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In the competition to attract athletes and produce champion teams, universities increased their spending on college athletics four times faster than overall university spending from 2001 through 2003. Schools have poured money into athletic programs even though studies show that this practice does not increase winning rates or alumni donations ("Review & Outlook," Wall Street Journal, May 27, 2005, W15). Nonetheless, suppose that money does matter in producing championships. m A University A spends mA on its football team and University B spends mg. The fraction of the time that UniversityA wins is WA = W, and the fraction of time that A B "13 B wins is wB = (1 -wA) = m. Suppose that each university wants to maximize its prot from having sports teams. The expected prot of University i, i=A, B, is A B m I- = V , where Vi is the value to University i of winning a game. ' i r\"A + "'8 Show that if VA = V3, in the Nash equilibrium each school wins one-half of its games. If VA = VB = v, then each school will win one-half of its games because each school will spend mi = D on athletics. (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a fraction can be created with the / character.)