Competition and Bargaining in Wireless Networks with Spectrum Leasing

Abstract

Abstract-The case for a competitive market operated by a Mobile Network Operator (MNO) and a Mobile Virtual Network Operator (MVNO) is analysed in the paper. The resource that is leased by the MNO to the MVNO is spectrum. The MNO and the MVNO competeà la Bertrand posting subscription prices and the mobile users may choose to subscribe to one operator. The scenario is modeled by a three-level game comprising a bargaining game, which models the spectrum leasing by the MNO; a competition game, which models the price competition between the MNO and the MVNO; and a subscription game, which models the subscription choice by the mobile users, and the outcome of which may be either not to subscribe, to subscribe to the MNO or to subscribe to the MVNO. The game is solved through backward induction, and each level has a specific solution concept: Shapley value, for the bargain; Nash equilibrium, for the competition; and Wardrop equilibrium, for the subscription. The paper assesses which conditions lead to an equilibrium where the competition does take place, which are expressed as restrictions for the spectrum leasing price agreed at the bargaining, and the spectrum efficiency improvement achieved by the MVNO. Furthermore, it argues that the amount of the leased spectrum should be fixed exogenously in order to achieve optimal user and social welfares.

Automated spectrum trading mechanisms: understanding the big picture

“…Bargaining games are a subset of game theory on their own but they can also be casted to an equivalent problem of another subset of game theory which is cooperative games (see section ''C. Operators bargaining-first phase'' of [64]). In bargaining games, the strategies of a player are the offers to make to the other entity and whether to accept them or not.…”

“…Again, recently the idea is to incorporate dynamics to the bargaining model, so that it takes into account multiple negotiations with the same entity, trying to improve its solutions [82,92]. Bargaining research is also in the direction of using it in multi-stage market models to speed up the trading [57,64].…”

Pricing for Mobile Virtual Network Operators: The contribution of u-map

“…Then, F p max (x) = 1 − e − x µ and f p max (x) = e − x µ /µ. From (9), we derive the optimal price scheme for MVNO as p * = µ + c, which also satisfies (10). As a result, the pricing strategy of MVNO is to transfer the wholesale cost directly to the…”

“…To gain further insight on the pricing behavior of both operators, we also examine the specific one, where the WtPay follows exponential distribution with mean value µ [10]. Then, F p max (x) = 1 − e − x µ and f p max (x) = e − x µ /µ.…”

“…In [10], Guijarro et al model a wireless access market, where an MVNO leases spectrum from an MNO, which is also active in the retail market, and resales it to end-users. The competition between operators is modeled and the optimal amount of spectrum to be leased is determined.…”