In game theory, 'Guess 2/3 of the Average' is a game where n people are asked to choose a real number between 0 and 100 inclusive. The person with the closest answer to 2/3 of the average value wins. It can be shown that there is a unique pure strategy Nash equilibrium where everyone picks the number 0.
Now if we change the rule to be whoever's answer is closet to the average value wins, how do we develop a strategy, or a Nash equilibrium now? The original thought process is no longer applicable.