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The competitive loss‐averse newsvendor problem with quantity‐oriented reference point
Author(s) -
Xie Kun,
Guo Yongjiang
Publication year - 2020
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2593
Subject(s) - newsvendor model , loss aversion , risk aversion (psychology) , competition (biology) , economics , nash equilibrium , supply chain , microeconomics , computer science , mathematical optimization , expected utility hypothesis , mathematical economics , mathematics , business , ecology , marketing , biology
Abstract 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.