Two firms, 1 and 2, simultaneously pick prices, p1 and p2, respectively, where p1,p2 ≥0. Both firms have constant (and identical) marginal costs, denoted c>0. Demand is given by D(p), where p is the lowest price, p = min {p1,p2}, If the two firms charge the same price, then each gets half of the demand. Firms have to supply whatever is demanded of them. D(p) is continuous and strictly positive for all p <p* and zero for all p ≥ p*, where p*>c>0 is a constant. Monopoly profit is assumed to be single-peaked and maximized at pm, where c <pm<p*

Characterize the set of weakly dominated actions (prices). Are there any weakly dominant actions (prices)? Explain your answer.

Do you agree that if action (price) is the best response for some action (price) of the other player, then that action (price) cannot be weakly dominated. Explain your answer

Do you agree that if an action is never a best response, then that action must be weakly dominated? Carefully explain your answer.

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