http://www.gametheory.net/News/Items/108.html

http://www.cscs.umich.edu/~crshalizi/notebooks/ethics-biology.html

Where are Irrationality, Justice, and Morality in Game Theory?

The entire field of game theory seems to be built upon the concept of rationality. In each situation, players will play the strategy which maximizes their individual payoff. Any experience with the real world however, will lead us to the conclusion that this assumption is inherently flawed and there is another factor besides profit that drives us. Even in an example as simple as the ultimatum game, we can see that the results of experiments are far from the predicted equilibrium results. The predicted results tell us that the optimal strategy, and thus the one most played, would be to offer the smallest increment possible. Actual experiments however, contradicts this and find that most people offer a fair split and that offers of less than 20% are often rejected. Rationality would say that, any profit is better than no profit. So why would people ever reject offers? I believe the answer to this question, in a word, is Justice.

When a player offers a highly unfair split he is being unjust, and the moral solution is to punish this injustice, thus restoring justice, even at a cost of hurting oneself. Even though the decision to punish the offending player is visibly irrational from an economist standpoint, I believe that when this decision is applied consistently and repeatedly it is an optimal and rational strategy. To show this lets take the case where there are 2 just players and 2 unjust players our “world”. Now suppose just one of these players is given the opportunity to make offers to each of the other “residents” in turn. If he is unjust, he will offer a 99:1 split, which will be accepted by the other unjust player (since he is completely rational), but rejected by the 2 just players. This gives him a net payoff of 99. However, if he were a just player, he will offer each person a 50:50 split, which would be accepted by all 3, giving him a net of 150. In this case, the just player, although he makes irrational decisions, comes out with a larger payoff then the perfectly rational game theorist.

Although this situation is a bit contrived, I think our society today and our world as a whole, gives us a bit of indirect evidence that justice, (and irrationality) is optimal. If we make the assumption that, a larger profit will give us a greater chance to survive and reproduce (which is a very believable assumption) then Darwin’s theory of natural selection leads us to believe in morality. Darwin’s theory can be paraphrased as “survival of the fittest”. After 200,000 years of evolution, natural selection must have reach, or at least approached, the Nash equilibrium of human behavior. Since we are all at least somewhat irrational, with morals and a sense of justice, then those behaviors and ideas must somehow be “better” than the completely rational alternative. Therefore, when predicting equilibriums from a payoff matrix, it seems somewhat silly to say with definitiveness that this is what people will do, because they are all rational and it is the best choice. I am not saying that completely irrational choices are better, but simply that the rationality of a choice cannot always be contained in a 2×2 payoff matrix.