标题： 单领导者多追随者博弈存在性定理，具有直接偏好映射 显示英文标题

标题： An existence theorem for single leader multi-follower games with direct preference maps

摘要： 本文研究了一类单领导者多随从博弈（SLMFG）解的存在性问题，其中随从联合求解一个抽象经济问题。回顾一下，抽象经济问题是广义纳什均衡问题（GNEP）的推广，这意味着每个参与者的偏好可以用非数值标准来描述。 因此，本文的结果扩展了关于SLMFG解存在性的已知文献。 由于下层问题缺乏准则函数，我们所用的技术与处理GNEP的方法有很大不同。 特别是，我们论证了随从的抽象经济配置，即{\itshape 即，}约束-偏好对，属于一个特定的度量空间，在该空间中证明了反应映射是上半连续的。 显示英文摘要

摘要： This paper concerns with an existence of a solution for a single leader multi-follower game (SLMFG), where the followers jointly solve an abstract economy problem. Recall that an abstract economy problem is an extension of a generalized Nash equilibrium problem (GNEP) in the sense that the preference of each player can be described without numerical criteria. The results of this paper therefore extend the known literature concerning an existence of a solution of a SLMFG. Due to the lack of criterion functions in the lower-level, the technique we used is quite different from those that deal with GNEPs. In particular, we argue that the follower's abstract economy profiles, {\itshape i.e.,} constraint-preference couples, belong to a particular metric space where the response map is proved to be upper semicontinuous.