# Dominant Strategies: Managerial Economics

12. The following payoff matrix represents the long-run payoffs for two duopolists faced with the option of buying or leasing buildings to use for production. Determine whether any dominant strategies exist and whether or not there is a Nash equilibrium.

Firm 1

Lease

Building Buy

Building

Lease F1 = 500 F1 = 750

Firm 2 F2 = 500 F2 = 400

Buy F1 = 300 F1 = 600

F2 = 600 F2 = 200

13. Suppose Market Demand is given by the demand function: . Suppose Marginal Cost is constant at MC=0. Find the Market Equilibrium price, quantity, and total profits to all firms in the market for each of the different market structures below

a. Monopoly

b. Stackelberg Duopoly

c. Cournot Duopoly

d. Pure Competition

14. Suppose There are three farmers (Farmer A and Farmer B and Farmer C). The current zoning allows the land to be used for any purpose. Farmer A has chosen Pig Farming. A Pig Farm will earn $50,000 profit, every year, forever.

a. Assume the interest rate is 10% per year. Using a present value equation--

(PV = Y/(1+r)n

What is the Pig Farm worth?

b. Suppose the next best use of Farmer A's property is residential, where it could earn $20,000 per year. What is the minimum one-time payment Farmer A would accept to agree to restrict his land for residential use forever?

c. Why would Farmer B agree to pay 60% of this cost (from question 14-b) and Farmer C would only pay 40%?

© BrainMass Inc. brainmass.com October 24, 2018, 9:26 pm ad1c9bdddfhttps://brainmass.com/economics/demand-supply/dominant-strategies-managerial-economics-126857

#### Solution Summary

This job considers the existence of any dominant strategies.

Managerial Economics: Game Theory, Dominant Strategy, and Nash Equilibrium

Please help with the following problem.

Two players, Ben and Diana, can choose strategy X or strategy Y. If both Ben and Diana choose strategy X, each earns a payoff of $1000. If both players choose strategy Y, each earns a payoff of $200. If Ben chooses strategy X and Diana chooses strategy Y, then Ben earns $0 and Diana earns $130. If Ben chooses strategy Y and Diana chooses strategy X, then Ben earns $130 and Diana earns $0.

a. Write the above game in matrix (normal) form.

b. Find each player's dominant strategy, if it exists.

c. Find the Nash equilibrium (or equilibria) of this game.