Can you help with network structure question please

thank you

Consider the set-up for the bipartite graph auction, with an equal number of buyers and sellers, and with each buyer having a valuation for the object being sold by each seller. Suppose that we have an instance of this problem in which there is a particular seller i who is the favorite: every buyer j has a strictly higher valuation for seller i's object than for the object being sold by any other seller k. (In notation, we have Vij Vkj for all choices of j and ki.) Consider a set of market-clearing prices in this situation. Must it be the case that the price charged by seller i is strictly higher as the price charged by any other seller? Consider the set-up for the bipartite graph auction, with an equal number of buyers and sellers, and with each buyer having a valuation for the object being sold by each seller. Suppose that we have an instance of this problem in which there is a particular seller i who is the favorite: every buyer j has a strictly higher valuation for seller i's object than for the object being sold by any other seller k. (In notation, we have Vij Vkj for all choices of j and ki.) Consider a set of market-clearing prices in this situation. Must it be the case that the price charged by seller i is strictly higher as the price charged by any other seller