Published March 30, 2024 | Version CC-BY-NC-ND 4.0
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Auction in Impartial Games

  • 1. Department of Computer Science, University of Liverpool, United Kingdom.

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Abstract: Combinatorial game theory (CGT) is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. We prove an importance of a tiebreaking marker related with N-position and P-position in the bidding variant of Impartial combinatorial games.

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Dates

Accepted
2024-03-15
Manuscript received on 07 March 2024 | Revised Manuscript received on 13 March 2024 | Manuscript Accepted on 15 March 2024 | Manuscript published on 30 March 2024.

References

  • Berlekamp, Elwyn R., John H. Conway, and Richard K. Guy. Winning ways for your mathematical plays, volume 4. AK Peters/CRC Press, 2004. https://doi.org/10.1201/9780429487309
  • Bhat J, Payne S. Bidding Chess. The Mathematical Intelligencer. 2009;4(31):37-9. https://doi.org/10.1007/s00283-009-9057-7
  • Conway JH. On numbers and games. AK Peters/CRC Press; 2000 Dec 11. https://doi.org/10.1201/9781439864159
  • Develin M, Payne S. Discrete bidding games. The Electronic Journal of Combinatorics [electronic only]. 2010;17(1): Research-Paper. https://doi.org/10.37236/357
  • Hanner O. Mean play of sums of positional games.
  • Johnson W. The combinatorial game theory of well-tempered scoring games. International Journal of Game Theory. 2014 May;43(2):415-38. https://doi.org/10.1007/s00182-013-0386-6
  • Lazarus AJ, Loeb DE, Propp JG, Stromquist WR, Ullman DH. Combinatorial games under auction play. Games and Economic Behavior. 1999 May 1;27(2):229-64. https://doi.org/10.1006/game.1998.0676
  • Lazarus AJ, Loeb DE, Propp JG, Ullman D. Richman games. Games of no chance. 1996;29:439-49.
  • Milnor J. Sums of positional games. Ann. of Math. Stud. (Contributions to the Theory of Games, HW Kuhn and AW Tucker, eds.), Princeton. 1953 Mar 21;2(28):291-301. https://doi.org/10.1515/9781400881970-017
  • Payne S, Robeva E. Artificial intelligence for Bidding Hex. arXiv e-prints. 2008 Dec:arXiv-0812.
  • Siegel AN. Combinatorial game theory. American Mathematical Soc.; 2013 Aug 1. https://doi.org/10.1090/gsm/146
  • Bashir, S. (2023). Pedagogy of Mathematics. In International Journal of Basic Sciences and Applied Computing (Vol. 10, Issue 2, pp. 1–8). https://doi.org/10.35940/ijbsac.b1159.1010223
  • Kumar, S., & Dwivedi, B. (2019). A Novel Zero-Sum Polymatrix Game Theory Bidding Strategy for Power Supply Market. In International Journal of Recent Technology and Engineering (IJRTE) (Vol. 8, Issue 2, pp. 5669–5675). https://doi.org/10.35940/ijrte.b2889.078219
  • Al-Odhari, A. M. (2023). Algebraizations of Propositional Logic and Monadic Logic. In Indian Journal of Advanced Mathematics (Vol. 3, Issue 1, pp. 12–19). https://doi.org/10.54105/ijam.a1141.043123
  • Narayanan, V., Yegnanarayanan, V., & Srikanth, R. (2019). On Prime Numbers and Related Applications. In International Journal of Innovative Technology and Exploring Engineering (Vol. 8, Issue 12, pp. 4150–4153). https://doi.org/10.35940/ijitee.l3652.1081219
  • Sivaraman, Dr. R., López-Bonilla, Prof. J., & Vidal-Beltrán, S. (2023). On the Polynomial Structure of ( ). In Indian Journal of Advanced Mathematics (Vol. 3, Issue 2, pp. 4–6). https://doi.org/10.54105/ijam.a1162.103223