Sybil Attack means one node counterfeits multiple identities. It poses great threats to the routing of wireless ad hoc networks. Many existing solutions employ local detection method to capture misbehavior and then enhance the detection accuracy by information exchange. However, they ignore the rationality of member nodes. To save resource, rational nodes are reluctant to share information, therefore, how to guarantee reliable information exchange becomes a challenge issue. This paper presents a cooperative detection method against Sybil attack. Our method adopts the reputation mechanism which relies on the observation exchange to differentiate Sybil identities from legitimate ones. To promote the observation exchange, we present a cooperative detection game with initial condition, which helps nodes be aware that with which to share the observations can bring the maximum utilities. The theoretical and numerical analysis indicate that only benign and unselfish nodes can be accepted by their rational neighbors while Sybil nodes are excluded from the information exchange.