HH homework

5. Games are a "prisoner's dilemma" if every player has a dominant strategy, leading to a Nash equilibrium that results in every player being worse off than they'd have been if they cooperated at the outset. Is this such a game? Game theory helps us understand why people or firms do things that can end up hurting everyone, including themselves. Explain: why is oligopoly characterized by the prisoner's dilemma? What other situations in life are also prisoner's dilemmas?

S wants to sell her home in the Beach area of Toronto for 3 million dollars. S values her house at 3 million dollars.

(a) (5 marks) B puts an offer in for 3 million dollars conditional on financing. B values the house at 4 million dollars. A bidding war starts. Before B and S sign a contract for a price of 3 million dollars, C offers to buy the house for 3.5 million dollars. C further assures S that his offer is unconditional in that his financing is pre-approved, B puts a counter-offer for 4 million dollars, but it is still conditional on financing.

Assuming zero (0) transaction costs, what contract should S accept in order to obtain the most socially optimal outcome? Be sure you fully explain why your answer is correct including any important assumptions you make about how S evaluates the offers.

(b) (5 marks) S accepts C's offer for 3.5 million dollars. Before completion of the contract, C loses his job and now values the house at 2 million. B resubmits her original offer at 3 million to S. Assuming zero (0) transaction costs, explain the bargaining outcome for surpluses among S, B and C if S sells to B and has a remedy to sue C for expectation damages?

(c) (5 marks) Assuming zero (0) transaction costs, explain the bargaining outcome for surpluses among S, B and C if S has a remedy to sue C for specific performance instead of expectation damages?

(d) (5 marks) Assuming transaction costs are high enough to prevent bargaining in parts (b) or (c), fully explain which remedy is more socially efficient?

11) Establish and maintain a process for gathering, completing, and tracking travel requests and reimbursement forms within 3 days of receipt 90% of the time.

12) Develop and implement parent and family engagement plans for afterschool program to include 2-4 high quality family outings and 2-4 on-site events.

13) Lead a process to assess the current service learning program to determine goals, objectives, needs, opportunities, and target audiences.

14) Reach at least six new agencies or community groups and recruit at least two of them to participate in a series of classes.

15) Improve documentation of program impact.

16) Schedule and hold at least two check-in meetings with employees to talk about their work, progress and goals, and issues by November 2015.

17) Develop and lead at least three staff development sessions for the team during the calendar year under the coordination of the County Director.

18) Complete training on reading and reconciling eReports and travel by March 2015.

19) Identify and participate in at least two professional development activities during the review period that focus on an understanding of and appreciation for diversity.

20) Attend two professional development programs outside the office within the calendar year.

Oligopoly" refers to the market structure in which two or more firms compete in an industry, but the number of competing firms is small enough that the firms take each other's actions into consideration and engage in "strategic interaction." In doing so, the firms can be said to play a "game." We can use "game theory" to help model this kind of interaction.

Consider the following two-firm game, in which firms choose how much to produce. (This kind of game in which firms compete by choosing quantities of output is called a "Cournot game".) Suppose market demand is given by the equation P = 24 - Q, where Q = qA + qB, where qA and qB are the quantities produced by the two firms, A and B. Suppose each firm has only three options: produce 6, 7, or 8 units of output. Also assume that firms have no cost of production, for simplicity. Use this information to complete the following payoff matrix and answer the following questions.

Firm B 6 7 8 Firm A 6 66, 77 7 8

1. First, let's complete the matrix by filling in the cells with the game's "payoffs" - by which we mean each firm's profits. One cell is already completed for you - the one corresponding to {qA = 6, qB = 7}. To see how we got the profits shown in the cell, note that market output is Q = 6 + 7 = 13, so P = 24 - 13 = 11. Since we are assuming there are no costs, firm profits just equal market price times firm output for each firm. For A, that's 11 x 6 = 66, and for B that's 11 x 7 = 77. Do similar calculations for the other combinations of output, showing profits for each firm in all cells, listing A's profits first.

2. Thinking about the total combined profits for each output combination, which set of outputs maximizes joint profits? This is the combination the firms would choose if they cooperated with each other like a cartel does.

3. Now let's think about why the cooperative outcome you found above is not an equilibrium to the game. An equilibrium (technically, the Nash equilibrium) occurs when no player has an incentive to change given the other player's strategy or choice. One way to find the equilibrium is to ask, if Firm B chose "6", what quantity would be best for Firm A? Given A's choice then, what would Firm B choose instead of 6 (if anything). Once you've found the combination from which neither player has an incentive to change, you've found the equilibrium.

4. Another way to think about solving games like this is to look for "dominant strategies" - choices that always yield a higher payoff regardless of what other players do. Does Firm A have a dominant strategy in this game? Does Firm B? If all players have a dominant strategy, that strategy combination is the Nash equilibrium for the game. Verify this!

5. Games are a "prisoner's dilemma" if every player has a dominant strategy, leading to a Nash equilibrium that results in every player being worse off than they'd have been if they cooperated at the outset. Is this such a game? Game theory helps us understand why people or firms do things that can end up hurting everyone, including themselves. Explain: why is oligopoly characterized by the prisoner's dilemma? What other situations in life are also prisoner's dilemmas?

S wants to sell her home in the Beach area of Toronto for 3 million dollars. S values her house at 3 million dollars.

(a) (5 marks) B puts an offer in for 3 million dollars conditional on financing. B values the house at 4 million dollars. A bidding war starts. Before B and S sign a contract for a price of 3 million dollars, C offers to buy the house for 3.5 million dollars. C further assures S that his offer is unconditional in that his financing is pre-approved, B puts a counter-offer for 4 million dollars, but it is still conditional on financing.

Assuming zero (0) transaction costs, what contract should S accept in order to obtain the most socially optimal outcome? Be sure you fully explain why your answer is correct including any important assumptions you make about how S evaluates the offers.

(b) (5 marks) S accepts C's offer for 3.5 million dollars. Before completion of the contract, C loses his job and now values the house at 2 million. B resubmits her original offer at 3 million to S. Assuming zero (0) transaction costs, explain the bargaining outcome for surpluses among S, B and C if S sells to B and has a remedy to sue C for expectation damages?

(c) (5 marks) Assuming zero (0) transaction costs, explain the bargaining outcome for surpluses among S, B and C if S has a remedy to sue C for specific performance instead of expectation damages?

(d) (5 marks) Assuming transaction costs are high enough to prevent bargaining in parts (b) or (c), fully explain which remedy is more socially efficient?