IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v43y2014i2p415-438.html
   My bibliography  Save this article

The combinatorial game theory of well-tempered scoring games

Author

Listed:
  • Will Johnson

Abstract

The general behavior of combinatorial scoring games is not well-understood. In this paper, we focus on a special class of “well-tempered” scoring games. By analogy with Grossman and Siegel’s notion of even- and odd-tempered normal play games, we declare a dicot scoring game to be even-tempered if all its options are odd-tempered, and odd-tempered if it is not atomic and all its options are even-tempered. Games of either sort are called well-tempered. These show up naturally when analyzing one of the “knot games” introduced by Henrich et al. We consider disjunctive sums of well-tempered scoring games, and develop a theory for them analogous to the standard theory of disjunctive sums of normal play partizan games. We isolate a special class of inversive well-tempered games which behave like normal play partizan games or like the “Milnor games” considered by Milnor and Hanner. In particular, inversive games (modulo equivalence) form a partially ordered abelian group, and there is an effective description of the partial order. Moreover, the full monoid of well-tempered scoring games (modulo equivalence) admits a complete description in terms of the group of inversive games. We also describe several examples of well-tempered scoring games and provide dictionaries listing the values of some small positions in two of these games. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Will Johnson, 2014. "The combinatorial game theory of well-tempered scoring games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 415-438, May.
  • Handle: RePEc:spr:jogath:v:43:y:2014:i:2:p:415-438
    DOI: 10.1007/s00182-013-0386-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00182-013-0386-6
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00182-013-0386-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Eric Duchêne & Matthieu Dufour & Silvia Heubach & Urban Larsson, 2016. "Building Nim," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 859-873, November.
    2. Jonathan Chappelon & Urban Larsson & Akihiro Matsuura, 2018. "Two-player Tower of Hanoi," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(2), pages 463-486, May.
    3. Ravi Kant Rai & Urban Larsson & Neel Patel, 2021. "Discrete Richman-bidding scoring games," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 695-728, September.
    4. Urban Larsson & Richard J. Nowakowski & Carlos P. Santos, 2018. "Games with guaranteed scores and waiting moves," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(2), pages 653-671, May.

    More about this item

    Keywords

    Combinatorial games; Scoring games; Milnor games; 91A46;
    All these keywords.

    JEL classification:

    Statistics

    Access and download statistics

    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:spr:jogath:v:43:y:2014:i:2:p:415-438. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.