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Resource Allocation in Multiuser Multi-Carrier Cognitive Radio Network via Game and Supermarket Game Theory: Survey, Tutorial, and Open Research Directions
Resource Allocation in Multiuser Multi-Carrier Cognitive Radio Network via Game and Supermarket Game Theory: Survey, Tutorial, and Open Research Directions
KSII Transactions on Internet and Information Systems (TIIS). 2014. Nov, 8(11): 3674-3710
Copyright © 2014, Korean Society For Internet Information
  • Received : April 30, 2014
  • Accepted : July 21, 2014
  • Published : November 30, 2014
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About the Authors
Omar B. Abdul-Ghafoor
Department of Electrical, Electronic and System Engineering, University Kebangsaan Malaysia, Bangi, Malaysia
Mahamod Ismail
Department of Electrical, Electronic and System Engineering, University Kebangsaan Malaysia, Bangi, Malaysia
Rosdiadee Nordin
Department of Electrical, Electronic and System Engineering, University Kebangsaan Malaysia, Bangi, Malaysia
Musbah M. R. Shaat
Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Barcelona - Spain

Abstract
In this tutorial, we integrate the concept of cognitive radio technology into game theory and supermarket game theory to address the problem of resource allocation in multiuser multicarrier cognitive radio networks. In addition, multiuser multicarrier transmission technique is chosen as a candidate to study the resource allocation problem via game and supermarket game theory. This tutorial also includes various definitions, scenarios and examples related to (i) game theory (including both non-cooperative and cooperative games), (ii) supermarket game theory (including pricing, auction theory and oligopoly markets), and (iii) resource allocation in multicarrier techniques. Thus, interested readers can better understand the main tools that allow them to model the resource allocation problem in multicarrier networks via game and supermarket game theory. In this tutorial article, we first review the most fundamental concepts and architectures of CRNs and subsequently introduce the concepts of game theory, supermarket game theory and common solution to game models such as the Nash equilibrium and the Nash bargaining solution. Finally, a list of related studies is highlighted and compared in this tutorial.
1. Introduction
R ecent studies by the Federal Communication Commission (FCC) have shown that the conventional fixed spectrum allocation approach is becoming insufficient for addressing today’s rapidly developing wireless communications, and there is a call for open spectrum access [1] . To meet this drastic demand in wireless spectrum, dynamic spectrum access (DSA) and cognitive radio (CR) were introduced as intelligent approaches/techniques to solve the problems associated with the fixed spectrum approach and have received significant interest from researchers (see [2] for a comprehensive review). Cognitive radio (also referred to as secondary user (SU) or unlicensed user) can be defined as a technique in which wireless devices have the ability to sense and discover a specific range in the frequency spectrum to identify currently unused bands (also called spectrum holes) for transmission purposes without interfering with the owner of the spectrum (also referred to as primary user (PU) or licensed user).
One of the most commonly occurring problems when addressing CRNs is allocation of the available resources (e.g., power and subcarrier) to CRs. This is because both PUs and CRs occupy the same spectrum band and transmit independently. Thus, CRs require flexible PHY to allow dynamic reconfiguration of the transmitted power and the signal frequency. One of the most promising candidates that can provide proper flexibility and high performance in CRN is the multicarrier technique [3] .
Game theory is a mathematical tool that can be used to model scenarios in which the actions of decision makers, also called players, are in conflict. In CRNs, CR nodes attempt to access the licensed band, which belong to PUs, for their transmission purposes. Thus, the interaction among two decision makers (i.e., CRs and PUs) takes place, and game theory is shown to be an effective tool for analyzing and modeling resource allocation in such a scenario. The setup of spectrum allocation in CRNs is quite similar to the interaction of people in a real market, where the owner of the spectrum can ‘rent’ the temporary vacant band to CRs for their needs. This simple scenario makes adopting market theory as a game an interesting tool in modeling the problem of resource allocation in CRNs.
In this article, we have followed a simple strategy to introduce readers to the concept of (i) CRNs, (ii) game theory, (iii) supermarket game theory and (iv) resource allocation in Multiuser Multi-Carrier CRNs (MMC-CRNs) using game and supermarket game theory. Furthermore, we have tried our best to provide simple definitions and scenarios to facilitate a better understating of the problem of game/market resource allocation in MMC-CRNs.
- 1.1 Motivations for using game/supermarket game theory in MMC-CRNs
Game and supermarket game theory have become important fields of study for resource allocation in CRNs. This is because both “ game theory ” and “ supermarket game theory ” have proven to be a powerful decision making structure that able to provide excellent performance for CR nodes compared to that in ordinary optimization theory [4] . Moreover, game/supermarket game theory provides fast convergence of resource allocation algorithms to a common point (i.e., steady-state point), which is another important issue to consider when adopting game/supermarket game theory in CRNs. The motivations behind adopting game and supermarket game theory in MMC-CRNs can be summarized as follows:
  • (1) Interaction among independent users: In CRNs, there are two types of users (i.e., PUs and CRs), also called decision makers, with conflicts of interest, interacting with each other independently, trying to access the same spectrum band. This interaction adds certain obstacles in analyzing the problem of resource allocation in MMC-CRNs. Game theory, in contrast, appears to be one of the most attractive tools for removing these obstacles because it is mainly used to model scenarios where the action of one player impacts/conflicts with that of other players in the network[4]. Moreover, the availability of a common solution in game theory such as the Nash equilibrium and Nash bargaining add another advantage in modeling the problem of resource allocation via game theory.
  • (2) Spectrum supermarket and real supermarket: The behavior of PUs and CRs in allocating their resources in MMC-CRNs is quite similar to the interactions among people in actual markets. Both include the following features: (i)Pricing, where the owner of the spectrum can gain benefits by renting the available spectrum holes to the tenants in the network (i.e., CR nodes). Thus, mutual benefits exist whereby the PUs improves their revenue and CRs enjoy access to the band for their needs. (ii)Auction, where CRs compete with each other in an auction scenario to obtain access to certain bands. The similarities between the concept of CRs and the interaction among people in a real supermarket make the adoption of economics concepts in analyzing the problem of resource allocation in MMC-CRNs another attractive tool.
- 1.2 Research Contributions
In this article, we have provided a tutorial on the application of game and supermarket game theory to the problem of resource allocation in MMC-CRNs. This tutorial is driven by the following problems: (i) how to build a cognitive radio network on a licensed spectrum; (ii) how CRs allocate their resources without harming the owner of the spectrum; (iii) how to apply game/market theory to the problem of resource allocation in MMC-CRNs; (iv) how to define the solution associated with game/market theory (e.g., Nash equilibrium, Nash bargaining), and (v) how to prove the existence and uniqueness in the defined game/market. We address these issues by making the following contributions:
  • 1) Spectrum sharing and spectrum access in CRNs: We have provided a simple introduction to the concept of spectrum access and spectrum sharing techniques in CRNs. This includes related issues, objectives, and comparisons for recently developed spectrum sharing/access technique in CRNs.
  • 2) Game theory and supermarket game theory: This includes the following:
  • • We have provided a simple introduction and analysis to the fundamentals of (i) non-cooperative game theory, (ii) cooperative game theory, and (iii) market theory.
  • • Instead of mathematical approach for the NE, we have proposed a visual mathematical approach that facilitates a better understanding of the mathematical solution of the game (i.e., Nash equilibrium).
  • • We have proposed several definitions, scenarios and examples for the application of game and market theory to the problem of resource allocation in MMC-CRNs.
  • 3) Resource allocation and management in MMC-CRNs: We have included a survey of recent and related studies in the literature on the resource allocation problem in MMC-CRNs based on game/supermarket game theory by summarizing its main features and objectives.
To the best of our knowledge, this paper is the first tutorial that offers concrete descriptions related to the resource allocation problem in MMC-CRNs based on game and supermarket game theory.
- 1.3 Organization of the paper
This tutorial is organized as follows. In Section 2, we introduce the concept of (i) CR architecture, (ii) resource management in CRNs, and (iii) MMC-CRNs. The concepts of game theory and its solutions are presented in Section 3. Spectrum trading and supermarket game theory are explored in Section 4. An overview of resource allocation in MMC-CRNs and a survey of the related studies in the literature are presented in Section 5. Open research directions and the conclusion of the study are presented in Section 6 and Section 7, respectively.
2 Cognitive Radio Network
This section summarizes the main concept for (i) CRN models, (ii) spectrum sharing and spectrum access techniques in CRNs, and (iii) multicarrier techniques for CRNs.
- 2.1 CRN Models
In CRNs, there are two general types of models that can be defined as follows [5] , [6] : (i) Infrastructure-based model: A CR base station, abbreviated as “CRBS”, is the main component in this approach and facilitates the residence of CRs in the licensed spectrum. Moreover, monitoring the spectrum band utilization and guiding the CRs to the vacant band is another feature of CRBS. (ii) Ad-hoc-based model: No permanent infrastructure exists in this approach. Thus, CRs must communicate among themselves independently to determine their actions while minimizing the amount of interference generated to PUs based on their own monitoring [6] . Table 1 provides the main components for both approaches. In this tutorial, the application of game and supermarket game theory is considered in both infrastructure and ad-hoc approaches.
Main Components of the CRN Models.
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Main Components of the CRN Models.
- 2.2 Spectrum Sharing and Recourse Management in CRNs
In this section, we summarize the features and concepts of spectrum sharing and spectrum access in CRNs.
- 2.2.1 Spectrum Sharing in CRNs
A key challenge in CRN spectrum sharing is to answer the following question: “ how do you allocate transmission resources ( e.g., power and subcarrier ) efficiently among CRs over a wide range of available spectra with the available activities of neighboring PUs? [5] To be specific, spectrum sharing in CRNs must take into account the following essential issues: (i) providing the capability to maintain good QoS for CRs and (ii) minimizing the generated interference to the PUs by wisely assigning the transmission resources to CRs. To address the above mentioned issues, two main spectrum sharing techniques in CRNs are briefly described as follows [7] :
  • 1) “Open spectrum sharing”: If CR users only access the unlicensed band, e.g., scientific and medical band (ISM band) or TV white space, then the spectrum sharing model is defined as an “open spectrum sharing”, where all CR users have the same rights among themselves to utilize the spectrum and allocate their resources accordingly.Fig. 1provides an example of open spectrum sharing.
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Example of open spectrum sharing in CRNs.
  • 2) “Hierarchical spectrum sharing”: If CR users access the licensed spectrum together with PUs, then the spectrum sharing model is defined as a “hierarchical spectrum sharing”, where the CRs strictly follow certain policies (e.g., spectrum sensing) to access the available spectrum.Fig. 2provides an example of hierarchical spectrum sharing.
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Example of hierarchical spectrum sharing in CRNs.
Moreover, hierarchical spectrum sharing can be divided into two main approaches: (i) overlay spectrum sharing and (ii) underlay spectrum sharing. The main features of the overlay and underlay approaches are summarized based on the following:
  • 1) Overlay spectrum access: CRs, in this approach, have permission to access the available spectrum opportunistically/rationally if and only if the spectrum is not being occupied by the PUs. Moreover, CRs are able to use a portion of their power for cognitive transmission and the rest of the power to help (relay) the transmission of PUs[8]. The main objective of this technique is to manage and control the access of CRs to spectrum holes[5],[9].Fig. 3shows an example of overlay spectrum access.
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Overlay spectrum access.
  • 2) Underlay spectrum access: CRs, in this approach, share the spectrum simultaneously with PUs. Thus, PUs must be protected by applying a spectral mask on the CRs signals to make the generated interference from active CRs below the acceptable threshold for PUs to run smoothly and to provide fair communication services among PUs and CRs[8].Fig. 4illustrates an example of underlay spectrum access.
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Underlay spectrum access.
Both spectrum access techniques have been widely adopted in the literature to allow CRs to communicate among them using the licensed spectrum band. However, more attention is being given to analyzing the underlay spectrum access caused by the difficulties associated with controlling the behavior of CRs attempting to minimize the generated interference to the owner of the spectrum.
- 2.3 Multiuser Multicarrier CRNs (MMC-CRNs): Concepts and Interference Analysis
In CRNs, the key features of CRs are (i) their ability to sense the available spectrum band and (ii) their ability to communicate with each other without interfering with the service of PUs to obtain better spectrum utilization than that in the fixed spectrum approach [10] . To fulfill the first point 1 , CRs must be prepared with spectrum sensing capability, and to achieve the second point, the PHY of the CR must be sufficiently flexible.
The multicarrier technique, in contrast, is envisioned as a promising candidate for CRNs that can satisfy the PHY issues for CRs. Moreover, multicarrier technique, abbreviated as (MC) have been seen to provide reliability and flexibility in allocating the available resources among CRs, which results in a better communication environment among CRs and PUs [11 - 13] . Additionally, MC-based CRNs can provide excellent coexistence among PUs and CRs based on the following abilities: (i) nulling the subcarriers that are currently occupied by active PUs and (ii) nulling the subcarriers that may produce certain amounts of interference for other users in the network [14] .
Orthogonal frequency division multiplexing (OFDM) is a special case of MC techniques and is considered one of the most promising multicarrier candidates that can provide proper performance and flexibility in dynamically allocating spectrum holes among CRs. Moreover, adopting OFDM to the problem of resource allocation in CRNs facilitates the monitoring of the PU’s activity and the occupancy of spectrum holes accordingly [3] . Another multicarrier candidate that can be adopted in the problem of resource allocation is the filter bank multicarrier (FBMC 2 ) technique [15] . Compared to OFDM, (i) FBMC can provide better spectral efficiency in CRNs by separating the transmission of PUs and CRs through filtering [16] , and (ii) FBMC promises very low out-of-band energy for each subcarrier signal [17] . Knowing this, in multiuser multicarrier networks, a multiple access scheme is required, e.g., an orthogonal frequency multiple access technique (OFDMA), to allocate both subcarriers and power to CR nodes.
To demonstrate the idea of MMC-CRN and the related issues, we provide the following motivating example
Motivating Example_1: “MMC-CRN Architecture and Interference Analysis”: Assuming that we have a CR-based-OFDM network, consisting of two types of mobile radio devices (PUs and CRs) coexisting in the same geographical area and communicating using the same band as shown in Fig. 5 -a, where communication links and channel gains of different links can be defined as follows: (i) the sold lines indicate the intended signal links; (ii) the spotted lines are the interference links; (iii)
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and
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are the interference gains from CR-to-PU and PU-to-CR, respectively; and (iv) the superscripts ( c ) and ( p ) refer to the cognitive radio and the primary users, respectively.
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a) Conceptual interference model in CRNs. b) Frequency distribution of PU activities.
Moreover, in MMC-based CRNs (i.e., OFDM), both CRs and PUs exist in side-by-side spectrum bands [18] as shown in Fig. 5 -b. Thus, a mutual interference among PUs and CRs arises in this scenario and requires special consideration to maintain acceptable performance in both networks [19] . Assuming that CRNs consist of K CRs and the available band is divided into N subcarrier with Δ f bandwidth, based on Fig. 5 -(a & b), the generated interference from CRs to the band of active PUs can be defined based on the following definition:
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Note that the active PUs also generates an amount of interference to the CRs, and that amount of interference should be formulated mathematically 3 to provide for a concrete analysis for mutual interference in MMC-CRNs.
The first point (i.e., spectrum sensing technique) is beyond the scope of this tutorial article.
Please refer to [16] for a comprehensive tutorial on OFDM and FBMC.
Please refer to appendix-I for details on interference’ mathematical formulation.
3. Application of Game Theory in MMC-CRNs
Details related to the concepts and applications of game theory including both “non-cooperative game theory” and “cooperative game theory” are discussed in the following sections.
- 3.1 Game theory: Basic Concepts
Game theory was first introduced by J.V. Neumann and O. Morgenstern in 1944 [22] and is extensively used in microeconomics. Its application has commonly been recognized as a great tool for analyzing several engineering problems. Game theory can be defined based on 2 .
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Moreover, game theory can be classified into two main approaches: (i) Non-cooperative game theory: In this approach, the decision makers (or players) behave selfishly, aiming to maximize their own revenue. (ii) Cooperative game theory: In this approach, the players behave cooperatively to maximize the revenue of their network.
Furthermore, the strategies in game theory can be divided into two types: (i) pure strategy and (ii) mixed strategy. Table 2 gives a brief comparison among players’ strategies in game theory.
Comparison of player behavior in a non-cooperative game4.
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Comparison of player behavior in a non-cooperative game4.
In addition, it is worth mentioning that in [26] and [27] , the authors provide a comprehensive survey on the application of game theory in CRNs and general wireless networks respectively. Furthermore, details related to fundamentals and concepts of game theory have been included as well. Hence, readers are advised to refer to [26] and [27] for more details regarding the mathematical formulations that illustrate the concepts of game theory. Our work, in contrast focuses on the applications of game theory and supermarket game theory to the problem of resource allocation in MMC-CRNs.
To simplify the concept of game theory and to show how the components of game theory and the elements of MMC-CRNs related to each others, we provide the following scenario as follows
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In the following sections, details of both branches of game theory are presented by providing definitions, examples, scenarios and discussion regarding the common solution when a game is adopted. Hence, the interested readers can better understand the concept of game theory and its applications in the problem of resource allocation in MMC-CRNs.
- 3.2 Non-cooperative Game Theory Approach: Concepts and Theorems
Non-cooperative game theory is widely adopted in modeling resource allocation problem in CRNs and can be defined based on 3 :
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The motivation of adopting NCGT in the problem of resource allocation in MMC-CRNs is the noticeable improvement in term of efficiency, spectrum utilization and the ability to guide selfish players to more stable resource allocation outcomes. To familiarize the reader with the concept of NCGT, we provide the following scenario:
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- 3.2.1 Common Solution to NCGT
When using NCGT, one should answer the following question: “ What will occur when interactions among rational players take place in certain applications? ” One of the most commonly used solutions to predict the output of a game is the Nash equilibrium , which can be defined based on 4 .
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To simplify the idea of the NE, we provide a visual approach to describe how the NE works in a given scenario as presented in Fig. 6 .
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Visual description for the NE.
Another significant issue in the solution of NCGT (or NE) is the investigation of two important properties: (i) Existence of an NE: The existence of an NE can be obtained using specific mathematical properties related to certain utility functions (e.g., supermodularity and supermodular games) [31] . (ii) Uniqueness: In addition to the existence property, the uniqueness of an NE must also be considered in the solution to NCGT. Moreover, Theorem 1 and Theorem 2 provide the necessary conditions for both properties as follows:
Theorem 1 [29] , [32] : An NE exists in a game
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if for ∀ i K , the following conditions hold:
  • 1) The action profile of playeriis a nonempty, convex and compact subset of some Euclidean space.
  • 2) The utility functionπiis a continuous and quasi-concave function over its action set.
Theorem 2: An NE in NCGT is unique if a game
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modeled using the following special game technique is thus shown to reach a unique NE:
  • 1) Potential game[33]5;
  • 2) Standard function[34]6.
If a utility function in NCGT is carefully selected and the above mentioned theorems are fulfilled, then the NE is guaranteed to exist.
- 3.3 Cooperative Game Theory Approach: Concepts and Theorems
In contrast to NCGT, players in cooperative game theory (abbreviated as CGT) are collaborating with each other wisely to maximize the total utility of their network, and, thus, the performance of the network can be improved accordingly. In this section, we discuss two popular forms of cooperative game theory: (i) bargaining game and (ii) coalition game.
- 3.3.1 Bargaining Game
In bargaining game, abbreviated as BG, the players have a choice to cooperate and negotiate with each other. Thus, the players have the opportunity to reach a commonly beneficial agreement where all the players gain the maximum profit [35] , [36] . The idea of a bargain game can be explained via the following scenario:
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Similar to NCGT, there is a common solution used for CGT, which is the topic of the following subsection.
- 3.3.2 Common Solution to CGT
One of the most commonly used solutions in CGT is called the Nash bargaining solution ( NBS ). This solution provides an optimal and fair resource allocation among players and can be defined as a function
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that assigns a BG problem to a unique element of S based on the Nash axiom constraints 7 [36] .
Moreover, the two important properties (i) existence and (ii) uniqueness are also associated with NBS and must also be examined in the problem.
Theorem 3 “Existence and Uniqueness of NBS”: A unique and fair NBS
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can be obtained by maximizing a Nash product term based on
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Proof: If the problem of resource allocation in MMC-CRNs is formulated as in (3), then the NBS satisfies all the Nash axioms and is shown to provide a fair and unique solution as presented in [37] , [40] .
- 3.3.3 Coalition Game
The second type of CGT is called a coalitional game and is abbreviated as CG. CGs have been shown to be an important tool for designing efficient, fair, and collaborative strategies in CRNs and can be divided into three categories 8 [41] : (i) canonical coalitional games, (ii) coalition formation games, and (iii) coalitional graph games.
CG theory describes how a set of players collaborate with each other by creating collaborating groups and can be defined as follows:
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To demonstrate the idea of a K -player CG , we provide the following basic example:
Motivating Example 2:“Modeling of a Coalition Game in MMC-CRNs”: Consider the problem of subcarrier allocation in MMC-CRNs. The concept of a CG can be adopted to model K -players based on the following steps [37] : (i) Forming step: K players are grouped into pairs, named a coalition. (ii) Two-player negotiation step: Each coalition follows the procedures listed in ( scenario 2 ) so that pairs in each coalition can negotiate with each other and exchange the information about available subcarriers. (iii) Reforming and convergence step: All the players are regrouped and continue their negotiation until convergence occurs.
Please refer to [26] for more details on the concept of pure strategy game, mixed strategy game and correlated equilibrium (CE)
Please refer [33] for additional details about potential game.
Please refer to [34] for additional details about the standard function and uniqueness of NE.
Please refer to [37] definition_2 for addition details about the Nash bargaining intuitive axioms
Please refer to [41] for a comprehensive survey on coalition game and the definition of its categories.
4 Application of Supermarket Game in MMC-CRNs
In this section, we introduce the concepts of supermarket game theory, which includes the following: “ pricing theory ”, “ auction theory ”, and “ oligopolistic competition ” and their relevance to game theory.
- 4.1 Supermarket Game Theory: An Introduction
The concepts of a game as labeled in section (3) highlighted the following fact: game theory provides mathematical tools to study the scenario where rational players interact with each other . Based on this fact, game theory can be applied to a real supermarket scenario to study how individuals interact and negotiate with each other as buyers and sellers in the arena of a supermarket. The application of game theory to the market scenario is extremely interesting in the field of MMC-CNR for the following main reasons: (i) PUs enter the supermarket with the unused band as a commodity for sale to increase their revenue; and (ii) CRs, in contrast, enter the market looking for a commodity to buy (i.e., spectrum holes) to conduct a transmission with their partner. Thus, game theory can be applied to a spectrum supermarket to study the interaction among buyers and sellers accordingly.
- 4.2 Pricing Theory
Pricing theory was first introduced and adopted in the arena of economics. In the field of spectrum market approaches, pricing theory becomes one of the important tools in the problem of resource allocation for the following reasons: (i) In the case of NCGT, pricing can provide an efficient NE by guiding selfish players to a more efficient operating point 9 [29] . (ii) In the case of CG, pricing can provide a better negotiation environment and fair distribution of the available resources so that the seller/buyers of the spectrum (i.e., PUs/CRs) are satisfied. (iii) Finally, pricing acts as a punishment technique for those buyers that generate certain amounts of interference to PUs, and, subsequently, interference to the owner of the spectrum can be minimized. To understand the general idea behind pricing, we have provided the following definition:
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- 4.3 Auction Theory
Auction theory [42] is extensively used in the field of economics to determine, for example, the value of commodities that have uncertain prices. Recently, it has been applied to solve issues related to the problem of resource allocation in wireless networks. The common auction scenario can have the following components [43 , 44] : (i) bidders, (2) a seller, (3) an auctioneer, and (iv) the commodity. Table 3 provides a mapping between basic components of auction theory and the entities of MC-CRNs.
Mapping of auction theory elements to MC-CRNs.
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Mapping of auction theory elements to MC-CRNs.
Generally speaking, the auction supermarket adopts the following scenario: (i) The buyers compete with each other by submitting an ( ask ) asking about the price of the product to be sold in the spectrum market to obtain one of the available commodities. (ii) The sellers, in certain scenarios, compete with each other to obtain additional buyers to increase their revenue by submitting a ( bid ) indicating the bidding price for the requested product [43] . Hence, game theory is the best mathematical tool to analyze the behavior of sellers, buyers and auctioneer in an auction scenario. Accordingly, the application of an auction as a game has generally been adopted in the problem of resource allocation in CRNs. In the following paragraph, we provide a scenario of the application of an auction game in MMC-CRNs as shown below.
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In Fig. 7 , the buyers are the CR nodes, the seller is the primary user base stations (PUBS) and the auctioneer is the PUBS itself. The sellers offer the unused subcarrier to the buyers at a certain price to increase their revenue. The buyers can accept the offer and make their transmissions accordingly.
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- 4.4 Oligopoly Market Competition
When a small number of firms compete with each other to maximize their revenue by managing the quantity or the price of the offered commodity, then the market can be called an “oligopolistic market” [45] with the following assumptions [46] : (i) few firms are available in the market; (ii) the firms compete with each other independently to increase their revenue; and (iii) each firm should take into account the available strategies of other firms in the market.
Moreover, the behavior of firms in an oligopoly market (i.e., interaction and competition) can be modeled using the concept of game theory. However, modeling an oligopoly market as a game requires different models that have different supermarket structure and different strategies [47] . Table 5 summarizes features of the most familiar oligopoly game in the literature. To facilitate a better understanding to the concept of oligopoly market game, we have provided the following example:
Different types of oligopoly games.
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Different types of oligopoly games.
Motivating Example_3 [50] :“Modeling of Oligopoly-Bertrand Game in MMC-CRNs”
Assuming that L -PU spectrum service providers compete with each other in an MMC-CRN oligopoly-Bertrand scenario, the resource allocation problem can be described based on the following: (i) commodities are the vacant subcarriers offered by PU spectrum providers, (ii) firms (i.e., players) are the spectrum providers that compete with each other to obtain additional buyers (i.e., CRs) to maximize their profit, (iii) consumers are the CRs that willing buy/rent good commodities (i.e., subcarriers with less interference to PU) at a reasonable price, (iv) strategies of the firms are related to the supplied quantity or offering price, (v) the payoff of a firm is linked by its surplus function (revenue minus cost) for renting vacant subcarriers to CRs and (vi) the game solution is the NE.
Motivating Example_4: “Modelling of stacklberg in uplink MMC-CRNs”
Assuming an uplink scenario in OFDMA based CRNs as shown in Fig.8
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Stacklberg Game in MMC-CRNs
The PUBS is the owner of the spectrum and their users (i.e., PUs) transmit to the PUBS for free of charge. CRs, in contrast, need to pay to the PUBS in order to get subcarrier for their needs. The strategy between the PUBS and CRS can be modelled according to Stacklberg market game with the following assumptions: (i) PUBS is the leader of market game, (ii) PUBS sell its vacant band and charge a price for each CR to maximize its profit, (iii) the CRs are the followers in this scenario and need to follow the pricing policies generated by the PUBS, and (iv) after all prices distributed by PUBS, the CRs make a decision to utilize the subcarrier with controlled power to maximize their utility function based on NCGT.
Note that the same example can be simply applied to Cournot and Bertrand model by following the features listed in Table 5 .
Please refer to [29] for an example on how pricing method plays an important role in providing efficient NE.
5 Resource Allocation in MMC-CRNs
- 5.1 Resource Allocation in MMC-CRNs: An Overview
The resource allocation problem (e.g., power and subcarrier allocation) in MMC-CRNs brings to academics certain challenges because of the following facts: (i) two different mobile radio users (i.e., PUs and CRs) interact with each other, transmitting independently within the same band, and may be based on different standards [16] , (ii) CRs are rational, aiming to allocate their resource independently and, in some scenarios, selfishly and (iii) the interference that arises from CRs-to-PUs and vice versa is another concern that must be treated carefully in MMC-CRNs.
The first two points make game theory a promising tool for resource allocation in CRNs because game theory is extensively applied to study situations with conflicting interests. Moreover, in multicarrier techniques (e.g., OFDM and FBMC), the PUs leave some unused subcarrier during their idle period. Thus, CRs have the opportunity to utilize unused subcarriers. In another words, the CR pays the owner of the spectrum to temporarily rent his vacant bands. Therefore, a mutual benefit exists in this scenario, where the rental users (i.e., CRs) take the advantages by utilizing the vacant spectrum for their transmission purposes, and the owner of the spectrum can maximize their revenue accordingly [3] . This basic concept makes adopting market theory in the problem of resource allocation another promising solution. In addition, an overview of the problem of resource allocation in MMC-CRNs is shown in Fig. 8 and can be described based on the following example.
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Overview of resource allocation problem in MMC-CRNs
Motivating Example_5: “Resource allocation problem in OFDMA-CRNs” : Assuming that K -CR players are available in the network with N OFDM subcarrier frequency distributions as shown in Fig. 8 . Thus, the problem is to structure the following: (i) Problem formulation, which includes the design of the utility function (e.g., rate maximization) with a set of constraints (e.g., channel/power/interference constraints). (ii) Subcarrier allocations, abbreviated as SA , (i.e., subcarriers to CRs allocation matrix SA = [sa k,n ] K×N ) where each subcarrier is assigned to only one CR. (iii) Non-cooperative power allocation game, abbreviated as NCPA , for each subcarrier (i.e., PA = [Pn]N×1 ), which can be determined based on maximum power and interference constraints.
The optimal solution to the resource allocation problem in MMC-CRNs is, in general, an NP hard problem. Thus, the suboptimal scheme is preferred in such a scenario and can be achieved by decomposing the resource allocation problem into two sub-problems (i.e., an SA problem and a NCPA problem). Moreover, the optimal NCPA algorithm can be achieved via a Lagrangian technique.
Furthermore, the problem of resource allocation in MMC-CRs can take the following three forms: (i) uplink resource allocation with multiple local power constraints (e.g., see [12] , [52] - [53] ); (ii) downlink resource allocation with global power constraints (e.g., see [54] - [55] ); and (iii) distributed resource allocation as in an ad-hoc scenario (e.g., see [56] - [57] ).
- 5.2 Resource allocation in MMC-CRNs via game/supermarket game theory
Studies on resource-allocation-based game theory in multicarrier wireless networks can be divided into two general approaches [58] : (i) rate-adaptive games as in [59] and (ii) margin-adaptive (i.e., MA) games as in [60] . However, another approach can be used when using game theory and supermarket game theory: (iii) spectrum-market game, which can be either rate-adaptive, margin-adaptive or a pure spectrum market as in [45] , where CRs are required to follow certain rules to obtain acceptable commodities (i.e., frequency spectrum), while the owners of the market increase their revenue accordingly.
In the case of rate-based resource allocation, the problem is normally formulated to maximize the total rate of the network subject to subcarrier, power and interference constraints as shown in Fig. 9 , whereas in margin-based resource allocation, the problem is formulated to minimize the total power subject to subcarrier and quality of service requirement for each user in the network.
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Taxonomy of resource allocation problems.
For the scenario of MMC-CRNs, most of the studies conducted in the literature focused on rate-adaptive compared to margin-adaptive classes because the latter technique makes the optimization problem more complex compared to the rate adaptation technique. Furthermore, the spectrum market game in the problem of resource allocation in MC-CRNs has received light attention, and more effort is needed in the field of spectrum market game theory.
- 5.3 Discussions on related works
In this tutorial, we have classified the studies conducted in the literature into five classes as shown in Table 6 .
Details of applications’ classes
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Details of applications’ classes
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In addition, to add to the presentation for the mentioned classes, we have provided to further assist readers. Moreover, all the related studies in the literature were classified similar to the details listed in 5 .
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Following the listed classes in Table 6 , we have provided a summary of studies related to the resource allocation problem in multicarrier technology based on game and supermarket game model as shown in Table 7 .
A summary of related studies on the applications of game and supermarket game theory in multicarrier techniques.
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A summary of related studies on the applications of game and supermarket game theory in multicarrier techniques.
In the following sub-sections, we demonstrate the main features of related studies conducted in the literature.
- 5.3.1 Game and supermarket game in non-cognitive MC scenarios
Game and supermarket game theory have been recently adopted to address the problem of resource allocation in wireless networks (see, for example, [59] , [63] , [64] , [66] , [70] and [71] ). Table 8 summarizes the main features of a number of selected studies conducted on the resource allocation problem in multicarrierwireless networks using both game theory and supermarket game theory.
Main features for RA in MC-wireless scenarios.
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Main features for RA in MC-wireless scenarios.
- 5.3.2 Cognitive Radio MMC Scenario
In the case of MMC-CRNs, game theory and supermarket game were proven to provide efficient and effective spectrum sharing among CRs and the owner of the spectrum because they can properly define the interaction and competition among players [47] . There are a number of studies that adopted game and supermarket game theory in multicarrier CRNs to address the related issues to spectrum access (i.e., power, subcarriers and rate) as in [43] , [61] , [64] , [67 - 69] , [72 - 76] . To be more specific we provide a review to a number of related studies conducted in the literature as shown below.
In [61] , a spectrum monopoly-market scenario based on non-cooperative game theory was proposed for OFDM-based CRNs. The most interesting point in this work is that the CRs performing two interesting tasks as follows: (i) using part of the leased band to help the PUs by relaying tier data from the source to destination and (ii) use the remaining part of the leased band for their own activities. Moreover, the PUs enters the market aiming to sell certain amount of its vacant band to CRs and the CRs, in contrast, enters the market aiming to transmit with optimal power in order to fulfil the above mentioned tasks. The authors adopted non-cooperative game in order to find optimal power for the CRs in the leasing-market scenario.
Instead of Stackelberg game, the authors employed auction to solve the spectrum leasing scenario where the CRs are involved in the leasing decisions which consider another interesting contribution of this work among others in the literature. The authors guided the readers to some selected references for the mathematical verification of the existence and uniqueness of the NE. However, the convergence of the proposed algorithm to a stable point is a bit slow. Hence it is not appropriate for more particle scenario.
More complicated RA scenario in MMC-CRNs based on non-cooperative game has been proposed in [64] . Instead of multiuser-single cell scenario, the authors proposed RA algorithm in multiuser multi-cell MC-CRNs which resulted in NP-hard problem. To tackle this problem, the authors adopted the multiple access channels (MAC) technique in order to convert their problem to a concave optimization problem which is one of the novel contributions of this work.
Non-cooperative game theory based on MAC technique has been adopted in this work to allocate the subcarrier and power in uplink scenario. Existence and uniqueness of the NE are validated mathematically. However, the authors didn’t provide any evidence to show that the proposed power algorithm convergence to unique NE via simulation. Moreover, the cheating scenario among the selfish CRs has been ignored in this work.
One of the most important problems to tackle while allocating subcarriers among CRs in MC technique is how to mitigate the generated interference to the owner of the spectrum (i.e., PUs). This significant problem has been considered in [67] in order to designed not only efficient RA algorithm but also optimal subcarrier allocation with minimal interference in MC-CRNs. Firstly, the authors adopted an interference mitigation objective in the utility function and defined the potential function where the NE is always guaranteed. Secondly, the authors proposed modified subcarrier-game scheme know as autonomous number of subcarrier selection (ANSS) method which considered as etiquette provider for the whole network. Through ANSS scheme the players are allowed to have some interaction among them before the start of the real game. This makes each player aware of its environment and the available recourses and can easily measure the amount of interference from neighbor players within its radius of interference. The novelty of this work comes from introducing potential game with means of cooperation and self-awareness in the player’ utility function and introducing sequential best response play in order to make the ANSS-game model converge to unique stable point (i.e., NE). However, the proposed algorithm shows slow convergence to a stable point which is the main drawback for the proposed algorithm.
An overlay spectrum sharing based on game-pricing approach in MC-CRNs has been considered in [72] . The main contribution of this work is by adopting pay-off function that comes with two parts: (i) rate-based utility function and (ii) pricing function. The pricing function, in contrast, composed of two parts in order to manage: (i) the interference generated among CRs in the network represented by normal pricing function, and (ii) the negative effect from active CRs to PU’ sub-band represented by exponential pricing function. Accordingly, sufficient and fair spectrum sharing can be achieved in this work by provide adequate protection to the PUs. Furthermore, the existence and uniqueness of the proposed objective function has been verified mathematically and via simulation as well. The authors considered a distributed scenario; however the cheating scenario among the selfish CRs has been ignored in this work. Unlike [61] and [67] the proposed algorithm in [72] resulted in a fast convergence to the NE. Hence, it is more appropriate for more practical scenario.
Resource allocation in MC-CRNs based on market-game has been considered in [73] . The most interesting issue in this work, among others, is that the authors adopted Colonel Blotto market game to model the problem of subcarrier and power allocation in both uplink and downlink scenario. Unlike [64] , the authors proposed a simple optimization problem by adopting interference temperature constraint instead of global power constraint and Blotto game used to allocate the resources among the players which resulted in a fair allocation and fast convergence to NE. Moreover, the cheating scenario has been introduced in this work which is another obvious issue in this work compared to that in [72] . The existence and uniqueness of the NE have been verified mathematically and via simulation as well. However, the convergence of the proposed algorithm is slightly slower than that in [72] .
In [74] , the authors proposed new and dynamic pricing scheme in a competitive spectrum- supermarket. The noticeable advantages of this work compared to other studies related to spectrum market, is that the buyers play an important role in the convergence of the market by evaluating the spectrum sellers in a different way based on the quality of goods provided by sellers and the prices offered by the sellers. The sellers, based on buyer’s evaluation, are trying their best to show the available spectrum at affordable prices to attract not only quality sensitive buyers but also the price wise buyers. Therefore, the performance of the spectrum market can be improved accordingly. Game theory has been adopted in [74] to analyze the profit of the sellers. Convergence of the market has been well investigated by simulation and the market convergence to stable points where all buyers and sellers are satisfied in their commodities and profit respectively. However, the proposed market mode is not practical in heterogeneous spectrum market where many buyers and sellers are available because of the long time required by the buyers to evaluate different goods with different prices provided by different sellers.
The authors in [76] proposed an energy-efficient algorithm for joint power and subcarrier allocation in the uplink MC- underlay CRNs based on pricing-game model. The objective of the proposed game model is to maximize the EE utility function and to guarantee the PU’ QoS. To fulfil this objective, the authors adopted a linear bandwidth-pricing scheme to improve the efficiency of the NE. Unlike [72] , where the authors proposed non-linear pricing scheme, authors in [76] proposed a linear pricing function which reduced the complexity of the optimization problem. Both uniqueness and existence of the NE have been proved mathematically. However, the authors didn’t show the convergence of their algorithm in the simulation results. The selfishness scenario has been considered in this work. However, the cheating scenario which considered an important scenario to consider especially in EE paradigm has been ignored. Hence it is not sure how apply the proposed distributed algorithm in more realistic EE scenario.
In addition to the above review, Table 9 summarized the main features of the related studies conducted in the literature to solve the problem of RA in MMC-CRNs with the aid of game and supermarket game theory. This will help the interested readers to memorize the most important components of game/market theory which are: players, strategies and utility function and how these components are related to the objective of the game/market scenario.
Main features for RA in MC-wireless scenarios.
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Main features for RA in MC-wireless scenarios.
Finally, it is worth mentioning that in [43] and [69] , the authors provide a comprehensive survey for the application of auction and spectrum leasing in CRNs, respectively, and discuss fundamentals and concepts of supermarket game theory.
6. Open Research Directions
Game and supermarket game theory were proven to be an effective tools in analyzing the problem of resource allocation in MMC-CRNs. However, there are still a number of shortcomings in certain areas where game and supermarket game must attract more attention as follows:
  • 6.1 MC-CR relay game networks10: Cooperative communication with the aid of relay nodes in MC-CRNs has been recently acknowledged as a promising technology in dynamic spectrum sharing because of the assured enhancement in the performance of both CRs and PUs by providing flexible and efficient resource allocation among all the residents (i.e., players) in a given network. Research on MC-CR relay networks has recently been conducted in the literature, see for example,[79]-[81]. However, extensive studies have not been conducted on the problem of resource allocation in MC-CR relay networks using the concept of game and supermarket game theory. Thus, the problem of resource allocation in MC-CR relay networks remains an open issue that must be addressed.
  • 6.2 Multi-cell MC-CRNs: Most of the studies in the literature focused on single-cell scenarios to address the problem of subcarrier and power allocations among players caused by the simplicity associated with single cell scenario. However, to provide a more practical scenario for real applications, multi-cell scenarios should be considered. Game theory and supermarket game theory can be adopted to facilitate the scenario of multi-cell MC-CRNs in the following proposed scenario: (i) Network-user game/market: In this scenario, the network has the opportunity to select good players that follow the network renting policies (i.e., renting spectrum with minimal interference to PUs) while punishing the players with high spectrum renting prices. (ii) User-network game/market: In this scenario, the users have the opportunity to choose the network that offers a good commodity with a good QoS.
  • 6.3 CRNs over 4G networks: Cognitive radio has become one of the most recognized technologies in 4G networks, e.g., Long Term Evolution Advanced (LTE-A), to solve the spectrum insufficiency problem[8]. OFDM, in contrast, is chosen as the PHY air interface for 4G downlink transmissions because of its promising advantages in providing proper performance and flexibility in allocating spectrum. Thus, adopting game theory and supermarket game theory in the problem of resource allocation in MC-4G-based cognitive radios can be an interesting direction of future study.
  • 6.4 Green Spectrum-Market Game: Research on green technology wireless networks has received significant amounts of attention recently and has become a very important area of investigation for the improvement of the energy efficiency (EE) of networks. In fact, a number of researchers investigated the problem of resource allocation in EE-MMC-CRNs (see, for example,[82]). However, the application of game theory and supermarket game theory to the problem of resource management in MC-Green-CRNs is ignored in recent studies, and a significant amount of effort is needed in this significant field of research. Game theory and supermarket game theory play important roles in designing green CRNs. By applying game theory and supermarket game theory, CR nodes can avoid transmission on certain spectrum that is frequently used by PUs. Furthermore, a green spectrum market can be achieved by applying intelligent supermarket game theory, where CRs incorporate a wide variety of activities, including renting the vacant spectrum wisely by informing other CRs about renting policies (e.g., pricing) so that CRs have the ability to rent spectrum holes that provide minimal interference to nearby PUs. Moreover, by applying a green spectrum market, the CRs can change their expense behavior by buying from good sellers that offer reasonable price for the available spectrum with a good QoS.
Please refer to [78] for examples of the application of game theory to interference coordination in OFDMA relay networks.
7. Conclusion
Game theory and supermarket game theory have become promising tools for modeling and analyzing the interactions of CRs in the context of resource allocation problems in CRNs. In this article, we have presented a comprehensive tutorial on the concepts and applications of “game theory” and “supermarket game theory” to the problem of resource allocation in MMC-CRNs. The game model, in this article, is categorized based on the behavior and interactions among CRs and PUs as non-cooperative, cooperative and supermarket games. In addition, a set of definitions, examples and scenarios related to each model were presented in this tutorial to facilitate an understanding of the concepts of game and supermarket game theory accordingly. The similarities between the behavior of players in MMC-CRNs and the interactions among people in a real market make supermarket game theory better suited to analyze the spectrum trading in MMC-CRNs. However, research on the applications of game and supermarket game theory in MMU-CRNs remains in its infancy, and more problems must be investigated properly. Finally, we hope that this tutorial will provide important information for interested researchers in the areas of game and supermarket game theory.
Acknowledgements
The authors are very appreciative to the Universiti Kebangsaan Malaysia and Malaysia’s Ministry of Higher Education (ERGS/1/2013/ICT03/UKM/02/1) for funding of this work. The authors would also like to thank the editor and the anonymous reviewers for their valuable feedback.
BIO
Omar B. Abdulghafoor is a Ph.D. candidate in the Department of Electrical, Electronics and System Engineering, Universiti Kebangsaan Malaysia (UKM). He received his B.Sc. in Control and Computer Eng. from University of Technology, 2001 and the MEng. in Computer and Communication from Universiti Kebangsaan Malaysia in 2005. His research interests include cognitive radio, wireless communications, resource allocation and game theory applications.
Mahamod Ismail joined the Department of Electrical, Electronics and System Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia (UKM) in 1985, and currently, he is a Professor in Communication Engineering. He is also appointed as the Deputy Director (Education and Research) Centre of Information Technology, UKM. He received the B.Sc. degree in Electrical and Electronics from University of Strathclyde, U.K. in 1985, the M.Sc. degree in Communication Engineering and Digital Electronics from University of Manchester Institute of Science and Technology (UMIST), Manchester U.K. in 1987, and the Ph.D. from University of Bradford, U.K. in 1996. He was with the first Malaysia Microsatellite TiungSat Team Engineers in Surrey Satellite Technology Ltd. U.K. for 9 months started in June 1997. His research interests include mobile and satellite communication as well as wireless networking, particularly, on the radio resource management for the next generation wireless communication. He also published more than 300 technical publications in local and international conferences and journals. He is an active member in professional bodies such as Institute of Electrical and Electronics Engineers (IEEE), USA and Malaysia Society of Engineers and Technologist (MSET) and currently the Vice Chair of IEEE Malaysia Section and executive committee member for Joint Communication and Vehicular Technology Society Chapter IEEE Malaysia.
Rosdiadee Nordin received his B.Eng. from Universiti Kebangsaan Malaysia in 2001 and Ph.D. from University of Bristol, United Kingdom in 2011. He is currently a senior lecturer in Department of Electrical, Electronics and System Engineering in Universiti Kebangsaan Malaysia. His research interests include resource allocation, green radio, Multiple-Input Multiple-Output (MIMO), Orthogonal Frequency-Division Multiple Access (OFDMA), carrier aggregation (CA), cognitive radio and indoor wireless localization.
Musbah M Shaat obtained his engineering degree major in communication and control from the Electrical and Computer Engineering Department at the Islamic University of Gaza (IUG), Palestine (1999-2004). He worked for one year (2004-2005) as full time teaching assistant at the electrical engineering department at the IUG. He awarded the DAAD "German Academic Exchange Service" master scholarship and got the master degree in communication and electronics engineering from Jordan University of Science and Technology (JUST), Jordan (2005-2007). He obtained his PhD degree from the Signal Theory and Communication department (TSC) at the Polytechnic University of Catalonia (UPC), Spain (2007-2012). He worked as a research associate in the Access Technologies Area in Centre Tecnologic de Telecomunicacions de Catalunya (CTTC)-Spain until he joined the electrical engineering department at the Islamic university of Gaza in September 2012.
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