An Exact Double-Oracle Algorithm for Zero-Sum Extensive-Form Games with Imperfect Information
Developing scalable solution algorithms is one of the central problems in computational game theory. We present an iterative algorithm for computing an exact Nash equilibrium for two-player zero-sum extensive-form games with imperfect information. Our approach combines two key elements: (1) the comp...
Gespeichert in:
| Veröffentlicht in: | The Journal of artificial intelligence research Jg. 51; S. 829 - 866 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
San Francisco
AI Access Foundation
01.01.2014
|
| Schlagworte: | |
| ISSN: | 1076-9757, 1076-9757, 1943-5037 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Developing scalable solution algorithms is one of the central problems in computational game theory. We present an iterative algorithm for computing an exact Nash equilibrium for two-player zero-sum extensive-form games with imperfect information. Our approach combines two key elements: (1) the compact sequence-form representation of extensive-form games and (2) the algorithmic framework of double-oracle methods. The main idea of our algorithm is to restrict the game by allowing the players to play only selected sequences of available actions. After solving the restricted game, new sequences are added by finding best responses to the current solution using fast algorithms.
We experimentally evaluate our algorithm on a set of games inspired by patrolling scenarios, board, and card games. The results show significant runtime improvements in games admitting an equilibrium with small support, and substantial improvement in memory use even on games with large support. The improvement in memory use is particularly important because it allows our algorithm to solve much larger game instances than existing linear programming methods.
Our main contributions include (1) a generic sequence-form double-oracle algorithm for solving zero-sum extensive-form games; (2) fast methods for maintaining a valid restricted game model when adding new sequences; (3) a search algorithm and pruning methods for computing best-response sequences; (4) theoretical guarantees about the convergence of the algorithm to a Nash equilibrium; (5) experimental analysis of our algorithm on several games, including an approximate version of the algorithm. |
|---|---|
| AbstractList | Developing scalable solution algorithms is one of the central problems in computational game theory. We present an iterative algorithm for computing an exact Nash equilibrium for two-player zero-sum extensive-form games with imperfect information. Our approach combines two key elements: (1) the compact sequence-form representation of extensive-form games and (2) the algorithmic framework of double-oracle methods. The main idea of our algorithm is to restrict the game by allowing the players to play only selected sequences of available actions. After solving the restricted game, new sequences are added by finding best responses to the current solution using fast algorithms.
We experimentally evaluate our algorithm on a set of games inspired by patrolling scenarios, board, and card games. The results show significant runtime improvements in games admitting an equilibrium with small support, and substantial improvement in memory use even on games with large support. The improvement in memory use is particularly important because it allows our algorithm to solve much larger game instances than existing linear programming methods.
Our main contributions include (1) a generic sequence-form double-oracle algorithm for solving zero-sum extensive-form games; (2) fast methods for maintaining a valid restricted game model when adding new sequences; (3) a search algorithm and pruning methods for computing best-response sequences; (4) theoretical guarantees about the convergence of the algorithm to a Nash equilibrium; (5) experimental analysis of our algorithm on several games, including an approximate version of the algorithm. Developing scalable solution algorithms is one of the central problems in computational game theory. We present an iterative algorithm for computing an exact Nash equilibrium for two-player zero-sum extensive-form games with imperfect information. Our approach combines two key elements: (1) the compact sequence-form representation of extensive-form games and (2) the algorithmic framework of double-oracle methods. The main idea of our algorithm is to restrict the game by allowing the players to play only selected sequences of available actions. After solving the restricted game, new sequences are added by finding best responses to the current solution using fast algorithms. We experimentally evaluate our algorithm on a set of games inspired by patrolling scenarios, board, and card games. The results show significant runtime improvements in games admitting an equilibrium with small support, and substantial improvement in memory use even on games with large support. The improvement in memory use is particularly important because it allows our algorithm to solve much larger game instances than existing linear programming methods. Our main contributions include (1) a generic sequence-form double-oracle algorithm for solving zero-sum extensive-form games; (2) fast methods for maintaining a valid restricted game model when adding new sequences; (3) a search algorithm and pruning methods for computing best-response sequences; (4) theoretical guarantees about the convergence of the algorithm to a Nash equilibrium; (5) experimental analysis of our algorithm on several games, including an approximate version of the algorithm. |
| Author | Kiekintveld, C. Pechoucek, M. Bosansky, B. Lisy, V. |
| Author_xml | – sequence: 1 givenname: B. surname: Bosansky fullname: Bosansky, B. – sequence: 2 givenname: C. surname: Kiekintveld fullname: Kiekintveld, C. – sequence: 3 givenname: V. surname: Lisy fullname: Lisy, V. – sequence: 4 givenname: M. surname: Pechoucek fullname: Pechoucek, M. |
| BookMark | eNptkE1LAzEQhoNUsK0e_AcBTx623c8mOZba1kKhB_UiyJJkJ5qyu6lJ1o9_b9Z6EPEwzDA87zvDO0KD1rSA0GUST5JZkk33XNtJnhNygoZJTGYRIwUZ_JrP0Mi5fRwnLE_pED3NW7z84NLjG9OJGqKd5bIGPK-fjdX-pcHKWPwI1kR3XRNQD63TbxCtjG3wmjfg8Hvg8KY5gFUQjDZtkDTca9Oeo1PFawcXP32MHlbL-8VttN2tN4v5NpIpS30kqqISrKIKOGWpVJQCEEGpIoKrPA3FiMxkTgtSyExwWmVhQ4RgjAqgkI3R1dH3YM1rB86Xe9PZNpws06LIY8bSWRao6ZGS1jhnQZVS--8_veW6LpO47DMs-wzLPsOguP6jOFjdcPv5D_sFhop2CQ |
| CitedBy_id | crossref_primary_10_1016_j_apenergy_2025_126051 crossref_primary_10_1016_j_artint_2016_03_005 crossref_primary_10_1016_j_asoc_2022_109846 crossref_primary_10_1109_TDSC_2023_3299225 crossref_primary_10_1016_j_artint_2020_103248 crossref_primary_10_1109_TRO_2025_3567506 crossref_primary_10_1007_s13235_023_00519_6 crossref_primary_10_1016_j_ejor_2019_02_017 crossref_primary_10_1016_j_ejor_2020_10_015 crossref_primary_10_1016_j_cose_2019_101578 crossref_primary_10_1016_j_cose_2019_101579 crossref_primary_10_1016_j_ijepes_2023_109294 crossref_primary_10_1016_j_paid_2020_110343 crossref_primary_10_3390_electronics11060896 crossref_primary_10_1007_s10107_018_1336_7 crossref_primary_10_1007_s11704_020_9307_6 crossref_primary_10_1002_nav_21834 crossref_primary_10_1016_j_ijar_2017_11_010 crossref_primary_10_1016_j_neucom_2023_126471 crossref_primary_10_1016_j_artint_2022_103838 |
| ContentType | Journal Article |
| Copyright | 2014. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the associated terms available at https://www.jair.org/index.php/jair/about |
| Copyright_xml | – notice: 2014. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the associated terms available at https://www.jair.org/index.php/jair/about |
| DBID | AAYXX CITATION 8FE 8FG ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- P62 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI |
| DOI | 10.1613/jair.4477 |
| DatabaseName | CrossRef ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology collection ProQuest One Community College ProQuest Central ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition |
| DatabaseTitle | CrossRef Publicly Available Content Database Advanced Technologies & Aerospace Collection Computer Science Database ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central ProQuest One Applied & Life Sciences ProQuest One Academic UKI Edition ProQuest Central Korea ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | CrossRef Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1076-9757 1943-5037 |
| EndPage | 866 |
| ExternalDocumentID | 10_1613_jair_4477 |
| GroupedDBID | .DC 29J 2WC 5GY 5VS AAKMM AAKPC AALFJ AAYFX AAYXX ACGFO ACM ADBBV ADBSK ADMLS AEFXT AEJOY AENEX AFFHD AFKRA AFWXC AKRVB ALMA_UNASSIGNED_HOLDINGS AMVHM ARAPS BCNDV BENPR BGLVJ CCPQU CITATION E3Z EBS EJD F5P FRJ FRP GROUPED_DOAJ GUFHI HCIFZ K7- KQ8 LHSKQ LPJ OK1 OVT P2P PHGZM PHGZT PIMPY PQGLB RNS TR2 XSB 8FE 8FG ABUWG AZQEC DWQXO GNUQQ JQ2 P62 PKEHL PQEST PQQKQ PQUKI |
| ID | FETCH-LOGICAL-c292t-bd5db9d8fea892cf88ee7b88f7baf42af497c3c48575c3ba8d34977bb998be8e3 |
| IEDL.DBID | K7- |
| ISICitedReferencesCount | 58 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000350466400011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1076-9757 |
| IngestDate | Sun Nov 09 08:24:24 EST 2025 Tue Nov 18 22:30:21 EST 2025 Sat Nov 29 05:27:05 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c292t-bd5db9d8fea892cf88ee7b88f7baf42af497c3c48575c3ba8d34977bb998be8e3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://www.proquest.com/docview/2554099263?pq-origsite=%requestingapplication% |
| PQID | 2554099263 |
| PQPubID | 5160723 |
| PageCount | 38 |
| ParticipantIDs | proquest_journals_2554099263 crossref_citationtrail_10_1613_jair_4477 crossref_primary_10_1613_jair_4477 |
| PublicationCentury | 2000 |
| PublicationDate | 2014-01-01 |
| PublicationDateYYYYMMDD | 2014-01-01 |
| PublicationDate_xml | – month: 01 year: 2014 text: 2014-01-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | San Francisco |
| PublicationPlace_xml | – name: San Francisco |
| PublicationTitle | The Journal of artificial intelligence research |
| PublicationYear | 2014 |
| Publisher | AI Access Foundation |
| Publisher_xml | – name: AI Access Foundation |
| SSID | ssj0019428 |
| Score | 2.4162772 |
| Snippet | Developing scalable solution algorithms is one of the central problems in computational game theory. We present an iterative algorithm for computing an exact... |
| SourceID | proquest crossref |
| SourceType | Aggregation Database Enrichment Source Index Database |
| StartPage | 829 |
| SubjectTerms | Algorithms Artificial intelligence Card games Computation Equilibrium Game theory Games Iterative algorithms Iterative methods Linear programming Search algorithms |
| Title | An Exact Double-Oracle Algorithm for Zero-Sum Extensive-Form Games with Imperfect Information |
| URI | https://www.proquest.com/docview/2554099263 |
| Volume | 51 |
| WOSCitedRecordID | wos000350466400011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 1076-9757 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0019428 issn: 1076-9757 databaseCode: DOA dateStart: 19930101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1076-9757 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0019428 issn: 1076-9757 databaseCode: K7- dateStart: 19930101 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1076-9757 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0019428 issn: 1076-9757 databaseCode: BENPR dateStart: 19930101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Publicly Available Content Database customDbUrl: eissn: 1076-9757 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0019428 issn: 1076-9757 databaseCode: PIMPY dateStart: 19930101 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LSwMxEA6-Dl58i_VRgnjwEm2zqUlOUqVVQWvxhQqybJJZH9RWt6v4851sU0UQLx6WhezsEnaSmW8emSFkwzllK04IhnfOhIgk0xIEAwDloAJgCofb1bFstdT1tW4Hh1s_pFUOZWIhqF3Peh_5NkJfNEU034l2X16Z7xrlo6uhhcYoGa9yFMI-KCvZVxRBCz44Cid3cAY1GSoLoQbbfkoesy0hpPypj36K40LHNKf_O7sZMhXQJa0PlsMsGYHuHJkedm6gYSPPk7t6lzY-EptTBNCmA-w0S_AFWu_c41fzh2eKWJbeQtZj52_PSBry3FkTIS498Jm11Htw6RGi7sxnhNBwrsnzeYFcNhsX-4csNFpglmueM-NqzminUkiU5jZVCkAapVJpklRwvLS0kRW-m6eNTKJchCPSGLTVDCiIFslYt9eFJUKrPIVKNQGlFeo9I02Nu6JGnEa7xDlRIpvD3x3bUIXcN8PoxN4aQc7EnjOx50yJrH-RvgxKb_xGtDpkSBx2Xz_-5sby349XyCQCIDFwqaySsTx7gzUyYd_zx35WJuN7jVb7rFzY6eViaeFY--ikffMJ_9LZzA |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3dS9xAEB_UFvSl1o9SW9suRcGX1XOz5-4-FDlarx53vQp-IILE7O7EWs47m4u1_af6N3Y2H4ogffOhDyGQbAKT_WVmfrOzMwAr3mvX8FJyOgsuZaS4USg5ImqPDURbBNyOeqrf18fHZm8C_tR7YUJaZa0TC0XtRy7EyDfI9SUqYsRWtH31g4euUWF1tW6hUcKii79viLKNP3Q-0fyuCtHeOfi4y6uuAtwJI3JufdNb43WKiTbCpVojKqt1qmySSkGHUS5yMrSudJFNtI_oirKWiIlFjRG9dxKeyEir8F91Fb9dtTBSlFvv1BZJ3FRVJSOymBvfk4tsXUql7tu_--q_sGnt2f_tazyHZ5X3zFol3OdgAofzMFt3pmCVolqA09aQ7fxKXM6IINgB8q9ZQg-w1uCcpMi_XTLy1dkJZiO-f31JQ6s8ft4mF559DpnDLESoWYdYRRYyXli1byvgeBEOH0XIFzA1HA3xJbBNkWJjM0FtNNl1q2xT-KIGniHe5b1cgrV6emNXVVkPzT4GcWBbhIQ4ICEOSFiC97dDr8rSIg8NWq4BEFfaZRzfzf6rf99-B9O7B196ca_T776GGXL2ZBk-WoapPLvGN_DU_cwvxtnbAsgMzh4bK38Be0c2YQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+Exact+Double-Oracle+Algorithm+for+Zero-Sum+Extensive-Form+Games+with+Imperfect+Information&rft.jtitle=The+Journal+of+artificial+intelligence+research&rft.au=Bosansky%2C+B.&rft.au=Kiekintveld%2C+C.&rft.au=Lisy%2C+V.&rft.au=Pechoucek%2C+M.&rft.date=2014-01-01&rft.issn=1076-9757&rft.eissn=1076-9757&rft.volume=51&rft.spage=829&rft.epage=866&rft_id=info:doi/10.1613%2Fjair.4477&rft.externalDBID=n%2Fa&rft.externalDocID=10_1613_jair_4477 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1076-9757&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1076-9757&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1076-9757&client=summon |