[20\%] There are two players. Each player has to write down a real number greater than or equal to 1 ; thus the strategy sets are S1=S2=[1,). Payoffs are as follows ( x is the number written by Player 1 and y is the number written by Player 2): 1(x,y)={x10ifxyifxy a) [6%] Show that (x,y)=(1,1) is a Nash equilibrium. b) [6%] Find the best response function for each player. c) [8%] Show that there is no other Nash equilibrium besides (1,1). [20\%] There are two players. Each player has to write down a real number greater than or equal to 1 ; thus the strategy sets are S1=S2=[1,). Payoffs are as follows ( x is the number written by Player 1 and y is the number written by Player 2): 1(x,y)={x10ifxyifxy a) [6%] Show that (x,y)=(1,1) is a Nash equilibrium. b) [6%] Find the best response function for each player. c) [8%] Show that there is no other Nash equilibrium besides (1,1)