2025/04/04 by Yutthakan Chummongkhon, Chummongkhon, Yutthakan, Poom Kumam +3
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Game Theory and Voting Systems #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2504.03399
openalex publication_date 2025/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.