How Are Matters Affected If The Time Horizon Is Finite?

Consider a context with n (≥ 3) firms involved in an oligopolistic market for a homogeneous product, the production cost being constantly equal to zero for all of them. The (inverse) demand function is linear, as given by

where xi is the production (and sales) of firm i = 1, 2, . . . , n. Further suppose that

(i) firms compete `a la Cournot over time, i.e., choose their outputs simultaneously

every period t = 1, 2, . . . ;

(ii) each firm,when making its choice at any particular t, knows only (besides

its own past choices) the prices materialized in past periodsτ <>t;

(iii) the firms are “infinitely patient,” i.e., their intertemporal payoffs coincide

with their limit average profits along the whole process.

Answer the following questions:

(a) What is the range of average profits sustainable at a subgame-perfect equilibrium?

(b) Compare your answer in (a) with the conclusion of Theorem 8.7.