3. Consider a variation on the beauty contest game from class. Each player must simultaneously choose an integer between 0 and 100 (inclusive). The average of the chosen numbers will be calculated; call this average x. The player whose number is closest to x will win and earn a positive payoff. If two or more players are equally close to x, the winner will be chosen at random among them. Players who do not win earn a payoff of zero. a) What are the pure strategy Nash equilibria if there are two players? b) What are the pure strategy Nash equilibria if there are three players? c) Let the number of players be ‘large’. Let the level 0 strategy be to choose a number at random. Find the outcome when all players are level k reasoners with k > 0.

Name and describe the three most important measures of central tendency. choose the correct answer below. a. the mean, sample size, and mode are the most important measures of central tendency. the mean of a data set is the sum of the observations divided by the middle value in its ordered list. the sample size of a data set is the number of observations. the mode of a data set is its highest value in its ordered list. b. the sample size, median, and mode are the most important measures of central tendency. the sample size of a data set is the difference between the highest value and lowest value in its ordered list. the median of a data set is its most frequently occurring value. the mode of a data set is sum of the observations divided by the number of observations. c. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is the product of the observations divided by the number of observations. the median of a data set is the lowest value in its ordered list. the mode of a data set is its least frequently occurring value. d. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is its arithmetic average. the median of a data set is the middle value in its ordered list. the mode of a data set is its most frequently occurring value.