The leasing of idle computing resources over the net is one way to motivate more participants to join the grid computation initiative. Since the participating parties are independent bodies, negotiation activities are required. In this research, we propose a new automated negotiation mechanism that allows each party to reach an agreement. The mechanism includes two methods: a co-evolutionary method and a game theory based method that is a trusted third party mediated game to facilitate the automation of negotiation between two participants. This mechanism allows them to reach a state that exhibits Pareto efficiency and Nash Equilibrium without knowing each other's utility function.