On Nash Equilibria in Play-Once and Terminal Deterministic Graphical Games
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916659399229440 |
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| author | Boros, Endre Gurvich, Vladimir Makino, Kazuhisa |
| author_facet | Boros, Endre Gurvich, Vladimir Makino, Kazuhisa |
| contents | We consider finite $n$-person deterministic graphical games and study the existence of pure stationary Nash-equilibrium in such games. We assume that all infinite plays are equivalent and form a unique outcome, while each terminal position is a separate outcome. It is known that for $n=2$ such a game always has a Nash equilibrium, while that may not be true for $n > 2$.
A game is called {\em play-once} if each player controls a unique position and {\em terminal} if any terminal outcome is better than the infinite one for each player. We prove in this paper that play-once games have Nash equilibria.
We also show that terminal games have Nash equilibria if they have at most three terminals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Nash Equilibria in Play-Once and Terminal Deterministic Graphical Games Boros, Endre Gurvich, Vladimir Makino, Kazuhisa Theoretical Economics Computer Science and Game Theory We consider finite $n$-person deterministic graphical games and study the existence of pure stationary Nash-equilibrium in such games. We assume that all infinite plays are equivalent and form a unique outcome, while each terminal position is a separate outcome. It is known that for $n=2$ such a game always has a Nash equilibrium, while that may not be true for $n > 2$. A game is called {\em play-once} if each player controls a unique position and {\em terminal} if any terminal outcome is better than the infinite one for each player. We prove in this paper that play-once games have Nash equilibria. We also show that terminal games have Nash equilibria if they have at most three terminals. |
| title | On Nash Equilibria in Play-Once and Terminal Deterministic Graphical Games |
| topic | Theoretical Economics Computer Science and Game Theory |
| url | https://arxiv.org/abs/2503.17387 |