 ## Review Tutorial

### Short Questions  博弈论作业代写

SQ1. Can a weakly dominated strategy be a best response? Brieflfly explain.

SQ2. Assume the stock market is low with probability 0.4 and high with probability 0.6. A lottery yields \$1 if the market is low. If the market is high, the lottery yields \$0 with probability 0.5 and \$10 with probability 0.5. If the agent’s preferences satisfy the assumptions of the expected utility theorem, then will she choose the lottery or an offffer which gives \$3 with probability 1?

### Problem Solving  博弈论作业代写

LQ1. Three (3) fifirms use water from a lake. Each fifirm has two (2) possible actions: treat sewage (T) or dump sewage (D). If no or only one (1) fifirm dumps sewage, the lake remains clean. If two (2) or more fifirms dump sewage, the lake becomes polluted. Each fifirm gets a revenue of 4 if the lake is clean, and a revenue of 1 if the lake is polluted. The cost of treating sewage is 1. There is no cost to dumping sewage. Each fifirm’s payoffff is given by its revenue minus sewage treatment cost, if any.

(a) Describe this situation as a normal form game using payoffff matrices.

(b) Is there a (strongly or weakly) dominated action for each player? If yes, which one? If no, explain why.  博弈论作业代写

(c) Find all pure strategy Nash equilibria of this game.

LQ2. (Cournot’s duopoly game with imperfect information) A single good is produced by 2 fifirms. The unit cost of fifirm 1 is c, and fifirm 2’s cost is either cH or cL < cH. Firm 2 knows its cost, and fifirm 1 believes it is cL with probability θ (0, 1) and cH with probability 1θ. If the total output is Q then the price is P(Q) = max{αQ, 0}. Assume 0 < cL < cH < α and 0 < c < α. Find all pure strategy Bayesian Nash equilibrium of this game.

LQ3. Find all Nash equilibria (in pure and mixed strategies) of the following game. 