then he will get $2 and $4 is better than $2.
The game above is what game theorists call the centipede game:
1 comment:
It is easy to see the correct strategy is to take the $4 in the first move.
However, a rational player will profitably incorporate an estimate about the probability of their opponent making mistakes.
If I had the second turn, and was given that chance to take it by observing my opponent deviate from the correct strategy, I might anticipate another mistake by him and rationally deviate myself. I presumably have to anticipate only a 1/4 chance of a correct strategy being played on the next turn in order to deviate.
Game theory is really hard, though, and I am sure I am missing much here.
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