前景理论框架下基于期望的损失厌恶报童博弈

摘要

Based on prospect theory , this paper considers the influence of loss -averse newsbvendor's expectation level on the de-gree of loss aversion , extends the loss -averse newsvendor model to a game setting where multiple expectation -based loss -averse newsvendors are competing for inventory from a risk -neutral supplier and researches the influence of newsvendor's related parameters on the equilibrium total quantity . Introducing expectation reference profits under stochastic demand , this paper firstly uses prospect theory to es-tablish the utility function of a single expectation-based loss-averse newsvendor , secondly deduces the game model of multiple expecta-tion-based loss-averse newsvendors , then proves the existence and uniqueness of pure strategy Nash equilibriumh in the game model , deduces the expression of the equilibrium total quantity and analyzes the relationship between the equilibrium total quantity and newsvendor number , loss-averse coefficient , expectation level , finally demonstrates the correctness of the relationship through numerical example and compares the risk-neutral newsvendor's optimal order quantity , the optimal order quantity of a single expectation -based loss -averse newsvendor with the equilibrium total quantity . We find that the equilibrium total quantity increases with the newsvendor number , and de-creases with the loss -averse coefficient , and decreases with the expectation level . Moreover , the optimal order quantity of a single expec-tation-based loss-averse newsvendor is smaller than risk -neutral newsvendor's optimal order quantity and the equilibrium total quantity .%本文运用前景理论 ,考虑了损失厌恶报童期望水平对其损失厌恶程度的影响 ,扩展了损失厌恶报童模型 ,分析了多个基于期望的损失厌恶报童向一个风险中性供应商竞争订货的情形 ,研究了报童相关参数对报童均衡总订货量的影响.在随机需求情形下引入期望参考利润水平 ,首先基于前景理论建立单个基于期望的损失厌恶报童效用函数 ,其次推导出多个基于期望的损失厌恶报童博弈模型 ,然后证明了该博弈模型对称纯策略纳什均衡的存在性和唯一性 ,推导出均衡总订货量的表达式并分析了均衡总订货量与报童数量、损失厌恶系数、期望水平的关系 ,最后通过算例论证了均衡总订货量与报童数量、损失厌恶系数和期望水平之间关系的正确性 ,进而比较分析了风险中性报童最优订货量、单个基于期望的损失厌恶报童最优订货量以及均衡总订货量之间的关系.结果表明 ,均衡总订货量随着报童数量的增多而增加 ,随着损失厌恶系数的增大而减少 ,随着期望水平的增大而减少 ;单个基于期望的损失厌恶报童最优订货量要小于风险中性报童最优订货量以及均衡总订货量.