We study a two-newsvendor competition problem in which both newsvendors are loss-averse and have adaptive quantity-oriented reference points. Each newsvendor faces stochastic demand determined by some demand reallocation rule and aims to choose an optimal inventory level to maximize her expected utility. Since the demand reallocation rule indicates that one newsvendor's demand affects the inventory level of the other newsvendor, this problem can be formulated as a two-person game. We prove that this competitive newsvendor problem exhibits a unique symmetric Nash equilibrium. We also show that the optimal inventory level decreases in the loss aversion degree and reference level, and increases in the competition intensity. Unlike conventional findings in the integrated risk-neutral supply chain, we find that a low (high) reference level leads to inventory overstocking (understocking), which is illustrated jointly by the loss aversion degree, reference level, and competition intensity. Finally, we conduct numerical experiments to provide engineering confirmations of our theoretical findings and to generate additional insights.

中文翻译：

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具有面向数量参考点的竞争性损失规避报摊问题

我们研究了两个报摊商竞争问题，其中两个报摊商都是损失厌恶的并且具有自适应的面向数量的参考点。每个报贩面临由一些需求重新分配规则决定的随机需求，并旨在选择最佳库存水平以最大化其预期效用。由于需求重新分配规则表明一个报童的需求会影响另一个报童的库存水平，所以这个问题可以表述为一个两人博弈。我们证明了这个竞争性报童问题表现出独特的对称纳什均衡。我们还表明，最优库存水平降低了损失厌恶程度和参考水平，而竞争强度增加。与综合风险中性供应链中的传统发现不同，我们发现低（高）参考水平会导致库存积压（understocking），这由损失厌恶程度、参考水平和竞争强度共同说明。最后，我们进行数值实验以提供对我们理论发现的工程确认并产生更多见解。