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2 Prisoners' Dilemma games Exercise 5 (A prisoner's dilemma game, by Kim Swales) Firms Alpha and Beta serve the same market. They have constant average costs of 2 per unit. The firms can choose either a high price (10) or a low price (5) for their output. When both firms set a high price, total demand = 10,000 units which is split evenly between the two firms. When both set a low price, total demand is 18,000, which is again split evenly. If one firm sets a low price and the second a high price, the low priced firm sells 15,000 units, the high priced firm only 2,000 units. Analyse the pricing decisions of the two firms as a non-co-operative game. 1. In the normal from representation, construct the pay-off matrix, where the elements of each cell of the matrix are the two firms' profits. 2. Derive the equilibrium set of strategies. 3. Explain why this is an example of the prisoners' dilemma game

Exercise 6 (An example of the Tragedy of Commons, by Kim Swales) Show how the phenomena of overfishing can be represented as a Prisoners' Dilemma. (hint: set up the game with two players, each of which can undertake low or high fishing activity).

Exercise 4 (by Kim Swales) Companies A and B can compete on advertising or R+D. The table below represents the pay-offs measured in profits (, million) in a one-shot simultaneous move game, with complete information. Company A's profits are shown first. Company A Company B Advertising R&D Advertising 50, 25 10, 70 R&D 20, 40 60, 35 1. Find the mixed strategy equilibrium. 2. What are the expected pay-offs for both firms?

Exercise 3 (by Kim Swales) The table below represents the pay-offs in a one-shot, simultaneous move game with complete information. (Player As pay-offs are given first) Player A Player B Left Middle Right Top 7, 17 21, 21 14, 11 Middle 10, 5 14, 4 4, 3 Bottom 4, 4 7, 3 10, 25 Find the Nash equilibria in pure strategies for the game whose pay-offs are represented in the table above. What is the likely focal equilibrium and why?

There are two consumers who consume good x (private good) and good y (public good).

The sum of consumption between both consumers = T (T1+T2)

price of a private good x= $1

Price of a unit T = $2

Income = $100

Utility function:

U = log X + log(T1 + T2 )

Use the given utility function along with prices, and income to find...

a. socially optimal (efficient) level of production of a public good.

b. market (private) level of provision of a public good.

1. (25 points) Suppose two countries: Zimbabwe and Zambia, use only capital (K) and labor (L) for production. Zimbabwe has 2,075 units of capital and 932 units of labor, and Zambia has 832 units of capital and 295 units of labor. Both countries produce two goods: Cloth and Phone. In Zambia, there are 384 units of capital and 176 units of labor employed in the phone industry. In Zimbabwe, there are 956 units of capital and 632 units of labor employed in the phone industry. a. (4 points) Which country is labor abundant? Which country is capital abundant? Which good is labor intensive? Which good is capital intensive? b. (4 points) Assume identical preferences and technologies between the two countries. Use graphical analysis to present the autarky equilibrium in each country. Which country will have lower relative price of phone in autarky? c. (4 points) Use graphical analysis of the relative demand and relative price of labor in terms of capital for each industry to show how the equilibrium relative price of labor and the equilibrium relative quantities of labor in each industry are determined in Zambia. d. (4 points) Suppose now that the countries open to trade. What will happen to the relative price of phone in Zambia? Show the new trade equilibrium in Zambia on your graph. Clearly indicate how much phone will be produced and consumed in Zambia after the country opens up to trade. What is the good that Zambia will export? e. (4 points) Use graphical analysis to show the effects of trade on the relative factor prices and relative factor demands in Zambia. Put relative wage on the Y-axis and relative labor on the X-axis. Write a clear statement about the direction of the relative factor price change and the changes in relative labor demand in each sector. What will happen to real wages and real rental on capital in Zambia? f. (5 points) (Standalone question): (True/False) According to the standard Heckscher-Ohlin model with two factors (capital and labor) and two goods, the movement of Turkish migrants to Germany would decrease the amount of capital-intensive products produced in Germany. Explain.