# Influence of initial conditions in $$2\times 2$$ 2 × 2 symmetric games

Influence of initial conditions in $$2\times 2$$ 2 × 2 symmetric games It is known that quantum game is characterized by the payoff matrix as well as initial states of the quantum objects used as carriers of information in a game. Further, the initial conditions of the quantum states influence the strategies adopted by the quantum players. In this paper, we identify the necessary condition on the initial states of quantum objects for converting symmetric games into potential games, in which the players acquire the same payoff matrix. The necessary condition to preserve the symmetric type and potential type of the game is found to be the same. The present work emphasizes the influence of the initial states in the quantization of games. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Influence of initial conditions in $$2\times 2$$ 2 × 2 symmetric games

, Volume 13 (12) – Sep 7, 2014
7 pages

/lp/springer_journal/influence-of-initial-conditions-in-2-times-2-2-2-symmetric-games-dswiL6IuIS
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-014-0820-0
Publisher site
See Article on Publisher Site

### Abstract

It is known that quantum game is characterized by the payoff matrix as well as initial states of the quantum objects used as carriers of information in a game. Further, the initial conditions of the quantum states influence the strategies adopted by the quantum players. In this paper, we identify the necessary condition on the initial states of quantum objects for converting symmetric games into potential games, in which the players acquire the same payoff matrix. The necessary condition to preserve the symmetric type and potential type of the game is found to be the same. The present work emphasizes the influence of the initial states in the quantization of games.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Sep 7, 2014

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