Short answers, pulled from the story.
Imperfect competition occurs when market characteristics fail to meet the necessary conditions of perfect competition. This failure results in market inefficiencies and often leads to market failure.
Four broad market structures result in imperfect competition including monopolistic competition, oligopoly, duopoly, and monopoly. Monopolistic competition features many buyers and sellers offering some product differentiation while oligopoly involves a small number of sellers where one firm's actions influence others.
The Herfindahl Index equals the sum of squared market shares of all firms operating in an industry. Large companies receive more weight in this calculation unlike the N-concentration ratio method with values ranging from 1/N to 1 depending on the number of firms present.
Economists dispute whether economic policy should be based on perfect competition assumptions since no pure examples exist. The argument for assuming perfect competition prevails due to widespread logic use despite lacking substantial consistent models.
Market power emerges from control over inputs, copyrights and patents, network economies, government licenses, natural monopolies, and barriers like market size constraints or control of raw materials. These sources explain why some firms achieve significant pricing power within their respective industries.