Cellular networks are now facing severe traffic overload problems due to the explosive growth of mobile data traffic. One of the promising solutions is to offload part of the traffic through WiFi. In this paper, we investigate an oligopoly offloading market, where several Mobile Virtual Network Operators (MVNOs) compete to serve end users using the network infrastructure leased from the host Mobile Network Operator (MNO) at the wholesale market. First, we study the competitive interactions among the MVNOs considering the overload problems of the offloading market. Specially, we formulate the interactions as a non-cooperative inventory competition game, where each MVNO determines the amount of cellular traffic it can provide to end users (named as the traffic inventory of each MVNO in this paper) simultaneously. We analyze and derive the existence of the Cournot equilibrium using game theory. Furthermore, we study the impact of the MNO's wholesale price strategy on the market equilibrium. Based on these analysis, we find the optimal initial inventory strategy for these competitors according to the Cournot equilibrium. Finally, our simulations present the process of achieving the market equilibrium and illustrate the impact of the host MNO to the MVNOs. © 2016 IEEE.