Intermediate Microeconomics

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3. For each of the following games, indicate (a) if there is a dominate solution— if there is one, state what it is and explain how you got it (make your explanation VERY clear if finding a dominant solution involves iterative dominance), and (b) all Nash equilibriums.

I		Player 2		II		Player 2
Player 1		Left	Middle	Right		Player 1		Left	Middle	Right
	Up	1,1	3,4	2,1			Up	1,1	5,0	0,0
	Center	2,4	2,5	8,1			Center	0,5	4,4	0,0
	Down	3,3	0,4	0,9			Down	0,0	0,0	3,3

4. There are two firms that are considering entering a new market and must make their decision without knowing what the other firm is going to do. Once a decision is made, it becomes a commitment that the firm cannot back out of or change after learning what the other firm will do. Unfortunately, the market is only big enough to support one of the two firms. If both firms enter the market, then they will each lose $10,000. If only one firm enters the market, that firm will earn a profit of $50,000 with the other firm breaking even (i.e., earning $0 profit). Obviously, if neither firm enters the market, neither will earn any profits in that market.

Draw the normal form game layout for the above problem and identify any dominant and pure Nash equilibrium solutions as well as any mixed-form Nash equilibrium strategies. If there is a mixed-form Nash equilibrium strategy, state it precisely. Show all work.