Uncertain Price Competition in a Duopoly with Heterogeneous Availability

We study the price competition in a duopoly with an arbitrary number of buyers. Each seller can offer multiple units of a commodity depending on the availability of the commodity which is random and may be different for different sellers. Sellers seek to select a price that will be attractive to the buyers and also fetch adequate profits. The selection will in general depend on the number of units available with the seller and also that of its competitor - the seller may only know the statistics of the latter. The setting captures a secondary spectrum access network, a non-neutral Internet, or a microgrid network in which unused spectrum bands, resources of ISPs, and excess power units constitute the respective commodities of sale. We analyze this price competition as a game, and identify a set of necessary and sufficient properties for the Nash Equilibrium (NE). The properties reveal that sellers randomize their price using probability distributions whose support sets are mutually disjoint and in decreasing order of the number of availability. We prove the uniqueness of a symmetric NE in a symmetric market, and explicitly compute the price distribution in the symmetric NE.Comment: 45 pages, Accepted for publication in IEEE Transaction on Automatic Contro

Spectrum Trading: An Abstracted Bibliography

This document contains a bibliographic list of major papers on spectrum trading and their abstracts. The aim of the list is to offer researchers entering this field a fast panorama of the current literature. The list is continually updated on the webpage \url{http://www.disp.uniroma2.it/users/naldi/Ricspt.html}. Omissions and papers suggested for inclusion may be pointed out to the authors through e-mail (\textit{[email protected]})

Quality Sensitive Price Competition in Spectrum Oligopoly:Part 1

We investigate a spectrum oligopoly market where primaries lease their channels to secondaries in lieu of financial remuneration. Transmission quality of a channel evolves randomly. Each primary has to select the price it would quote without knowing the transmission qualities of its competitors' channels. Each secondary buys a channel depending on the price and the transmission quality a channel offers. We formulate the price selection problem as a non co-operative game with primaries as players. In the one-shot game, we show that there exists a unique symmetric Nash Equilibrium(NE) strategy profile and explicitly compute it. Our analysis reveals that under the NE strategy profile a primary prices its channel to render high quality channel more preferable to the secondary; this negates the popular belief that prices ought to be selected to render channels equally preferable to the secondary regardless of their qualities. We show the loss of revenue in the asymptotic limit due to the non co-operation of primaries. In the repeated version of the game, we characterize a subgame perfect NE where a primary can attain a payoff arbitrarily close to the payoff it would obtain when primaries co-operate.Comment: Accepted for publication in IEEE/ACM Transactions on Networking. 41 pages single column format.Conference version is available at arXiv:1305.335

Quality Sensitive Price Competition in Spectrum Oligopoly

We investigate a spectrum oligopoly where primary users allow secondary access in lieu of financial remuneration. Transmission qualities of the licensed bands fluctuate randomly. Each primary needs to select the price of its channel with the knowledge of its own channel state but not that of its competitors. Secondaries choose among the channels available on sale based on their states and prices. We formulate the price selection as a non-cooperative game and prove that a symmetric Nash equilibrium (NE) strategy profile exists uniquely. We explicitly compute this strategy profile and analytically and numerically evaluate its efficiency. Our structural results provide certain key insights about the unique symmetric NE.Comment: Presented in ISIT' 2013, Istanbul Version 2 contains some modified versions of proofs of version 1. In IEEE Proceedings of International Symposium on Information Theory, 201

A Game-Theoretic Approach to Competitive Spectrum Sharing in Cognitive Radio Networks

“Cognitive radio ” is an emerging technique to improve the uti-lization of radio frequency spectrum in wireless networks. In this paper, we consider the problem of spectrum sharing among a pri-mary user and multiple secondary users. We formulate this prob-lem as an oligopoly market competition and use a Cournot game to obtain the spectrum allocation for secondary users. Nash equi-librium is considered as the solution of this game. We first present the formulation of a static Cournot game for the case when all sec-ondary users can observe the adopted strategies and the payoff of each other. However, this assumption may not be realistic in some cognitive radio systems. Therefore, we formulate a dynamic Cournot game in which the strategy of one secondary user is se-lected solely based on the pricing information obtained from the primary user. The stability condition of the dynamic behavior for this spectrum sharing scheme is investigated. Keywords-Spectrum sharing, cognitive radio, game theory, Nash equilibrium, stability analysis. I

Analysis of Radio Spectrum Market Evolution Possibilities

A tremendous growth in wireless traffic volumes and a shortage of feasible radio spectrum has led to a situation where the old and rigid spectrum regime is not a viable option for spectrum management and a shift towards a more market driven approach has begun. Great uncertainty still exists over how such a radio spectrum market will come about and what kind of shape it would take. This paper studies some long term macro level evolution possibilities for how this radio spectrum market could emerge and what would be the corresponding value chain configurations. The scenario planning and system dynamics methods are utilized to build four alternative future spectrum market scenarios.Spectrum Markets, Spectrum Policy, Flexible Spectrum Usage, Cognitive Radio, Value Networks, Scenario Planning, System Dynamics.

Game Theoretic Approach for Cognitive Radio Networks

Cognitive radio is a promising approach to make efficient use of spectrum by rapidly adapting the changes in wireless environment. In such networks, nodes are expected to be aware of their environment and must be able to learn from the outcomes of past decisions. Game theory which comprise of analytical tools designed to study interactive decision-making processes can be applied effectively to solve some of such complex problems. This paper discusses the significance of using game theory for cognitive radio networks and resource allocation, and various game theoretic approaches used for it. DOI: 10.17762/ijritcc2321-8169.15059