IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v13y2021i1p2-d707690.html
   My bibliography  Save this article

Partial Order Games

Author

Listed:
  • Valeria Zahoransky

    (Fachbereich Informatik, Université du Luxembourg, Maison du Nombre, 6 Avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg)

  • Julian Gutierrez

    (Faculty of Information Technology, Monash University, Woodside Building for Technology and Design, 20 Exhibition Walk, Clayton, VIC 3168, Australia)

  • Paul Harrenstein

    (Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK)

  • Michael Wooldridge

    (Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK)

Abstract

We introduce a non-cooperative game model in which players’ decision nodes are partially ordered by a dependence relation, which directly captures informational dependencies in the game. In saying that a decision node v is dependent on decision nodes v 1 , … , v k , we mean that the information available to a strategy making a choice at v is precisely the choices that were made at v 1 , … , v k . Although partial order games are no more expressive than extensive form games of imperfect information (we show that any partial order game can be reduced to a strategically equivalent extensive form game of imperfect information, though possibly at the cost of an exponential blowup in the size of the game), they provide a more natural and compact representation for many strategic settings of interest. After introducing the game model, we investigate the relationship to extensive form games of imperfect information, the problem of computing Nash equilibria, and conditions that enable backwards induction in this new model.

Suggested Citation

  • Valeria Zahoransky & Julian Gutierrez & Paul Harrenstein & Michael Wooldridge, 2021. "Partial Order Games," Games, MDPI, vol. 13(1), pages 1-49, December.
    • Handle: RePEc:gam:jgames:v:13:y:2021:i:1:p:2-:d:707690
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/13/1/2/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/13/1/2/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Koller, Daphne & Milch, Brian, 2003. "Multi-agent influence diagrams for representing and solving games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 181-221, October.
    2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Manish Jain & Jason Tsai & James Pita & Christopher Kiekintveld & Shyamsunder Rathi & Milind Tambe & Fernando Ordóñez, 2010. "Software Assistants for Randomized Patrol Planning for the LAX Airport Police and the Federal Air Marshal Service," Interfaces, INFORMS, vol. 40(4), pages 267-290, August.
    2. Battigalli, Pierpaolo & Bonanno, Giacomo, 1997. "The Logic of Belief Persistence," Economics and Philosophy, Cambridge University Press, vol. 13(1), pages 39-59, April.
    3. Szabó, György & Borsos, István & Szombati, Edit, 2019. "Games, graphs and Kirchhoff laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 416-423.
    4. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    5. Marc Le Menestrel, 2003. "A one-shot Prisoners’ Dilemma with procedural utility," Economics Working Papers 819, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Cheng‐Kuang Wu & Yi‐Ming Chen & Dachrahn Wu & Ching‐Lin Chi, 2020. "A Game Theory Approach for Assessment of Risk and Deployment of Police Patrols in Response to Criminal Activity in San Francisco," Risk Analysis, John Wiley & Sons, vol. 40(3), pages 534-549, March.
    7. Nasimeh Heydaribeni & Achilleas Anastasopoulos, 2019. "Linear Equilibria for Dynamic LQG Games with Asymmetric Information and Dependent Types," Papers 1909.04834, arXiv.org.
    8. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    9. Hitoshi Matsushima, 2019. "Implementation without expected utility: ex-post verifiability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 575-585, December.
    10. Dasgupta Utteeyo, 2011. "Are Entry Threats Always Credible?," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 11(1), pages 1-41, December.
    11. Baran Han, 2018. "The role and welfare rationale of secondary sanctions: A theory and a case study of the US sanctions targeting Iran," Conflict Management and Peace Science, Peace Science Society (International), vol. 35(5), pages 474-502, September.
    12. Carlos Pimienta & Jianfei Shen, 2014. "On the equivalence between (quasi-)perfect and sequential equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
    13. Asheim, Geir & Søvik, Ylva, 2003. "The semantics of preference-based belief operators," Memorandum 05/2003, Oslo University, Department of Economics.
    14. Wang, Yafeng & Graham, Brett, 2009. "Generalized Maximum Entropy estimation of discrete sequential move games of perfect information," MPRA Paper 21331, University Library of Munich, Germany.
    15. repec:dau:papers:123456789/6818 is not listed on IDEAS
    16. Tobias Harks & Martin Hoefer & Anja Schedel & Manuel Surek, 2021. "Efficient Black-Box Reductions for Separable Cost Sharing," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 134-158, February.
    17. Karbowski, Adam, 2011. "O kilku modelach samolubnego karania w ekonomii behawioralnej [Evolution of altruism in the light of behavioral economics]," MPRA Paper 69604, University Library of Munich, Germany.
    18. Ricardo F. Reis & Phillip C. Stocken, 2007. "Strategic Consequences of Historical Cost and Fair Value Measurements," Contemporary Accounting Research, John Wiley & Sons, vol. 24(2), pages 557-584, June.
    19. Costello, Christopher & Molina, Renato, 2021. "Transboundary marine protected areas," Resource and Energy Economics, Elsevier, vol. 65(C).
    20. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    21. Ginsburgh, Victor & Zang, Israël, 2012. "Shapley Ranking of Wines," Journal of Wine Economics, Cambridge University Press, vol. 7(2), pages 169-180, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jgames:v:13:y:2021:i:1:p:2-:d:707690. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.