Question

1. Macaroni Unlimited, Ltd. (MUL), is trying to decide whether or not to enter the spaghetti sauce market. It knows that its actions will be closely monitored by the local spaghetti sauce monopoly, Sicilian Scintillations (SS), which can then choose whether or not to set a high price for sauce or a low price. If Macaroni Unlimited does not enter, it earns profits of zero. If it does, then its profits depend on SS's price. If the price is low, Macaroni Unlimited loses $100. If the price is high, it makes $50. SS's profits with a low price are $10 if MU does not enter and $70 if MU does enter. SS's profits with a high price are $200 if MU does not enter and $50 if MU does enter.

a) Draw this game in the Normal Form (the boxed table like in this Module, payoff matrix).

b) Does either firm have a Dominant Strategy? If so, which?

c) Find all of the Nash Equilibria (in pure strategies).

Answer 1

a)   

  

b) No neither firm has a dominant strategy.The strategy of a firm is dependent of the strategy taken by the other firm if they want to maximise profits.

c)

To find the Nash equilibria, we examine actions taken by the firms in turn,

(Does not enter market, Price is low)

SS can increase its payoff from 10 to 200 by choosing to set High Price rather than the Low Price. Thus this action profile is not a Nash equilibrium.

(Does not enter market,Price is high)

MUL can increase its payoff from 0 to 50 by choosing to Enter the market rather than the to not enter the maket. Thus this action profile is not a Nash equilibrium.

(Enters the market, Price is low)

MUL can increase its payoff from -100 to 0 by choosing to not enter the market rather than to enter the market. Thus this action profile is not a Nash equilibrium.

(Enters the market, Price is high)

SS can increase its payoff from 50 to 70 by choosing to set low prices rather than to set high prices. Thus this action profile is not a Nash equilibrium.

Therefore a Nash equilibrium does not exist in this case.