We study bidding and pricing competition between two spiteful mobile network operators (MNOs) with considering their existing spectrum holdings. Given asymmetric-valued spectrum blocks are auctioned off to them via a first-price sealed-bid auction, we investigate the interactions between two spiteful MNOs and users as a three-stage dynamic game and characterize the dynamic game's equilibria. We show an asymmetric pricing structure and different market share between two spiteful MNOs. Perhaps counter-intuitively, our results show that the MNO who acquires the less-valued spectrum block always lowers his service price despite providing double-speed LTE service to users. We also show that the MNO who acquires the high-valued spectrum block, despite charing a higher price, still achieves more market share than the other MNO. We further show that the competition between two MNOs leads to some loss of their revenues. By investigating a cross-over point at which the MNOs' profits are switched, it serves as the benchmark of practical auction designs.
In wireless communications, the competition among MNOs have been addressed by many researchers @cite_13 -- @cite_16 . Yu and Kim @cite_13 studied price dynamics among MNOs. They also suggested a simple regulation that guarantees a Pareto optimal equilibrium point to avoid instability and inefficiency. Niyato and Hossain @cite_6 proposed a pricing model among MNOs providing different services to users. However, these works did not consider the spectrum allocation issue. More closely related to our paper are some recent works @cite_3 -- @cite_16 . The paper @cite_3 studied bandwidth and price competition (i.e., Bertrand competition) among MNOs. By taking into account MNOs' heterogeneity in leasing costs and users' heterogeneity in transmission power and channel conditions, Duan . presented a comprehensive analytical study of MNOs' spectrum leasing and pricing strategies in @cite_1 . In @cite_5 , a new allocation scheme is suggested by jointly considering MNOs' revenues and social welfare. X. Feng @cite_16 suggested a truthful double auction scheme for heterogeneous spectrum allocation. None of the prior results considered MNOs' existing spectrum holdings even if the value of spectrum could be varied depending on MNOs' existing spectrum holdings.
@cite_1 @cite_3 @cite_6 @cite_5 @cite_16 @cite_13
2018061752 2143535483 2132998716 2137663561
This paper presents a comprehensive analytical study of two competitive secondary operators' investment (i.e., spectrum leasing) and pricing strategies, taking into account operators' heterogeneity in leasing costs and users' heterogeneity in transmission power and channel conditions. We model the interactions between operators and users as a three-stage dynamic game, where operators simultaneously make spectrum leasing decisions in Stage I, and pricing decisions in Stage II, and then users make purchase decisions in Stage III. Using backward induction, we are able to completely characterize the dynamic game's equilibria. We show that both operators' investment and pricing equilibrium decisions process interesting threshold properties. For example, when the two operators' leasing costs are close, both operators will lease positive spectrum. Otherwise, one operator will choose not to lease and the other operator becomes the monopolist. For pricing, a positive pure strategy equilibrium exists only when the total spectrum investment of both operators is less than a threshold. Moreover, two operators always choose the same equilibrium price despite their heterogeneity in leasing costs. Each user fairly achieves the same service quality in terms of signal-to-noise ratio (SNR) at the equilibrium, and the obtained predictable payoff is linear in its transmission power and channel gain. We also compare the duopoly equilibrium with the coordinated case where two operators cooperate to maximize their total profit. We show that the maximum loss of total profit due to operators' competition is no larger than 25 percent. The users, however, always benefit from operators' competition in terms of their payoffs. We show that most of these insights are robust in the general SNR regime. We address the problem of spectrum pricing in a cognitive radio network where multiple primary service providers compete with each other to offer spectrum access opportunities to the secondary users. By using an equilibrium pricing scheme, each of the primary service providers aims to maximize its profit under quality of service (QoS) constraint for primary users. We formulate this situation as an oligopoly market consisting of a few firms and a consumer. The QoS degradation of the primary services is considered as the cost in offering spectrum access to the secondary users. For the secondary users, we adopt a utility function to obtain the demand function. With a Bertrand game model, we analyze the impacts of several system parameters such as spectrum substitutability and channel quality on the Nash equilibrium (i.e., equilibrium pricing adopted by the primary services). We present distributed algorithms to obtain the solution for this dynamic game. The stability of the proposed dynamic game algorithms in terms of convergence to the Nash equilibrium is studied. However, the Nash equilibrium is not efficient in the sense that the total profit of the primary service providers is not maximized. An optimal solution to gain the highest total profit can be obtained. A collusion can be established among the primary services so that they gain higher profit than that for the Nash equilibrium. However, since one or more of the primary service providers may deviate from the optimal solution, a punishment mechanism may be applied to the deviating primary service provider. A repeated game among primary service providers is formulated to show that the collusion can be maintained if all of the primary service providers are aware of this punishment mechanism, and therefore, properly weight their profits to be obtained in the future. Market-based mechanisms offer promising approaches for spectrum access in cognitive radio networks. In this paper, we focus on two market models, one with a monopoly primary user (PU) market and the other with a multiple PU market, where each PU sells its temporarily unused spectrum to secondary users (SUs). We propose a pricing-based spectrum trading mechanism that enables SUs to contend for channel usage by random access, in a distributed manner, which naturally mitigates the complexity and time overhead associated with centralized scheduling. For the monopoly PU market model, we first consider SUs contending via slotted Aloha. The revenue maximization problems here are nonconvex. We first characterize the Pareto optimal region, and then obtain a Pareto optimal solution that maximizes the SUs' throughput subject to the SUs' budget constraints. To mitigate the spectrum underutilization due to the “price of contention,” we revisit the problem where SUs contend via CSMA, and show that spectrum utilization is enhanced, resulting in higher revenue. When the PU's unused spectrum is a control parameter, we study further the tradeoff between the PU's utility and its revenue. For the multiple PU market model, we cast the competition among PUs as a three-stage Stackelberg game, where each SU selects a PU's channel to maximize its throughput. We characterize the Nash equilibria, in terms of access prices and the spectrum offered to SUs. Our findings reveal that the number of equilibria exhibits a phase transition phenomenon, in the sense that when the number of PUs is greater than a threshold, there exist infinitely many equilibria; otherwise, there exists a unique Nash equilibrium, where the access prices and spectrum opportunities are determined by the budgets elasticity of SUs and the utility level of PUs. The dynamic spectrum market (DSM) is a key economic vehicle for realizing the opportunistic spectrum access that will mitigate the anticipated spectrum-scarcity problem. DSM allows legacy spectrum owners to lease their channels to unlicensed spectrum consumers (or secondary users) in order to increase their revenue and improve spectrum utilization. In DSM, determining the optimal spectrum leasing price is an important yet challenging problem that requires a comprehensive understanding of market participants' interests and interactions. In this paper, we study spectrum pricing competition in a duopoly DSM, where two wireless service providers (WSPs) lease spectrum access rights, and secondary users (SUs) purchase the spectrum use to maximize their utility. We identify two essential, but previously overlooked, properties of DSM: 1) heterogeneous spectrum resources at WSPs and 2) spectrum sharing among SUs. We demonstrate the impact of spectrum heterogeneity via an in-depth measurement study using a software-defined radio (SDR) testbed. We then study the impacts of spectrum heterogeneity on WSPs' optimal pricing and SUs' WSP selection strategies using a systematic three-step approach. First, we study how spectrum sharing among SUs subscribed to the same WSP affects the SUs' achievable utility. Then, we derive the SUs' optimal WSP selection strategy that maximizes their payoff, given the heterogeneous spectrum propagation characteristics and prices. We analyze how individual SU preferences affect market evolution and prove the market convergence to a mean-field limit, even though SUs make local decisions. Finally, given the market evolution, we formulate the WSPs' pricing strategies in a duopoly DSM as a noncooperative game and identify its Nash equilibrium points. We find that the equilibrium price and its uniqueness depend on the SUs' geographical density and spectrum propagation characteristics. Our analytical framework reveals the impact of spectrum heterogeneity in a real-world DSM, and can be used as a guideline for the WSPs' pricing strategies.