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Peer to Peer networks can be seen as truly distributed computing applications in which peers communicate directly with one another to exchange information, distribute tasks, or execute transactions. The issues with peer to peer network are that the resource is not centralized. Moreover, peers may not know about the trustworthiness of other, so the trust framework should be designed in such a way that the peers reputation can be identified based on the services provided by them. This paper discusses the design of GaTMo a trust framework for evaluating the trust of peers in a network. The trust framework incorporates self experience and reputation to calculate trustworthiness of a peer. Various like Game theoretic strategies are used for selecting peers for doing the peer selection process. The experimental results prove that the GaTMo works effectively for different strategies thereby increasing the payoff of each peer which indirectly increases the life time of the peer to peer network.