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
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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. Dynamic spectrum access can significantly improve the spectrum utilization. For wireless service providers, the emergence of dynamic spectrum access brings new opportunities and challenges. The flexible spectrum acquisition gives a particular provider the chance to easily adapt its system capacity to fit end users' demand. However, the competition among several providers for both spectrum and end users complicates the situation. In this paper, we propose a general three-layer spectrum market model for the future dynamic spectrum access system, in which the interaction among spectrum holder, wireless service providers and end users are considered. We study a duopoly situation, where two wireless service providers participate in bandwidth competition in spectrum purchasing and price competition to attract end users, with the aim of maximizing their own profit. We believe we are the first one to explicitly study the relation of these two competitions in dynamic spectrum market. We formulate the wireless service providers' competition as a non-cooperative two-stage game. We first analyze the static game when full information is available for providers. Under general assumptions about the price and demand functions, a unique pure Nash equilibrium is identified as the outcome of the game, which shows the stability of the market. We further evaluate the market efficiency of the equilibrium in a symmetric case, and show that the gap with the social optimal is bounded within a small constant ratio. When the market information is limited, we provide myopically optimal adjustment algorithms for the providers. With such strategies, short term price updating converges to the Nash equilibrium of the given subgame, while long term bandwidth updating converges to a point close to the Nash equilibrium of the full game. To provide seamless mobility with high-speed wireless connectivity, future generation wireless networks must support heterogeneous wireless access. Pricing schemes adopted by different service providers is crucial and will impact the decisions of users in selecting a network. In this article, we provide a comprehensive survey of the issues related to pricing in heterogeneous wireless networks and possible approaches to the solution of the pricing problem. First, we review the related work on pricing for homogeneous wireless networks in which a single wireless technology is available to the users. Then, we outline the major issues in designing resource allocation and pricing in heterogeneous wireless access networks. To this end, we propose two oligopolistic models for price competition among service providers in a heterogeneous wireless environment consisting of WiMax and WiFi access networks. A non-cooperative game is formulated to obtain the price for the service providers. Two different equilibria, namely, the Nash and the Stackelberg equilibria are considered as the solutions of the simultaneous-play and leader-follower price competitions, respectively. To accommodate users' ever-increasing traffic in wireless broadband services, the Federal Communications Commission (FCC) in the U.S. is considering allocating additional spectrum to the wireless market. There are two major directions: licensed (e.g. 3G) and unlicensed services (e.g. Wi-Fi). On the one hand, 3G service can realize a high spectrum efficiency and provide ubiquitous connection. On the other hand, the Wi-Fi service (often with limited coverage) can provide users with high-speed local connections, but is subject to uncontrollable interferences. Regarding spectrum allocation, prior studies only focused on revenue maximization. However, one of FCC's missions is to better improve all wireless users' utilities. This motivates us to design a spectrum allocation scheme that jointly considers social welfare and revenue. In this paper, we formulate the interactions among the FCC, typical 3G and Wi-Fi operators, and the endusers as a three-stage dynamic game and derive the equilibrium of the entire game. Compared to the benchmark case where the FCC only maximizes its revenue, the consideration of social welfare will encourage the FCC to allocate more spectrum to the service which lacks spectrum to better serve its users. Such consideration for the social welfare, to our delight, brings limited revenue loss for the FCC. Auction is widely applied in wireless communication for spectrum allocation. Most of prior works have assumed that all spectrums are identical. In reality, however, spectrums provided by different owners have distinctive characteristics in both spacial and frequency domains. Spectrum availability also varies in different geo-locations. Furthermore, frequency diversity may cause non-identical conflict relationships among spectrum buyers since different frequencies have distinct communication ranges. Under such a scenario, existing spectrum auction schemes cannot provide truthfulness or efficiency. In this paper, we propose a Truthful double Auction mechanism for HEterogeneous Spectrum, called TAHES, which allows buyers to explicitly express their personalized preferences for heterogeneous spectrums and also addresses the problem of interference graph variation. We prove that TAHES has nice economic properties including truthfulness, individual rationality and budget balance. Results from extensive simulation studies demonstrate the truthfulness, effectiveness and efficiency of TAHES.