Bidding, Pricing, and User Subscription Dynamics in Asymmetric-Valued Korean LTE Spectrum Auction: A Hierarchical Dynamic Game Approach

The tremendous increase in mobile data traffic coupled with fierce competition in wireless industry brings about spectrum scarcity and bandwidth fragmentation. This inevitably results in asymmetric-valued long term evolution (LTE) spectrum allocation that stems from different timing for twice improvement in capacity between competing operators, given spectrum allocations today. This motivates us to study the economic effects of asymmetric-valued LTE spectrum allocation. In this paper, we formulate the interactions between operators and users as a hierarchical dynamic game framework, where two spiteful operators simultaneously make spectrum acquisition decisions in the upper-level first-price sealed-bid auction game, and dynamic pricing decisions in the lower-level differential game, taking into account user subscription dynamics. Using backward induction, we derive the equilibrium of the entire game under mild conditions. Through analytical and numerical results, we verify our studies by comparing the latest result of LTE spectrum auction in South Korea, which serves as the benchmark of asymmetric-valued LTE spectrum auction designs.