4. [25 points] Two twin brothers (Castor and Pollox) have a tradition in which they punch each other on their shared birthday simultaneously. Each will choose to punch with a force measured in pounds per square inch (psi) where f. denotes the amount of force that Castor exerts and f, denotes the amount of force that Pollox exerts. Suppose that Castor's utility function is: Uc(fe. f,) = 1200f, =~ f.f, = f.% and Pollox's utlity function is: 1 1.2 Up(fc: fp) = 1600f, ;fcfp - Ea . a. Derive each brother's Best Response Function. b. Derive the Nash Equilibrium. c. Would either brother would benefit from increasing or decreasing his force by 100 psi