【作者】 周斌；

【导师】 陈新； 孙海琳；

【作者基本信息】 南京师范大学 ， 计算数学， 2021， 硕士

【摘要】 本文研究了在随机市场环境下,决策者通过制定两阶段决策进行非合作博弈来达到均衡的过程.与单阶段决策相比,两阶段决策可以更好地利用未来的信息,所以在竞争日趋激烈的今天,生产者更倾向于采用两阶段决策来规避风险,这使得在随机环境下,多厂商之间的两阶段随机非合作博弈变得非常重要.本文主要考虑了风险规避的两阶段非合作博弈问题.利用带有集值映射的随机变分不等式(SVI),给出了风险规避的非合作博弈模型的一阶最优性条件.在标准假设下,由于(·)+函数的不可微性以及第二阶段问题解多值性,我们提出了一种光滑正则化方法,利用光滑化函数以及正则化方法对第二阶段问题进行近似.相应地给出了问题的收敛性分析.进一步地,又考虑了两阶段随机非线性互补问题(SNCPs).我们将文献[8]要求第二阶段函数是连续可微的条件弱化到了只需要第二阶段函数是Lip连续的.在这样更弱的条件下,之前的强单调性结果依然成立.更多还原

【Abstract】 This paper studies the process of non-cooperative games by making two-stage decisions in a random market environment to achieve equilibrium.Compared with single-stage decision-making,two-stage decision-making can make better use of future information.Therefore,in today’s increasingly fierce competition,producers are more inclined to adopt two-stage decision-making to avoid risks,which makes the two-stage stochastic non-cooperative game between multiple manufacturers become significant in the random environment.A convex two-stage non-cooperative game with risk-averse players under uncertainty is formulated as a two-stage stochastic variational inequality(SVI)for pointto-set operators.Due to the indifferentiability of function(·)+ and the discontinuity of solution mapping of the second-stage problem,under standard assumptions,we propose a smoothing and regularization method to approximate it as a two-stage SVI in point-to-point case with continuous second stage solution functions.The corresponding convergence analysis is also given.Furthermore,the two-stage stochastic nonlinear complementarity problem(SNCPS)is considered.We reduce the conditions in reference[8]that the second-stage function is continuously differentiale to the requirement that the second-stage function is Lipschitz continuous.Under these weaker conditions,the strong monotony holds true.更多还原