Question

In: Statistics and Probability

Exercise #6 (game theory and choice question) PLEASE TYPE OUT ANSWER We are presented with...

Exercise #6 (game theory and choice question) PLEASE TYPE OUT ANSWER

We are presented with land use choices. Individuals are free to choose their own development strategy based on the profit potential of the development

.

a) Does either landowner have a dominant strategy? (5 Points) A dominant strategy is what you are going to do, knowing what they are going to do—this leads to the Nash Equilibrium Explain how and what the dominant strategy is (hint, there does not need to be two dominant strategies).

b) Is there a Nash equilibrium? Explain. (5 Points)

d) What is the socially optimal solution? (5 Points)

e) How can we arrive at the optimal solution (consider the Coase Solution). Explain the necessary payoff. (5 Points)

Payoff Matrix

Davis

Alfalfa Dairy Farm

Apartment House B: Profit =$700 B: Profit = $400

D: Profit =$180 D: Profit = $425

Benson Commercial Real Estate B: Profit =$650 B: Profit = $455

D: Profit =$400 D: Profit = $500

Expert Solution

Answer:-----

a)

If Davis chooses Dairy farm, his (i.e. Davis's) payoff is always more than the payoff if he would have chosen Alfalfa (i.e. 425 > 180 and 500 > 400).

This means Davis will always be better off by choosing Dairy Firm over Alfalfa. So, the Dairy Farm is the dominant strategy of Davis.

However, for Benson, 700 > 650 for Davis taking Alfalfa but 400 < 455 for Davis taking Dairy Firm.

So, Benson does’nt have any dominant strategy.

b)

Davis takes Alfalfa => Best strategy for Benson is Apartment House (as 700 > 650)

Davis takes Dairy Firm => Best strategy for Benson is Commercial Real Estate (as 455 > 400)

Benson takes Commercial Real Estate => Best strategy for Davis is Dairy Firm (as 500 > 400)

Benson takes Apartment House => Best strategy for Davis is Dairy Firm (as 425 > 180)

We underline these observations and find the matrix as,

	Payoff Matrix
		Davis
		Alfalfa	Dairy Farm
Benson	Apartment House	B: Profit = 700 D:Profit = 180	B: Profit = 400 D: Profit = 425
	Commercial Real Estate	B: Profit = 650 D: Profit = 400	B: Profit = 455 D: Profit = 500

Payoff Matrix Davis Alfalfa B: Profit 700B:Profit 400 D: Profit 180 D: Profit 425 Dairy Farm Benson Apartment House Commercial

Note that the fourth quadrant is marked complete, so, the Nash equilibrium is Davis taking Dairy Farm and Benson taking Commercial Real Estate.

d)

A socially optimal solution is that for which the total payoff of both the players is the maximum.

e)

This happens for Davis taking Alfalfa and Benson taking Commercial Real Estate. The total payoff is 1050 which is larger than the other three combinations.

orchestra answered 1 year ago

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