Bertrand competition and captive customers
研究了成本不对称的寡头市场中，每个卖家都有一批忠实买家时的价格竞争。当忠实买家趋近于零时，成本最低的卖家以第二低边际成本的价格卖给所有买家，但其他卖家有正概率设定垄断价格。
We study a Bertrand oligopoly with asymmetric costs in which each seller has some “captive” buyers. In the limit as captive buyers vanish, the lowest-cost firm sells to all buyers at a price equal to the second-lowest marginal cost. However, the closest competing price arises from non-degenerate mixed strategies, firms play exclusively undominated strategies, and with positive probability all but one firm sets the monopoly price. • A vanishing small set of captive buyers selects an equilibrium of classic Bertrand oligopoly. • The lowest-cost firm sells to all buyers at a price equal to the second-lowest marginal cost. • The closest competing price arises from non-degenerate mixed strategies. • Firms play exclusively undominated strategies. • With positive probability all but one firm sets the monopoly price.