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Abstract-In the mobile communication services, users wish to subscribe to high quality service with a low price level, which leads to competition between mobile network operators (MNOs). The MNOs compete with each other by service prices after deciding the extent of investment to improve quality of service (QoS). Unfortunately, the theoretic backgrounds of price dynamics are not known to us, and as a result, effective network planning and regulative actions are hard to make in the competitive market. To explain this competition more detail, we formulate and solve an optimization problem applying the two-stage Cournot and Bertrand competition model. Consequently, we derive a price dynamics that the MNOs increase and decrease their service prices periodically, which completely explains the subsidy dynamics in the real world. Moving forward, to avoid this instability and inefficiency, we suggest a simple regulation rule which leads to a Pareto-optimal equilibrium point. Moreover, we suggest regulator's optimal actions corresponding to user welfare and the regulator's revenue.

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Due to the emergence of smart devices, mobile data traffic grows exponentially. A Cisco report predicts that global mobile data traffic will increase 26-fold between 2010 and 2015. Therefore, the spectrum shortage continues and the spectrum price increases, which will eventually lead to decrease of user welfare. Another side effect of the data traffic growth is the polarization of data traffic among users. To resolve these problems, we introduce two subsidy schemes (i.e., price and quality of service (QoS) subsidy schemes) and mathematically analyze the effect of each scheme. We identify that if the regulator has sufficient spectrum amount for the network service, then the QoS subsidy scheme will be a good choice for all players in the network service market. Otherwise, the price subsidy scheme can be better from user welfare perspective. Even though our analytic results are derived under some assumptions for mathematical tractability, it will provide good intuitions for spectrum regulation.