Resource Allocation in Multiuser Multi-Carrier Cognitive Radio Network via Game and Supermarket Game Theory: Survey, Tutorial, and Open Research Directions

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

Recent 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:

1.2 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:

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.

Table 1.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]:

Fig. 1.Example of open spectrum sharing in CRNs.

Fig. 2.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:

Fig. 3.Overlay spectrum access.

Fig. 4.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 point1, 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 (FBMC2) 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) and 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.

Fig. 5.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 Δf 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:

Note that the active PUs also generates an amount of interference to the CRs, and that amount of interference should be formulated mathematically3 to provide for a concrete analysis for mutual interference in MMC-CRNs.

 

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 definition 2.

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.

Table 2.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

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 definition 3:

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:

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 definition 4.

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.

Fig. 6.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 if for ∀i ∈ K , the following conditions hold:

Theorem 2: An NE in NCGT is unique if a game modeled using the following special game technique is thus shown to reach a unique NE:

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:

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 that assigns a BG problem to a unique element of S based on the Nash axiom constraints7 [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 can be obtained by maximizing a Nash product term based on

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 categories8 [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:

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.

 

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 point9 [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:

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.

Table 4.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.

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.

Fig. 7.

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:

Table 5.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

Fig. 8.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.

 

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.

Fig. 8.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 = [sak,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.

Fig. 9.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.

Table 6.Details of applications’ classes

In addition, to add to the presentation for the mentioned classes, we have provided scenario 5 to further assist readers. Moreover, all the related studies in the literature were classified similar to the details listed in Scenario 5.

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.

Table 7.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.

Table 8.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.

Table 9Main 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:

 

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.