4. Consider the following p-beauty contest game with n participants (Ho et al. 1998). Participant i = 1,2,..., n is asked to guess a number, x, simultaneously from some closed interval [a, b]. Denote the simple average of the guesses by x mean = 1/n sum xi, and define the number y = pxmean, where p 0. The winners are those individuals whose guess is closest to y. That is, the winners belong to the set W = {i: ly - xi| l y - xj|; j = 1,2,..., n}