Rationality assumptions of game theory and the backward induction paradox
Andrew M. Colman · 2000
Abstract Backward induction is a form of logical reasoning, based on the technique of mathematical induction, that is applicable to certain sequential games. I shall illustrate it with a simple version of the ancient game of nim. There are 20 matches on the table, and two players take turns in removing either one or two matches, the winner being the player who takes the last one, leaving the other player unable to move. Ernst Zermelo (1912) proved the first major theorem of game theory to the effect that, in games of this type, either one player or the other must have a guaranteed winning strategy. In this case, which player wins, and how?