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A q-player impartial avoidance game for generating finite groups

Author

Listed:
  • Bret J. Benesh

    (College of Saint Benedict, Saint John’s University)

  • Marisa R. Gaetz

    (Massachusetts Institute of Technology)

Abstract

We study a q-player variation of the impartial avoidance game introduced by Anderson and Harary, where q is a prime. The game is played by the q players taking turns selecting previously-unselected elements of a finite group. The losing player is the one who selects an element that causes the set of jointly-selected elements to be a generating set for the group, with the previous player winning. We introduce a ranking system for the other players to prevent coalitions. We describe the winning strategy for these games on cyclic, nilpotent, dihedral, and dicyclic groups.

Suggested Citation

  • Bret J. Benesh & Marisa R. Gaetz, 2018. "A q-player impartial avoidance game for generating finite groups," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(2), pages 451-461, May.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:2:d:10.1007_s00182-018-0624-z
    DOI: 10.1007/s00182-018-0624-z
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    References listed on IDEAS

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    1. Anderson, M & Harary, F, 1987. "Achievement and Avoidance Games for Generating Abelian Groups," International Journal of Game Theory, Springer;Game Theory Society, vol. 16(4), pages 321-325.
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