Athletes are preparing for the coming Olympics

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Athletes are preparing for the coming Olympics. Let us now assume the intrinsic superiority of Adidas is not as great, and that network effects are stronger for Nike. These modifications are reflected in different payoffs. Now, the payoff from having Nike is 60n and from having Adidas is 15+5a; x number of athletes are simultaneously deciding between Nike and Adidas.

a. Find all Nash Equilibria.

b. With these new payoffs, let us now suppose that a third option exists, which is to buy Puma; it has a payoff of 1,000. Athletes simultaneously decide among Nike, Adidas, and Puma. Find all Nash equilibria