1 [30 points] A Steel factory dumps effluent in the river. Without cleaning water, the factory profit is $500 and the fisherman’s profit is $100. If the water is clean, the fishermen’s profit increases by $400 to $500. There are two ways to clean water: factory can install a filter system at the cost of $200 or fishers can install a treatment plant at the cost of $300.
QUESTION
1 [30 points] A Steel factory dumps effluent in the river. Without cleaning water, the factory profit is $500 and the fisherman’s profit is $100. If the water is clean, the fishermen’s profit increases by $400 to $500. There are two ways to clean water: factory can install a filter system at the cost of $200 or fishers can install a treatment plant at the cost of $300.
 a) [10 points] Find the profit for factory and fishermen under the following scenarios. Fill out the following table. What is the efficient outcome?
No filter + No treatment  filter + no treatment  No filter + treatment  
Factory’s profit  
Fishermen’s profit  
Total profits 
 b) [6 points] Suppose there is no welldefined property rights and no cooperation between fishers and factory. What will be the outcome? Is it efficient?
 c) [6 points] What is the outcome of bargaining if fishers have right to clean water? Who, factory or fishers, get the benefits?
 d) [8 points] Suppose factory have the right to emit effluent. What is the maximum amount fishers are willing to pay for clean water? What is the minimum factory is willing to accept to install filter? Is there any possibility for bargaining? In that case what will be the outcome?
2 [15 points] Two investors have each deposited $10 with a bank. The bank has invested these deposits in a longterm project. If the bank is forced to liquidate its investment before the project matures, a total of $16 can be recovered. If the bank allows the investment to reach maturity, however, the project will payout a total of $30. In each case, the return is equally divided among investors. There are two dates at which the investors can make withdrawals from the bank: date 1 is before the bank’s investment matures; date 2 is after. For simplicity assume there is no discounting. If both investors make withdrawals at date 1 then each receives $8 and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives $10, the other receives $6, and the game ends. Finally, if neither investor makes a withdrawal at date 1 then the project matures and the investors make withdrawal decisions at date 2. If both investors make withdrawal at date 2 then each receives $15 and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives $20, the other receives $10., and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns $15 to each investor and the game ends. The following matrices of payoffs illustrate the game described above.
Date 1  
Investor 1  Investor 2  
Withdraw  Don’t  
Withdraw  8, 8  10, 6  
Don’t  6, 10  Next stage 
Date 2  
Investor 1  Investor 2  
Withdraw  Don’t  
Withdraw  15, 15  20, 10  
Don’t  10, 20  15, 15 
Use backward induction to find the two Subgame perfect equilibria of the game.
3 [20 points] Trust game: There are 2 players participating in the twostage game: player 1 and player 2.
 At the beginning, each player is endowed with $5.
 Stage 1: player 1 decides whether to Exit and keep his endowment, which results in ($5, $5) payoffs or to Engage and pass his money to player 2.
 Money sent is tripled.
 Stage 2: Before making his/her, move player 2 knows the decision of player 1.
 If player 1 decided to Exit, player 2 has no decision to make.
 If player 1 decided to Engage, player 2 can either Cooperate and reciprocate player 1’s behavior which results in payoffs ($7.5, $12.5) or Defect and keep all the money, which yields payoffs ($0, $20).
 a) [6 points] Draw the extensive form of the game.
 b) [9 points] draw the matrix of payoff for the normal form of the above game. Find all the Nash equilibria.
 c) [5 points] Find the subgame perfect Nash equilibria. Is it efficient?

ANSWER
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