CAJ | 학술논문

广义纳什均衡问题是一种非合作博弈，其每个竞争者的策略集和目标函数都要依靠其他竞争者的策略。它在经济学、管理科学及交通运输等领域都有广泛的应用，但如何有效地求解广义纳什均衡问题仍然是备受关注的课题。本文提出了带有BB步长的自适应投影法求解广义纳什均衡问题：首先，把广义纳什均衡问题转化成拟变分不等式问题，然后把BB步长推广到求解拟变分不等式问题上，并在函数余强制条件下证明了算法的全局收敛性。数值结果进一步说明该方法的有效性。
엄의납십균형문제시일충비합작박혁，기매개경쟁자적책략집화목표함수도요의고기타경쟁자적책략。타재경제학、관이과학급교통운수등영역도유엄범적응용，단여하유효지구해엄의납십균형문제잉연시비수관주적과제。본문제출료대유BB보장적자괄응투영법구해엄의납십균형문제：수선，파엄의납십균형문제전화성의변분불등식문제，연후파BB보장추엄도구해의변분불등식문제상，병재함수여강제조건하증명료산법적전국수렴성。수치결과진일보설명해방법적유효성。
The generalized Nash equilibrium problem( GNEP) is a noncooperative game in which the strategy set of each player,as well as his payoff function, depend on the rival players ’ strategies. It can be widely used in economics, management sciences and traffic assignment,but how to effective solve the generalized Nash equilibrium problem is still a subject of concern. In this paper, we present a self-adaptive projection method with the BB-step sizes for solving generalized Nash equilibrium problems:First, we give the reformulation of a generalized Nash equilibrium. Then, we extend the BB-step sizes to the QVI formulation of the GNEP,we adopt them in projection methods,and prove that under the condition that the underlying function is co-coercive,the sequence generated by the method converges to a solution of the quasi-variational inequality problem globally. Some preliminary computational results are reported, which illustrate that the new method is efficient.