A q-player impartial avoidance game for generating finite groups

Bret J. Benesh () and Marisa R. Gaetz ()
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Bret J. Benesh: College of Saint Benedict, Saint John’s University
Marisa R. Gaetz: Massachusetts Institute of Technology

International Journal of Game Theory, 2018, vol. 47, issue 2, No 4, 461 pages

Abstract: 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.

Keywords: Group theory; Game theory; Impartial game; Maximal subgroup; 91A46; 20D30 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00182-018-0624-z

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