# Now we extend the analysis of Exercise S7 to allow for defecting in a collusive triopoly. Exercise..

Now we extend the analysis of Exercise S7 to allow for

defecting in a collusive triopoly. Exercise S9 of Chapter 5 finds the Nash

outcome of a VLCC triopoly of Korea, Japan, and China.

(a) Now find the collusive outcome of the triopoly. That

is, what total quantity should be set by the three countries collectively in

order to maximize their joint profit?

(b) Assume that under the collusive outcome found in part

(a), the three countries produce equal quantities of VLCCs, so that each earns

an equal share of the collusive profit. How much profit would each country

earn? Compare this profit with the amount each earns in the Nash outcome.

(c) Now suppose the three countries are in a repeated

relationship. Once per year, they choose production quantities, and each can

observe the amount its rivals produced in the previous year. They wish to

cooperate to sustain the collusive profit levels found in part (b). In any one

year, one of them can defect from the agreement. If the other two countries are

expected to produce their share of the collusive outcome found in parts (a) and

(b), what is the best defecting quantity for the third to produce? What is the

resulting profit for a defecting country when it produces the optimal defecting

quantity while the other two produce their collusive quantities?

(d) Of course, the year after one country defects, both

of its rivals will also defect. They will all find themselves back at the Nash

outcome (permanently, if they use grim-trigger strategies). How much does the

defecting country stand to gain in one year of defecting from the collusive

outcome? How much will the defecting country then lose in every subsequent year

from earning the Nash profit instead of the collusive profit?

(e) For what interest rates will collusion be sustainable

if the three countries are using grim-trigger strategies? Is this set of

interest rates larger or smaller than that found in the duopoly case discussed

in Exercise S7, part (e)? Why?