Introducing Game Theory: A Graphic Guide (Introducing…)

Models are simple enough to analyze but still capture some important feature of the real-world problem. A cleverly chosen simple model can help us learn something useful about the complex real-world problem.

Game theorists solve the Guessing Game in a similar fashion using iterative elimination of dominated strategies.
Remember that you’re looking for 2/3 of the average number entered into the contest. If all contestants were to pick the highest permissible number, 100, the average would be 100. Hence, no matter what one expects the average to be, it makes no sense to ever guess a number greater than 2/3 of 100, which is 67.
In other words, any strategy with a guess greater than 67 is dominated by 67. A strategy is dominated if it (in this case, a guess higher than 67) is worse than another strategy (guessing 67) regardless of what other players do. Hence, even if no one else is rational, all strategies with a guess greater than 67 can be eliminated.

vidual benefits at the expense of others.