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Abstract Every now and then, we observe a fierce price war in a real world market, through which competing firms, selling a homogenous product, end up with Bertrand-like price competition. Despite this, not much has been known in the existing literature as to why a price competition market is formed. We address this question in the context of a choice between engaging in price competition and holding a price leader. Focusing on a duopoly market, we demonstrate that if the market is tight (or if the relative size of demand to supply exceeds a threshold value) and if the cost differential between firms is reasonably large, duopoly firms choose to engage in price competition. Otherwise, one firm becomes a price leader while the other firm a price follower.