Suppose that there are 10 people playing a guessing game. Each of the 10 people choose a number between 0 and 100. The average of these numbers is computed, and this average is multiplied by p = 2/3. We call the resulting number x. The person whose number is closest to x wins a big prize, while all others receive nothing. If everybody selects the same number, then the prize is split equally. What number would you select if your objective is to maximize the chance that you win the prize? Explain your strategy choice and then suggest an economic situation that illustrates the essence of this game.
Congratulations to Josh Busser for submitting a correct answer to this week's question. According to Josh, the dominant strategy in this guessing game is to submit the number 0 (zero). Read the comments to see Josh's explanation. This question comes from Andrew Schotter's Microeconomics (3e) and is a description of a class of games known among economists as "beauty contests."