(a) Two ice-cream makers, A and B, can both produce ice cream at zero marginal cost. Ice

cream is sold at a price of one pound per ice-cream cone. There is a single location (a

park) where they can sell their ice cream, and the maximum total number of ice-cream

cones that can be sold at that location is 100. Entering the market costs 30 to each

potential seller.

(i) Consider the following game between the two potential sellers:

I. A chooses whether or not to enter the market.

II. Having observed A's move, B decides whether or not to enter; if A has entered

and B does not enter, then the game ends and A's payoffs are 100 30 = 70

and B's payoff are zero. If A has not entered and B enters, then the game

ends, B's payoffs are 100 30 = 70 and A's payoff are zero. If neither enters

the game ends with zero payoffs for both.

III. If both A and B have entered, then A has two choices: it can passively accept

to share the market with B, in which case they both obtain a revenue of 50 and

a payoff of 50 30 = 20; or it can undermine B's sales through negative

advertising, incurring a cost of 20 and causing a reduction in sales for B from

50 to 20, while A's sales remain at 50; in this case A's payoff is

50 20 30 = 0 and B's payoff is 20 30 = 10.

Characterise a subgame perfect equilibrium of this game. Explain your answer.

(ii) Now consider a game as in (i) but where producing ice an ice-cream cone involves a

marginal cost of 1/2. Characterise a subgame perfect equilibrium of this game.

Explain your answer.

(iii) With reference to (ii), suppose that before stage I of the game (at a stage 0),

ice-cream maker A can incur a cost c to learn about a new process that reduces

marginal cost from 1/2 to zero. If A adopts this process, however, B can copy it at

zero cost. For what levels of c would A choose to learn about the new process?

Explain.