Quantum Coalition of “n Equipartition” Compound Mode in Minority Game

Abstract

We investigate the quantum coalition in an N-player quantum minority game proposed by Benjamin. N players share an initial entangled state and the measure of entanglement of the initial state is p. The coalition size is n (n < N). When N is odd and when N is even with the restricted condition $n\leq \frac {N}{2}$, we find a best quantum strategy which can make the expected payoff of each coalition player reach the maximal value in this paper. We compare the expected payoffs of the coalition players before and after the best coalition, and get that whether the players coalition or not is related to p when N is even; when N is odd, the expected payoff can always be improved by coalition which is independent of p. This result provides a theory basis for the choice of the initial state in a minority game. Moreover we propose a quantum minority game with clique-wise entanglement state which can make the expected payoff reach the upper limit and reduce the possibility of coalition.