A principal has to allocate a prize without monetary transfers. She wants to give it to the most valuable agent but does not know any agent’s value. Agents’ information is described by a network: Each agent knows her own value and the values of her neighbors. Given a principal’s prize allocation rule, agents compete for the prize and send messages about themselves (application) and about their neighbors (references) to the principal. They can lie, but only to a certain extent. Can full implementation be obtained? This means, is there a prize allocation rule such that the best agent gets the prize in every equilibrium? Bayesian-monotonicity and the revelation principle fail in this setup. I propose a mechanism which allocates the prize as a function of “best” applications and “worst” references. This mechanism fully implements the principal’s objective if the network is complete. In environments where agents only lie if it increases their chances of winning, an extended version of the mechanism fully implements the principal’s objective for a larger class of networks.