6) There are 200 airlines, and all of them are flying from Christchurch to London

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6) There are 200 airlines, and all of them are flying from Christchurch to London. Each airline is deciding whether to transit through Australia or Singapore. Australia has an airport fee of $100, while Singapore does not have an airport fee. In deciding on a route, each airline cares only about income, denoted y, and its travel time, denoted t (where we have made the dollar value of one unit of travel time equal to 1). An airline's payoff is its profit. Assume that an airline's income remains the same by travelling through either of two routes ($10,000). If m airlines transit through Australia, the travel time for an airline on this route is assumed to be m (in dollars). In contrast, if m airlines transit through Singapore, the travel time for this route is assumed to be 2m (again, in dollars). Airlines make simultaneous decisions as to whether to transit through Australia or Singapore.

a. Derive each player's payoff function (i.e., the expression that gives us a player's payoff as a function of his/ her strategy profile.)

b. Find a Nash equilibrium.

7. Go through the Operating System game from Lecture 8 before answering this question. 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