Perhaps I was too hard on the Scientific American article I discussed in my last post. After all the point of the Traveler’s Dilemma was to act as an informal reductio-ad-absurdum for the current state of game theory. Since all methods of formal analysis (not just Nash equilibrium) lead to the conclusion that 2 is the best answer, the fact that it’s actually a bad strategy is an indictment of the current state of formal game theory.
Most of us, on introspection, feel that we would play a much larger number and would, on average, make much more than $2. Our intuition seems to contradict all of game theory.
To that extent the article succeeds. The problem is that the author persists in calling the game theory result the “rational” choice and thus the common human decisions “irrational:”
Game theorists have made a number of attempts to explain why a lot of players do not choose the Nash equilibrium in TD experiments. Some analysts have argued that many people are unable to do the necessary deductive reasoning and therefore make irrational choices unwittingly.
I gave what I thought were three rational arguments for the near-100 strategy. Nonetheless, game theory is a rather complex subject, one in which closed-form solutions are rare. Rather than rejecting human choices as irrational I think it’s far more logical to assume that the human mind, evolved for complex social tradeoffs, actually solves these puzzles more optimally than any existing formal theory. In fact human problem solving ability is more akin to satisficing than maximizing. Humans will accept a “good enough” result when the gains from an optimal result are not worth the collateral costs. The TD problem is a perfect example. While it’s true that against a random opponent picking $96 makes 0.12% more on average than picking $100, it’s not clear that in a world where making fast judgments is an advantage in itself that time for the additional computation is worth the very small payoff. (Not to mention the social costs of looking overly greedy. Is that worth an average of 6 cents more?)
Comparing game theory results to human behavior and declaring human decisions irrational is as silly as applying the equations of fixed-wing aircraft to insects and declaring that bumblebees can’t fly. Interestingly the failure of game theory is almost never used as an attack on human abilities as it seems to be in the paper quoted above. Instead, like the bumblebee myth, it’s cited to show that logic and reason are insufficient to account for the power of human decision-making. In the 1956 Roger Corman movie It Conquered the World, Peter Graves argues that a purely rational being (like that invading Earth) is incapable of altruism because of its lack of feelings. “[…] Man is a feeling creature,” he declaims, “and because of it the greatest in the universe.”
More recent and much more interesting research on game theory has taken an empirical approach. Rather than trying to find formal solutions to well-defined problems, scientists and theorists have used computers to search for general satisficing strategies that more closely approximate human reason in stochastic games. Far from being irrational, these strategies constitute at least some of the rational basis for altruism as well as the other forms of group cohesion that Sci-Fi writers in the middle of the century believed to be incompatible with logic. We are more rational than we ever thought, but for a real-time, chaotic, social environment, not a chess board.
- jack*
UPDATE: More here.
The 'rational' approach leading to $2, based purely on the desire to beat someone else, reminds me of the old aphorism 'cut off your nose, to spite your face'. A notion any mom will quickly explain is NOT a rational behavior!
Posted by: Ma'at's Feather | June 13, 2007 at 10:34 AM