You are at a fork in the road. Down one path lies a treasure; down the other, only a dismal swamp. You are rational. Which path will you take? "The one leading to treasure". But you do not know which one that is. Suppose a normally reliable person has told you that the treasure lies to the right; and you know that he is normally reliable. You also have no reason to think the present situation abnormal so far as his reliability is concerned. Which path will you take? "The one on the right". Yes. But the treasure is on the left. The situation really is abnormal, and you are headed for the swamp.
How can rationality lead to such an outcome? The answer is obvious. A rational person is not one who chooses the best course of action. A rational person is one who chooses the best course of action relative to the information he has.
Elementary. Yet the point is often forgotten. The alleged chain store paradox is an example.
Reinhard Selten describes a game between a chain store ("player A") and 20 potential competitors ("players 1, 2 ..... 20") located in twenty towns where the chain store has branches) According to Selten, "game theoretical reasoning" dictates a certain course of action for the players, but Selten is quite convinced that neither he nor anyone he has met would take it. Hence the "paradox".
The game is played as follows. Player 1 decides whether or not to open a competing store in the first town. That is, he chooses between remaining IN the competition or staying OUT of it. If he chooses OUT, then player 2 makes his decision, for the second town, and so on. If a player chooses IN, then before the next player makes his choice, player A decides whether to adopt a COOPERATIVE or AGGRESSIVE pricing policy to meet the competition. The game ends after player 20 chooses OUT, or after player A makes his choice in response to a choice of IN by player 20. Throughout