Consider the following game. Players one and two simultaneously and independently choose real numbers, x1 and x2. Player one chooses x1 weakly between 40 and 120, x1 ε [40, 120] and player two chooses x2 weakly between 0 and 80, x2 ε [0, 80]. Player one's payoff is $1000 minus the distance between her real number and two times player two's real number. Player two's payoff is $1000 minus the distance between his real number and three fourths of player one's real number. u1(x1,x2) = 1000-|x1-2x2| and u2(x1,x2) = 1000-| x2-(3/4x2) |
a. Find BR1(0), BR1(40), BR1(41) and BR1(80). Show your work or briefly explain your logic.
b. Find BR2(40), BR2(41), BR2(80) and BR2(120). Show your work or briefly explain your logic.