A risk-averse competitive newsvendor problem under the CVaR criterion

We study a risk-averse newsvendor problem with quantity competition and price competition. Under the Conditional Value-at-Risk (CVaR) criterion, we characterize the optimal quantity and pricing decisions under both quantity and price competition. For quantity competition, we consider two demand splitting rules, namely proportional demand allocation and demand reallocation. Although competition always leads to overstocking, interestingly it does not necessarily lead to a profit loss in certain competitive environments, such as demand reallocation, by avoiding/reducing overstocking that results from competition under the risk-neutral criterion. For price competition, we consider both additive and multiplicative demand. We find that the order quantity, sale price, and the expected profit decrease in the degree of risk aversion. Further, both high price sensitivity and competition intensity force decision makers to lower their prices. However, high price sensitivity always reduces the order quantity while competition can have the opposite effect.