An existence theorem for single leader multi-follower games with direct preference maps
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915228143321088 |
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| author | Chummongkhon, Yutthakan Kumam, Poom Chaipunya, Parin |
| author_facet | Chummongkhon, Yutthakan Kumam, Poom Chaipunya, Parin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An existence theorem for single leader multi-follower games with direct preference maps Chummongkhon, Yutthakan Kumam, Poom Chaipunya, Parin Optimization and Control 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. |
| title | An existence theorem for single leader multi-follower games with direct preference maps |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.03399 |