Coalition Formation Game for Cooperative Cognitive Radio Using Gibbs Sampling

This paper considers a cognitive radio network in which each secondary user selects a primary user to assist in order to get a chance of accessing the primary user channel. Thus, each group of secondary users assisting the same primary user forms a coaltion. Within each coalition, sequential relaying is employed, and a relay ordering algorithm is used to make use of the relays in an efficient manner. It is required then to find the optimal sets of secondary users assisting each primary user such that the sum of their rates is maximized. The problem is formulated as a coalition formation game, and a Gibbs Sampling based algorithm is used to find the optimal coalition structure.Comment: 7 pages, 2 figure

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

Economics of Spectrum Allocation in Cognitive Radio Networks

Cognitive radio networks (CRNs) are emerging as a promising technology for the efficient use of radio spectrum. In these networks, there are two levels of networks on each channel, primary and secondary, and secondary users can use the channel whenever the primary is not using it. Spectrum allocation in CRNs poses several challenges not present in traditional wireless networks; the goal of this dissertation is to address some of the economic aspects thereof. Broadly, spectrum allocation in CRNs can be done in two ways- (i) one-step allocation in which the spectrum regulator simultaneously allocates spectrum to primary and secondary users in a single allocation and (ii) two-step allocation in which the spectrum regulator first allocates spectrum to primary users, who in turn, allocate unused portions on their channels to secondary users. For the two-step allocation scheme, we consider a spectrum market in which trading of bandwidth among primaries and secondaries is done. When the number of primaries and secondaries is small, we analyze price competition among the primaries using the framework of game theory and seek to find Nash equilibria. We analyze the cases both when all the players are located in a single small location and when they are spread over a large region and spatial reuse of spectrum is done. When the number of primaries and secondaries is large, we consider different types of spectrum contracts derived from raw spectrum and analyze the problem of optimal dynamic selection of a portfolio of long-term and short-term contracts to sell or buy from the points of view of primary and secondary users. For the one-step allocation scheme, we design an auction framework using which the spectrum regulator can simultaneously allocate spectrum to primary and secondary users with the objective of either maximizing its own revenue or maximizing the social welfare. We design different bidding languages, which the users can use to compactly express their bids in the auction, and polynomial-time algorithms for choosing the allocation of channels to the bidders