Consider a market with 12 buyers, each with a maximum willingness-to-pay, for one object, of $4, Firm A and firm B are sellers engaging in Bertrand competition. Firm A's constant marginal cost per unit is $1 and firm B's is $2. Prices must be denominated in pennies, so that allowable prices are 0, 0.01, 0.02, ...1.01, 1.02, ...2.01, 2.02, ....3.01, 3.02,...etc. If the two firms charge equal prices 4, six buyers will buy from A and six from B.

Is there a Nash equilibrium? Describe the strategies if there is one and explain why. Will your answer be different if prices can be chosen from the interval [0,4] (not in units of a penny). Explain your answer.