We study a loss averse competitive newsvendor problem with anchoring under prospect theory. We consider two demand-splitting rules for quantity competition, including proportional demand allocation and demand reallocation. We characterize the optimal order quantity decisions under both demand rules. We find that the newsvendor's order quantity is decreasing with the degree of loss aversion and the value of the anchor. Compared with an integrated risk-neutral supply chain, a positive anchor always leads to inventory understocking, whereas a negative anchor may result in a serious overstocking. Under competition with homogeneous newsvendors, competition always makes newsvendors order more, which does not necessarily lead to a loss of profit. For newsvendors with a high anchor, competition helps to prevent understocking caused by the anchoring effect, which leads to an increase in profit. For newsvendors with a low anchor, competition exacerbates overstocking, which results in a loss of profit. Under competition with heterogeneous newsvendors, a newsvendor with a higher degree of loss aversion or with a higher anchor adopts a more conservative strategy (i.e. choose a lower order quantity), which results in a smaller market share. (C) 2017 Elsevier Ltd. All rights reserved.