The Annan Plan for Cyprus was presented to the Greek and Turkish Cypriots for approval by simultaneous referendums held on 24.04.2004. The plan was anticipating a unified Cyprus. It was rejected by the Greek side so could not put into affect. This paper analyses the Annan Plan in relation to the Prisoner's Dilemma Game from a psychological perspective. It is concluded that contrary to what the dilemma suggests, it is always advantageous for the Turkish to cooperate. The fundamental elements of the cooperation, such as effective communication, genuine perception, mutual trust and willingness to solve the problem are missing in the Cyprus case. Also the United Cyprus Republic which was aimed in the Annan Plan was not a desired solution especially for the Greek Cypriots. In order to establish a peaceful resolution to the conflict a cooperative strategy which was adopted by both parties is necessary.