preprints.org > computer science and mathematics > algebra and number theory > doi: 10.20944/preprints202104.0298.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 10 April 2021 / Approved: 12 April 2021 / Online: 12 April 2021 (12:45:52 CEST)

This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results, which, to the best of our knowledge, are stated in this generality for the first time in the literature. The main conclusion of this paper is that the specific rules of a game are absolutely critical. The slightest variation may have important impact on the outcome of the game. It is the combination of two factors that determine who wins: (i) the sets of admissible moves for each player, and (ii) the order of moves, i.e., whether the same player makes the first and the last move. Quantum strategies do not a priori prevail over classical strategies. By carefully designing the rules of the game the advantage of either player can be established. Alternatively, the fairness of the game can also be guaranteed.

Quantum games; classical games; sequential quantum games; groups of actions; winning strategies

Computer Science and Mathematics, Algebra and Number Theory