When one auto maker offers a rebate, others will follow

Oligopoly models

Bertrand's model in oligopoly occurs when firms produce similar or differentiated goods at the same marginal cost. In this model, firms try to beat the prices of other companies by producing at lower costs. When one firm offers a rebate, it means that its prices will be lower than usual, thus leading to a price war; therefore, each firm will have to provide a refund to remain profitable as well.

Cournot model in an oligopoly is where firms sell homogenous products competing simultaneously on market share. Under this model, firms expect their rivals not to raise or reduce their output. When one company offers a rebate, it will generate more demand, thus forcing it to increase its production. Under this model, when one firm changes its output, the others react in a way to wipe out all the additional profits it gets. The reaction by these firms, in this case, would be to offer a rebate too.