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We consider a centralized multi-agent optimization problem with coupling constraint among agents, where the information is distributed between agents who are strategic, selfish and have the private value functions. To achieve a global optimal solution, we propose an incentive mechanism based on a message space and payment function, which makes a non-cooperative game among agents where an individual utility function of each agent aligns with the centralized optimization problem. We construct a family of payment function, which leads to a potential game among agents and ensures the strongly Nash implementation, budget balance and individual rationality of the induced mechanism using the linear matrix inequality approach.