On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games
We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model showed that Nash equilibria (resp. secure equilibria) are gu...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2013-02-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/790/pdf |
| _version_ | 1797268709535907840 |
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| author | Thomas Brihaye Véronique Bruyère Julie De Pril Hugo Gimbert |
| author_facet | Thomas Brihaye Véronique Bruyère Julie De Pril Hugo Gimbert |
| author_sort | Thomas Brihaye |
| collection | DOAJ |
| description | We study turn-based quantitative multiplayer non zero-sum games played on
finite graphs with reachability objectives. In such games, each player aims at
reaching his own goal set of states as soon as possible. A previous work on
this model showed that Nash equilibria (resp. secure equilibria) are guaranteed
to exist in the multiplayer (resp. two-player) case. The existence of secure
equilibria in the multiplayer case remained and is still an open problem. In
this paper, we focus our study on the concept of subgame perfect equilibrium, a
refinement of Nash equilibrium well-suited in the framework of games played on
graphs. We also introduce the new concept of subgame perfect secure
equilibrium. We prove the existence of subgame perfect equilibria (resp.
subgame perfect secure equilibria) in multiplayer (resp. two-player)
quantitative reachability games. Moreover, we provide an algorithm deciding the
existence of secure equilibria in the multiplayer case. |
| first_indexed | 2024-04-25T01:36:47Z |
| format | Article |
| id | doaj.art-9c126e73fa45467494468930fc21b751 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:36:47Z |
| publishDate | 2013-02-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-9c126e73fa45467494468930fc21b7512024-03-08T09:28:06ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742013-02-01Volume 9, Issue 110.2168/LMCS-9(1:7)2013790On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability GamesThomas BrihayeVéronique BruyèreJulie De PrilHugo GimbertWe study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model showed that Nash equilibria (resp. secure equilibria) are guaranteed to exist in the multiplayer (resp. two-player) case. The existence of secure equilibria in the multiplayer case remained and is still an open problem. In this paper, we focus our study on the concept of subgame perfect equilibrium, a refinement of Nash equilibrium well-suited in the framework of games played on graphs. We also introduce the new concept of subgame perfect secure equilibrium. We prove the existence of subgame perfect equilibria (resp. subgame perfect secure equilibria) in multiplayer (resp. two-player) quantitative reachability games. Moreover, we provide an algorithm deciding the existence of secure equilibria in the multiplayer case.https://lmcs.episciences.org/790/pdfcomputer science - computer science and game theorycomputer science - logic in computer scienced.2.4 |
| spellingShingle | Thomas Brihaye Véronique Bruyère Julie De Pril Hugo Gimbert On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games Logical Methods in Computer Science computer science - computer science and game theory computer science - logic in computer science d.2.4 |
| title | On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games |
| title_full | On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games |
| title_fullStr | On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games |
| title_full_unstemmed | On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games |
| title_short | On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games |
| title_sort | on subgame perfect secure equilibrium in quantitative reachability games |
| topic | computer science - computer science and game theory computer science - logic in computer science d.2.4 |
| url | https://lmcs.episciences.org/790/pdf |
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