Influence of initial conditions in \(2\times 2\) 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.
KeywordsQuantum game Symmetric games Potential games Quantum strategy
Author acknowledges the anonymous reviewer for critical suggestions which brought this work to the present form.
- 8.Bleiler, S.A.: A formalism for quantum games and an application. preprint arxiv:0808.1389v1[quantph]