There are two players. Each player has to write down a real number greater than or equal to 1; thus the strategy sets are S S = [1,00). Payoffs are as follows (x is the number written by Player 1 and y is the number written by Player 2): (x, y) = x-1 ifx y if x y { 1 a) Show that (x, y) = (1, 1) is a Nash equilibrium. b) Find the best response function for each player. c) Show that there is no other Nash equilibrium besides (1, 1).