The price of anarchy ( PoA) is introduced to quantify the efficiency of reverse supply chains that use price-only contracts． Considering the uncertainty existing in the supply of used products，the upper bounds of efficiency losses in a decentralized reverse supply chain are derived for different configurations: push or pull with two or more stages． The results show that a reverse supply chain is not just the reverse of a forward supply chain，because the uncertainty in a reverse supply chain comes mainly from the supply side，and it is necessary to take into account the out-of-stock risk due to the insufficient supply of used products． The PoA in a decentralized supply chain proves to be constant for both push and pull configurations． That is，who bears the risk has no effect on the loss of efficiency． Besides，the efficiency generally drops with the number of intermediaries in a reverse supply chain． For a reverse supply chain with fixed stages，however，the value of PoA turns out to be constant．