Reference no: EM133082748

(Sustainable cooperation in the long run) Two farmers, Joe and Giles, graze their animals on a common land. They can choose to use the common resource lightly or heavily and the resulting strategic interaction may be described as a simultaneous-move game. The payoff matrix is the following: Joe Giles light heavy light 40, 40 20, 55 heavy 55, 20 30, 30 1. Find the Nash equilibrium of the game and show that it is an example of "Prisoners' Dilemma" games. 2. Suppose that the same game is repeated infinitely. Is the {light, light} outcome a Nash equilibrium if both players play a Grim strategy and have a discount factor of 0.7?

Distinguish simultaneous-move games and dynamic games in terms of information. Explain why in dynamic games Nash equilibria may not be subgame perfect. Using examples, show how non-credible threats are ruled out using backward induction.

I have a question saying that. "Now, suppose there are only two electric vehicle producers - Tesla and BMW. Using game theory, explain whether BMW and Tesla will design the same plug or different plug. What factors should the firms take into consideration?"

I believe that either one of the firms (Tesla or BMW) is making its charging plug for the car, then according to game theory, another firm will do the same. But I don't understand why they would do that. I need help with answering this question. And how would you answer this question? I just need another point of view for someone.

Jerry the repairman works in the town of Prattville. Jerry would prefer not to pay income tax on the revenues he receives in exchange for performing household repairs. As such, he asks to be paid in cash by his clients whenever possible. If he is paid in cash, it makes it possible for him not to report the income and so to evade income tax. Suppose that his gain for not reporting his cash income is 10. If he does not report his income when he has been paid by check, however, he can anticipate a loss due to fines of 50. His clients prefer to pay by check since this does not require them to lose time going to the bank each time they call the repairman. The clients face a loss in terms of inconvenience of 5 when they pay by cash.

a. Depict the "game" played by Jerry and a representative client where the possible moves by Jerry are to "report" or "not report" income while the possible moves by the client are to pay in "cash" or "check". What is/are the Nash equilibrium of this game? Does the government collect any tax revenue at this equilibrium? Explain with payoff matrix.

b. The government now introduces a Value Added Tax (VAT) to be added onto the amount paid by the client when repair services are received. Jerry suggests the following to his clients: "If you pay me in cash, we will not increase the bill by the amount of the VAT. This will result in a payoff to you of 5. If you pay me by check, we must add the VAT to the amount of the bill." Show how the introduction of the VAT changes the payoffs in the game matrix of part (a). What is/are the new Nash equilibrium of this game? Does the government's tax revenue go up when the VAT is introduced? Explain with payoff matrix.

The custom T-shirt printing business has many competitors, so that the perfect competition model may be considered a good  approximation. Currently, the market demand curve is given by Q = 120 1.5 p, whereas the market supply is given by Q = 20 + 2 p.

(a) Determine the market equilibrium Suppose there is a T-shirt craze that increases demand by 10% (that is, for each price, demand is now 10% greater than it was before the craze).

(b) Determine the new demand curve.

(c) Determine the change in equilibrium quantity.

(d) If your answer to the previous question is different from 10%, explain the difference in values. Now go back to the initial demand curve and suppose there is an increase in the cost of blank T-shirts, an essential input into the business of selling custom T-shirts. Specifically, for each unit by each supplier, the production cost goes up by 10%.

(e) Determine the new supply curve.

(f) Determine the change in equilibrium price.

(g) If your answer to the previous question is different from 10%, explain the difference in values.