Question

2. Cournot competition: P1 and P2 (independently and simultaneously) choose quantities, qi and q2. The cost of producing q units is c(ai)i and the demand curve is given by P(O) 10 Q: (i.e., if P1 produces qi and P2 produces q2; each sells all his units at price 10 1 92 (a) Find all NE. b) Now suppose that the game is played twice. Each firm chooses both a production quantity, and, firm 2 can choose to donate some of his profits to firm 1 if he wishes. (Assume that firms cannot "donate" negative profits). Is there a SPNE in which firm 2 donates some of his profits in period 1? Either find one or explain why not (c) Repeat part (b) for NE. (i.e., is there a NE where some profits get donated in period 1?)

Answer 1

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Kindly note that without knowing the exact magnitude of profit donated by Firm 2, exact calculations are not possible. This was just an illustration to show that there will be a threshold quantity (hence derived profit amount) that will determine whether Firm 2 will donate part of his profits to Firm 1, and if yes, how much. Then only can the unique SPNE be derived.

Best!