很简单的博弈论问题。。。

      Suppose there are two oil-producing countries, A and B. Both canoperate at either tow production levels: 2 or 4 million barrels a day.Depending on their decisions, the total output on the world market will be 4,6, or 8 million barrels a day, the price per barrel in these three cases is$25, $15, and $10, respectively. Costs of production are $2 per barrel for Aand $4 per barrel for B.  

(1)  Draw a normal form matrix of thisgame and its payoffs.

(2)  Show that this matrix is aPrisoner’s Dilemma. What’s the Nash equilibrium for this game?

The battle ofsexes game

	Player 2 is Mary
Player 1 is Joe	Football (f2)	Shopping (s2)
Football (f1)	2, 1	0, 0
Shopping (s1)	0, 0	1, 2

Please compute the mixed strategyequilibrium, the final expected payoff of each player.


       Suppose that a particular goods are produced at a cost of $ ceach. The market demand equation for the products is p + q = M, in which M is much larger number than c.$ p is the price of a unit of theproduct. If the price is p, thennumber of products will be sold is q = M– p.     (1)  What are the total output,price, total profit and consumer surplus under the perfect market competition?
   (2)  How many products will amonopolist manufacturer produce if his aim is to maximize profit? Please alsocalculate the total output, price, total profit and consumer surplus.
   (3)  Assuming a duopoly situation orCournot model exists. Firm 1 produces q1and Firm 2 produces q2.Please compute the equilibrium quantity that each firm produced, total output,market price, total profit and consumer surplus.
   (4)  Assuming an Oligopoly situation(an oligopoly is an industry with nproducers, each of which is of appreciable size. No firm can therefore neglectthe effect that its own production decisions will have on the market price),there are n producers, the quantities of products are produced by these n firms are q1, q2,q3, …, qn. Then firm 1’s profitfunction is p1(q1, q2,q3, …, qn) = (M – c - q1- q2 -q3- … -qn)q1. Please compute theequilibrium quantity that each firm produced, total output, oligopoly marketprice, total profit, and consumer surplus.

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