Two firms are selling to a market with a fixed market demand. Market price is given by the market demand P(Q) = ( a ? bQ if Q ? a/b, 0 if Q > a/b where Q is the sum of the two firms' outputs. Each of them chooses a quantity to produce at a constant marginal cost c

In class we mainly studied the static games where the action set for each agent includes finite discrete actions. Sometimes the action set can be infinite and continuous. Consider the following example. Two firms are selling to a market with a fixed market demand. Market price is given by the market demand P(Q) : - bQ if Q s 0/8 018 0 if Q > where Q is the sum of the two firms' outputs. Each of them chooses a quantity to produce at a constant marginal cost c