The market inverse demand is given by p(q)=100-q where q denotes the total quantity provided. There are two firms, A and B. Both have the same and constant marginal cost is a constant 10.
i) Suppose they set how much to provide to the market simultaneously. Find Nash equilibrium.
ii) Suppose A moves first and B moves second. What are the subgame-perfect equilibrium strategies?
iii) Suppose both set prices simultaneously, where the seller with lower price catches the whole demand and if they tie they split demand equally. What do they set in Nash equilibrium?