firm still setting the competitive price (recall that it is willing to meet unlimited demand at price equals unit cost even though it earns no profit). No other price is an equilibrium. If both firms set the same price above unit cost and share the market, then each firm has an incentive to undercut the other by an arbitrarily small amount and capture the whole market and almost double its profits. So there can be no equilibrium with both firms setting the same price above marginal cost. This is due to the firms competing over goods and services that are considered substitutes; that is, consumers having identical preferences towards each product and only preferring the cheaper of the two. Also, there can be no equilibrium with firms setting different prices. The firms setting the higher price will earn nothing (the lower priced firm serves all of the customers). Hence the higher priced firm will want to lower its price to undercut the lower-priced firm. Hence the only equilibrium in the Bertrand model occurs when both firms set price equal to unit cost (the competitive price). Note that the Bertrand equilibrium is a weak Nash-equilibrium. The firms lose nothing by deviating from the competitive price: it is an equilibrium simply because each firm can earn no more than zero profits given that the other firm sets the competitive price and is willing to meet all demand at that price. Classic modelling of the Bertrand competition The Bertrand model of price competition in a duopoly market producing homogenous goods has the following characteristics: Players: Two firms with constant marginal cost ; Strategic Variables: Firm’s select the price level (i.e., ); Timing: Simultaneous move game; Firm Payoffs: Profit; and Information: Complete. Firm ’s individual demand function is downward sloping and a function of the price set by each firm: Important to note, in this case, the market demand is continuous; however, the firm's demand is discontinuous, as seen in the above function statement. This means the firm's profit function is also discontinuous. Therefore, firm aims to maximise its profit, as stated below, taking as given: In order to derive the best response for firm , let be the monopoly price that maximises total industry profit, where . This highlights the incentive for firms to 'undercut' rival firms. As if the rival sets the price at firm can reduce its price by the smallest