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This paper investigates mechanism design for allocating a good with a positive externality without monetary payments, in a setting where each agent knows not only their own valuation but also the valuations of other agents to whom they are connected in a network. The planner's goal is to allocate the good to the agent with the highest valuation. Given the externality — which increases with the valuation of the agent receiving the good — each agent prefers that the good be allocated to the agent with the highest valuation to maximize their own utility. The paper explores the concept of belief-free implementation as proposed by Bergemann and Morris (2009) and demonstrates that the planner can use this partial incentive align-ment to accurately identify the agent with the highest valuation. This is achieved by soliciting information from each agent about their own valuation and the valuations of their neighbors, regardless of the agents' beliefs. The paper identifies the net-work structures that allow for the belief-free implementation of efficient allocation. It proposes a mechanism that ensures efficient allocation, irrespective of agents' be-liefs, when the network includes at least one central agent who is connected to all other agents.
