The National Collegiate Athletic Association (NCAA) restricts the amount that colleges and universities may pay their students athletes. Suppose that there are just two colleges in the NCAA: Ivy and State. Each must choose between paying athletes according to NCAA rules or paying more. (a) Construct a game in strategic/matrix form to analyze the choices of Ivy and State. (Hint: student athletes will choose the college that pays them more and being indifferent between two colleges if paying the same.) (b) Identify the Nash equilibrium or equilibria. (c) Every year Ivy and State need to determine their choice of pay in NCAA. How to formulate a game? (Hint: what is the difference from (a) and (b)?) (d) The NCAA rules have government backing. In other words, colleges will be punished heavily if violating the NCAA rules in this case. How will this affect the game and the equilibrium or equilibria in (a) and (b)?