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Is there any market in which firms do not follow profit maximisation rules when they act?

Is there any market in which firms do not follow profit maximisation rules when they act?

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In economic theory the profit maximisation rules has been retained for the perfectly competitive, or monopolistic competitive firm, or monopolistic. However it is abandoned for the oligopoly firm because it is difficult to determine at what level of output it can maximize the profit. The interdependence and the diversity of the oligopolistic firms especially in terms of concentration ratios makes it difficult to determine the best strategy on pricing. If any of the firms in oligopoly cheats and causes a price war it wall cause reduction of profits even cause to operate at losses

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