The Influence Of Quantum Strategy On Three-party CHSH Game

Game theory is a branch of modern mathematics and an important subject of operations research.Game theory is also widely used in many fields,such as politics,economy,culture,military.In recent years,the combination of game theory and quantum information technology has formed a quantum game theory.With appropriate strategies,quantum games can show more superior features than classical games.In the theoretical researches,people discuss more about the two-party game.Quantum strategies,shared entanglement states and winning determination conditions have significant impacts on game players' payoff.In the existing CHSH game research,people pay more attention to the two-party game scenario and few to the three-party game scenario.This paper presents two modified three-party CHSH game models and conducts a detailed research.Firstly,a modified three-party CHSH game model ? is proposed.In this model,three participants,i.e.,Alice,Bob and Charlie share the entangled state |?? = ?|100?+ ?|010?+?|001?(?2+?2+?2?1).The decision condition is that a?b?c=x?(y?z).The numerical results show that when the degree of entanglement is zero,there is no more advantage in using quantum strategy than classical strategy.With the increase of entanglement degree,some specific quantum strategies are better than classical strategies.At maximum entanglement,the maximum winning probability is approximately 0.0362,which is higher than the maximum winning probability using the classic strategy.Secondly,a modified three-party CHSH game model ? is proposed.One participant adopts classical strategy.The other two participants adopt quantum strategies and share the entanglement state |??=?|01?+?|10?.The decision condition is that a?b?c = x?(y?z).The numerical results show that the maximum winning probability of the modified three-party CHSH game model is about 0.0625,which is higher than the maximum winning probability using the classic strategy.Finally,the influences of channel noises on the modified three-party CHSH game ? and ? are studied,which include bit-flipping channel,amplitude-damping channel and phase-reversal channel.For the modified three-party CHSH game model ? and ? at the maximum entanglement case,the winning probability gradually decreases as noise parameter ? increases.For model ?,quantum strategies have more advantage than classical strategies in the bit-flipping channel with ?<0.048 and the amplitude-damped channel with ?<0.282.For model ?,quantum strategies have more advantages than classical strategies in the bit-flipping channel with ?<0.038 or ?>0.962,in the amplitude-damped channel with ?<0.027 and in the phase-flipping channel with ?<0.113 or?>0.887.