Network virtualization and slicing technologies create opportunity for infrastructure-less virtual network operators (VNOs) to enter the market anytime and provide diverse services. Multiple VNOs compete to provide the same kinds of services to end users (EUs). VNOs lease virtual resources from the infrastructure provider (InP) and sell services to the EUs by using the leased resources. The difference between the selling and leasing is the gross profit for the VNOs. A VNO that leases resources without precise knowledge of future demand, may not consume all the leased resources through service offers to EUs. Consequently, the VNO experiences loss and resources remain unused. In order to improve resource utilization and ensure that new entrant VNOs do not face losses, proper estimation of initial resource demand is important. In this paper, we propose a Bayesian game with Cournot oligopoly model to properly estimate the optimal initial resource demands for multiple entrant competing VNOs (players) with the objective of maximizing the expected profit for each VNO. The VNOs offer the same kinds of services to EUs with different qualities (player's type), which are public information. The exact service quality with which a VNO competes in the market is private information. Therefore, a VNO assumes the type of its opponent VNOs with certain probability. We derive the Bayesian Nash equilibrium (BNE) of the presented game and evaluate numerically the effect of service qualities and prices on the expected profit and market share of the VNOs.