The rational secret sharing is an intersection direction between the traditional secret sharing and game theory.In the rational secret sharing scheme

the selfishness maybe impels rational players to deviate from the protocols so as to influence the fairness of scheme.In the existing threshold rational secret sharing schemes

the fairness of (2

2) rational secret sharing scheme

which is a special case

is hard to be realized

especially implementing on the asynchronous communication channel.To achieve fairness of (2

2) rational secret sharing over the asynchronous communication channel

this paper firstly analyzes rational players' utility by simultaneously discussing their short-term interest and long-term interest.Then through illustrating rational players' available actions and belief systems

and computing their expected utilities with the dynamic games of incomplete information

the perfect Bayesian equilibrium for reconstruction phase of (2

2) rational secret sharing is studied.Furthermore

combining with the VCG(Vickrey-Clarke-Groves)mechanism of design theory

the incentive compatibility mechanism

which is named recording interaction

is designed to restrict the behavior of rational players.Consequently

the fair (2

2) rational secret sharing scheme is presented

which does not need the dealer to keep on-line over the asynchronous communication channel.