Question

Two firms must make product decisions without collusion. Profits resulting from their decision are given in the following table:

                                                                                  Firm 1

                                                                     Sporty          Economy

                                                       Sporty          3,4              15,10

                              Firm 2             Economy     12,14                 2,5

Explain the Nash equilibrium. Does this game have dominant strategy equilibrium? Explain.

Is this game a prisoner's dilemma? Explain.

Is there an advantage in moving first? Explain.

What is the cooperative solution?

Answer 1

a)

i)

if firm 1 chooses sporty then firm 2 will choose Economy

if firm 1 chooses economy then firm 2 will choose Sporty

Similarly,

if firm 2 choose sporty then firm 1 will choose economy

if firm 2 choose economy then firm 1 will choose sporty

from above we can see that there are two Nash equilibriums

Firm 1 chooses Sporty and Firm 2 chooses Economy (12,14)

&

Firm 1 Chooses economy and firm 2 chooses sporty (15,10)

ii) There are no dominant strategy since action of one firm depends upon other firm's action

b)

No it is not a case of prisoner's dilemma since there are two Nash equilibriums. There is no unique Nash Equilibrium .

c)

Yes there is advantage in moving first

Suppose firm 1 moves first, then in this case;

if firm 1 chooses sporty then firm 2 will choose Economy (12(firm 2 payoff),14 (firm 1 payoff))

if firm 1 chooses economy then firm 2 will choose Sporty (15(firm 2 payoff),10 (firm 1 payoff))

Therefore firm 1 will choose sporty since it will give higher payoff ( 14 rather than 10)

Now suppose firm 2 moves first, then in this case;

if firm 2 choose sporty then firm 1 will choose economy (15(firm 2 payoff),10 (firm 1 payoff))

if firm 2 choose economy then firm 1 will choose sporty (12(firm 2 payoff),14 (firm 1 payoff))

therefore firm 2 will choose sporty then it will give higher payoff ( 15 rather than 12)

Both firms will choose sporty if they are allowed to move first.

d)

cooperative solution will the same Nash equilibiriums since both Nash are giving the firms higher payoffs in comparison to non-Nash Actions.