Games with $ω$-Automatic Preference Relations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912839127531520 |
|---|---|
| author | Bruyère, Véronique Grandmont, Christophe Raskin, Jean-François |
| author_facet | Bruyère, Véronique Grandmont, Christophe Raskin, Jean-François |
| contents | This paper investigates Nash equilibria (NEs) in multi-player turn-based games on graphs, where player preferences are modeled as $ω$-automatic relations via deterministic parity automata. Unlike much of the existing literature, which focuses on specific reward functions, our results apply to any preference relation definable by an $ω$-automatic relation. We analyze the computational complexity of determining the existence of an NE (possibly under some constraints), verifying whether a given strategy profile forms an NE, and checking whether a specific outcome can be realized by an NE. When a (constrained) NE exists, we show that there always exists one with finite-memory strategies. Finally, we explore fundamental properties of $ω$-automatic relations and their implications for the existence of equilibria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Games with $ω$-Automatic Preference Relations Bruyère, Véronique Grandmont, Christophe Raskin, Jean-François Logic in Computer Science Computer Science and Game Theory This paper investigates Nash equilibria (NEs) in multi-player turn-based games on graphs, where player preferences are modeled as $ω$-automatic relations via deterministic parity automata. Unlike much of the existing literature, which focuses on specific reward functions, our results apply to any preference relation definable by an $ω$-automatic relation. We analyze the computational complexity of determining the existence of an NE (possibly under some constraints), verifying whether a given strategy profile forms an NE, and checking whether a specific outcome can be realized by an NE. When a (constrained) NE exists, we show that there always exists one with finite-memory strategies. Finally, we explore fundamental properties of $ω$-automatic relations and their implications for the existence of equilibria. |
| title | Games with $ω$-Automatic Preference Relations |
| topic | Logic in Computer Science Computer Science and Game Theory |
| url | https://arxiv.org/abs/2503.04759 |