(a) (2%) Represent this game as a normal-form game.
(b) (4%) Identify all Nash Equilibria in pure strategies.
(c) (5%) Sony is thinking of randomizing between 140 lpi and 210 lpi, picking 140 lpi with probability R. It has discovered that there is a spy in its headquarters who will be able to tell Sharp the value of R, but not which standard is actually selected unless one of the nonrandom extremes of R=0 or R=1 is chosen. Should Sony randomize anyway, or give up and choose either R=0 or R=1? Explain.
d) (8%) Find equilibrium in mixed strategies.
3. (18%) Suppose that Bombardier had organized its sale to Air Canada or WestJet as a first-best price sealed-bid auction. The Value of wining for Air Canada is 80 and that for WestJet is 40. Possible bids are 20, 40, 60 or 80. Alternatively, each firm can decide not to participate in the auction. If bids are equal, Air Canada wins. The utility from wining is the Value of winning minus the bid.
(a) (6%) Represent this game as a normal-form game
(b) (6%) Find all Nash equilibria (in pure strategies)
(c) (6%) compare these results with the results we learned in class about first-best price auctions. Is it different or similar? If different, explain why.
4. (12%) There are two identical firms in a market, each with constant per- unit production costs of $20 per unit. The market demand is given by the equation P = 80 - 4Q, where P is the price per unit, in dollars, and Q is the number of units sold in the market. Determine the Cournot equilibrium quantities the firms will sell and the resulting market price.
5. (18%) Three firms produce an identical product, but at different costs: it costs Firm A $20 for every unit it produces, it costs Firm B $40 per unit, and it costs Firm C $80 per unit. The market demand is given by the equation P = 300 - Q, where P is the unit price, in dollars, and Q is the total number of units sold. (Since the firms' output is identical, they all sell at View More »