Nash Equilibrium - Economics Assignment Help

Assignment Task

1. (a) In the game below identify the mixed strategy Nash Equilibrium. Fully explain the meaning of your result.

(b) Assume that a dealer in second-hand cars can provide two levels of quality of service, High or Low. High-quality service is costlier to provide. High-quality service is more valuable than low-quality service to the customer. The customer prefers not to buy the service if she suspects that the quality will be low. Her choices are to buy or not to buy. Payoffs, which are known to both players, are given in the normal form shown below.

Fully discuss the outcome you would expect from the example given. How might a better outcome for both players be achieved?

2. In an established market, one firm (Firm 1) has a monopoly position. The market has a demand curve given as

P = 50 — Q

where P is the price, and Q the market output. Fixed costs are 200 and marginal cost is 2. A potential entrant (Finn 2) knows that it will be able to achieve the same fixed cost but will have a marginal cost of 8. Will entry be attractive to Firm 2:

(a) If a Cournot solution is established?

(b) If Finn I, being the dominant firm in the industry when Finn 2 enters, has first mover advantage as in the Stackleberg model?

Discuss whether the solutions you derive are Nash Equilibria.

3. Consider a two-period market entry game with a new entrant (Firm 1) and an incumbent (Firm 2). The entrant must decide whether to enter the market. Entry will be costless. If Firm 1 does not enter, the game ends, with a payoff of zero to the entrant and 8 to Firm 2. If Firm 1 enters, Firm 2 must decide whether to fight or to accommodate. Subsequent payoffs, which depend on whether the entrant is strong or weak, are shown in the table below.

(a) Sketch the extensive form representation of this game and identify the Nash equilibria when each firm knows the strength of Firm 1. Now assume that Firm 2 only knows that Firm 1 is either strong (with a probability 0 < q>

(b) For what values of q will a weak entrant be encouraged to enter the market? Suggest any factors which might influence the value of q. Discuss the significance of your results.

4. 'In 1974, Milton Friedman wrote that the West should not be worried about the power of OPEC to control the price and output of oil. As a Cartel, it was bound to collapse since its members all had an incentive to exceed their quota limits to increase revenue and profits.'

Use your knowledge of game theory and the prisoner's dilemma to explain this statement and suggest reasons why the collapse of OPEC has not occurred.

Explain and illustrate your answer in no more than 2,500 words. This limit includes tables and captions but excludes footnotes, endnotes, tables of figures and references. Answers that exceed this limit will result in a loss of marks. Full details of penalties for late submission, exceeding the word limit and other information can be found at the end of this assignment.

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