Answer 1

Question 1

Dick Smith and J.B. Hifi are two rival electronic items retailers with the same demand and cost structure. Each firm is trying to decide whether to obtain a dealership contract from Sony to sell their TVs and DVD accessories in their stores with the objective of increasing the market share. Obtaining the dealership involves a cost. It is assumed that these two firms supply the entire market. Each firm can choose whether to obtain the dealership or not.

- If both firms do not obtain the dealership they earn a profit of 30 each.

- If one firm obtains the dealership and the other does not, the firm which obtains the dealership earns a profit of 50 and the firm which does not obtain the dealership earns a profit of 10.

- If both firms obtain the dealership they each earn a profit of 20 each.

(All figures are in £ millions)

Required A

Explain under which market structure game theory may be used to analyse the behaviour of firms and why.

Required B

Depict the above game using a payoff table and explain the outcome.

Required C

Explain the prisoner’s dilemma game using a payoff table.

Required D

Explain how the prisoner’s dilemma game is relevant with regard to the behaviour of firms.

Answer 1

Game theory analyses situations involving the strategic behaviour of two or more decision makers who have conflicting objectives.

Game theory is used to analyse the behaviour of firms in an oligopoly market structure.

Oligopoly is characterised by a few (two or more) large firms which dominate the market.

The unique feature of this market is that the actions of one firm affects the behaviour of other firms and vice versa. Each firm has to consider the possible response of the other firm/s when embarking on a course of action.

For example mobile phone service providers or coffee beans producers. In this market structure game theory is useful to analyse the way in which two or more players choose actions or strategies which jointly affect each participant.

(B)

		Dick Smith
		Obtain Dealership	Do Not Obtain Dealership
J.B. Hifi	Obtain Dealership	A (20,20) Non-Cooperative	B (50,10)
	Do Not Obtain Dealership	C (10,50)	D (30,30) Cooperative

Explanation of the Outcome

In the above game in the first column if Dick Smith obtains the dealership, then J.B. Hifi will get a profit of 20 if it obtains dealership and will have 10 if it does not. Therefore J.B. Hifi will choose to obtain the dealership.

On the other hand (2^nd column) if Dick Smith does not obtain the dealership, J.B. Hifi will earn 50 if it obtains dealership but will earn 30 if it does not. Therefore J.B. Hifi will obtain the dealership.

The same reasoning holds for Dick Smith. If J.B. Hifi obtains dealership (1^st row), then Dick Smith will get a profit of 20 if it obtains dealership and will have 10 if it does not. Therefore Dick Smith will choose to obtain the dealership.

If J.B. Hifi does not obtain the dealership (2^nd row), then Dick Smith will get a profit of 50 if it obtains dealership and will have 30 if it does not. Therefore Dick Smith will choose to obtain the dealership.

Therefore no matter what strategy one firm follows, the other firm’s best strategy is to obtain the dealership. This is the outcome of the Game (cell A) where each firm earns 20.

However if the firms co-operate with each other they can earn 30 each by not obtaining the dealership which is the pareto optimal outcome.

(C)

		Prisoner B
		Confess	No Confess
Prisoner A	Confess	C (5years, 5years)	D (3months, 10years)
	No Confess	E (10years, 3 months)	F (1year, 1year)

Description of the Game

Prisoner A and B are partners in crime. They are caught by the police and are interviewed in separate rooms by the district attorney. They are not allowed to see each other. The district attorney says “ I have enough on both of you to send you to jail for a year. But I will make a deal with you: If you alone confess, you will get off with a 3 month sentence, while your partner will serve 10 years. If you both confess, you will both get 5 years”.

The outcome of the Game

What should prisoner A do? Should she confess and get a shorter sentence? She will look at prisoner B’s strategies. If Prisoner B confesses then its better for B to confess and get 5 years rather than 10 years (column 1). If Prisoner B does not confess its still better for B to confess and get 3 months rather than 1 year (column 2).

Prisoner B is in the same dilemma: if only he knew what prisoner A was thinking. Since he is unable to contact prisoner A, prisoner B will decide that it is better to confess using the same reasoning that prisoner A used above.

Therefore both prisoners will confess and the outcome of the Game is shown in cell C where each prisoner gets 5 years. The significant result here is that when both prisoners act selfishly by confessing, they both end up with long prison terms of 5 years. Only when they act co-operatively or collusively will they end up with short prison terms of 1 year.

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