Analyzing the Dynamic Data Sponsoring in the Case of Competing Internet Service Providers and Content Providers

El Amrani, Mohamed; Garmani, Hamid; Ait Omar, Driss; Baslam, Mohamed; Minaoui, Brahim

doi:https://doi.org/10.1155/2021/6629020

Mobile Information Systems

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Abstract Introduction Conclusion Appendix Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2021 | Article ID 6629020 | https://doi.org/10.1155/2021/6629020

Analyzing the Dynamic Data Sponsoring in the Case of Competing Internet Service Providers and Content Providers

Mohamed El Amrani,¹Hamid Garmani,¹Driss Ait Omar,¹Mohamed Baslam,¹and Brahim Minaoui¹

Academic Editor: Mirco Marchetti

Received18 Nov 2020

Revised24 Dec 2020

Accepted07 Jan 2021

Published19 Jan 2021

Abstract

With a sponsored content plan on the Internet market, a content provider (CP) negotiates with the Internet service providers (ISPs) on behalf of the end-users to remove the network subscription fees. In this work, we have studied the impact of data sponsoring plans on the decision-making strategies of the ISPs and the CPs in the telecommunications market. We develop game-theoretic models to study the interaction between providers (CPs and ISPs), where the CPs sponsor content. We formulate the interactions between the ISPs and between the CPs as a noncooperative game. We have shown the existence and uniqueness of the Nash equilibrium. We used the best response dynamic algorithm for learning the Nash equilibrium. Finally, extensive simulations show the convergence of a proposed schema to the Nash equilibrium and show the effect of the sponsoring content on providers’ policies.

1. Introduction

One of the principal trends on the Internet in the last few years is the explosion in demand for cellular data usage. Therefore, one of the main challenges for CP is how to motivate end-users to access their content to achieve a higher profit. In addition, this increase in cellular data usage needs higher investments in wireless capacity. ISPs launched a new type of data pricing called data sponsoring to get additional revenue and to increase the capacity of their existing network architectures [1]. The critical idea of data sponsoring is to allow the CPs to pay the ISP on behalf of the end-users the network access fees. Data sponsoring plans benefit all entities in the network; the ISPs can generate more revenue with CP’s subsidies, and end-users can enjoy free network access to the CPs, which increases the demand and attracts more traffic, resulting in higher income of the CP. As a real-world example, AT&T allows advertisers to sponsor video to attract more end-users to watch advertisements [2, 3], and GS Shop (Korea TV) has cooperated with SK Telecom to sponsor the traffic of its application [4].

Sponsoring data have recently been subject to modeling and analysis in the literature. The authors in [5] proposed a novel joint optimization approach of a Stackelberg contract game to characterize the market-oriented model for sponsored content market and to capture the interactions among the ISPs, CPs, and end-users. They have developed a Stackelberg game, where the ISP acts as the leader and the CPs and end-users act as the followers. In [6], the authors developed a new model to study the competition among CPs under sponsored data plans. The authors in [7] analyzed the interactions of three network entities, i.e., the end-users, the ISPs, and the CP, based on the game theory. The authors designed an effective data sponsoring control scheme using a novel dual-leader Stackelberg game model. The authors in [8, 9] investigated joint sponsored and caching content under the noncooperative game. The interactions among ISP, CP, and end-users are modeled as a three-stage Stackelberg game. In [10], the authors studied the sponsored data as the noncooperative game among ISPs. The authors derived the best response of the CP and the ISP and analyzed their implications for the sponsoring strategy. The authors in [11, 12] analyzed content sponsoring data from an economic point of view. They examined the implications of sponsored data on the CPs and the end-users and identified how the sponsored data influence the CP inequality. In [13], the authors studied the sponsorship competition among CPs in the Internet content market and demonstrated that the competitions improve the welfare of the ISP and the CP. The authors in [3] considered a sponsored data market with one ISP, one CP, and a set of end-users. They have modeled the interactions among three entities as a two-stage Stackelberg game, where the ISP and the CP act as the leaders determining the pricing and sponsoring strategies, respectively, in the first stage and the end-users act as the followers deciding on their data demand in the second stage. In [14], the authors analyzed the interaction among ISP and CPs and proposed a pricing mechanism for sponsored content that is truthful in CP’s valuation.

The sponsored content plan has been extensively investigated during the past few years; most papers focus on a simple model with a single ISP and a single CP interacting in a game-theoretic setting; few works study the completion between multiple CPs and multiple ISPs with content sponsoring plans. However, to the best of our knowledge, none of the current works includes the time constraint that makes sponsoring content more dynamic. The present paper moves toward this less explored direction. The main objective of this paper is to study a sponsored content market consists of multiple CPs, multiple ISPs, and end-users, with the time constraint using game theory.

Game theory has been used to solve many problems in communication networks [15–23]. It has been used to propose new pricing strategies for Internet services [24, 25]. Many other issues relating to wireless networks have been modeled and analyzed using game theory, such as resource allocation [26, 27], power control [28, 29], network routing [30], network caching [31], and security [32].

The contributions of this paper are as follows:(i)We present new features in the mathematical modeling that include sponsoring content, CPs revenues, and ISPs revenues with the time constraint.(ii)We model the interplay among ISPs as a function of two market parameters network access prices and quality of service; each ISP wants to maximize its utility. We formulate a competitive problem between ISP as a noncooperative game.(iii)We model the interplay between CPs as a function of three market parameters content access price, the credibility of content, and the number of sponsored content. The number of sponsored content is modeled as a function of time. We formulate a competitive problem between CPs as a noncooperative game.(iv)We analytically prove the existence and uniqueness of the Nash equilibrium in the noncooperative game between ISPs and between CPs, which means that there exists a stable state where all providers do not have an incentive to change their strategies. The best response algorithm is used to find the Nash equilibrium point.(v)Numerical analysis shows the effect of sponsoring content on providers’ policies.

This paper is organized as follows. Section 2 discusses the system model with temporality constraint. We prove the existence and uniqueness of a Nash equilibrium point in Section 3. Then, we present a numerical investigation in Section 4, and we conclude this paper in Section 5.

2. Problem Modeling

In our setting, we consider a telecommunication network with three types of actors: ISPs, CPs, and end-users. The ISP provides the network infrastructure to the end-users. The CPs provide content for end-users and sponsor a fraction of content on behalf of the end-users to lower the network access price. The sets two decision parameter network access price and quality of service (QoS) . Let and , respectively, be the content access price and the credibility of content decided by . End-users behavior is a function of CP and ISP policies (see (1)).

2.1. Demand Model

is the demand of end-users for the content provided by and transferred by which is a function of content access price , credibility of content , network access price , and QoS (see [33, 34]). This demand function is also a function of prices , credibilities , prices , and QoSs set by the opponents. The demand is decreasing with respect to and and increasing with respect to , and , , whereas it is increasing with respect to and and decreasing with respect to , and , . Then, the demand functions can be written as follows:

The parameter is the potential demand of end-users. and are two positive constants representing, respectively, the responsiveness of demand to content access price and credibility of . Moreover, and are two positive constants representing, respectively, the responsiveness of demand to network access price and QoS of .

Assumption 1. The sensitivity verifies the following:The sensitivity verifies the following:The sensitivity verifies the following:

Assumption 1 means that the effect of provider policies on its demand is greater than the effect of the policies of its opponent on its demand function [24, 35]. Assumption 1 will be used to prove the uniqueness of the Nash equilibrium.

2.2. Utility Model of the CP

The utility of can be modeled as follows:where is the fraction of content sponsored by for each subscriber. Let if full sponsoring is decided and if decides not to sponsor any content. Recall that sponsoring could be an incentive to consume more content. is the new demand for contents provided by and distributed by , which is a function of the proportion of sponsored content . The quantity reflects the change in the demand for the contents of the CP. is a nonnegative constant. is the cost to produce a unit of the credibility of content . is the transmission price of . is the sponsoring price of . The first term is the revenue of . The second term denotes the cost due to sponsorship. The third term is transmission fee results when the forwards to the end-users the demand with credibility of content . The fourth term is the cost to produce the credibility of content .

Credibility of content of is a linear function of the quality of service (QoS) and the quality content (QoC) , which is written as follows [16, 34, 36, 37]:where and are nonnegative constants. The QoS is defined as the expected delay (see [17, 34]). The QoC can be specified for a specific domain of content (e.g., video streaming).

Then, the utility of is expressed as follows:

2.3. Utility Model of the ISP

The utility function of is the difference between the revenue and the fee:

The first term is the revenue of network access. The second term is the revenue of sponsorship. The third term is the revenue of by forwarding the amount of content requests to the end-users. The fourth term is the investment of , where is a cost per unit of requested bandwidth and is the backhaul bandwidth. The QoS is defined as the expected delay computed by the Kleinrock function (see [38, 39]):this means that

Then, the utility of is given as follows:

2.4. Adding Temporality to the Model

We study in this section the impact of time on the number of sponsored content. We model the proportion of sponsored content by attaching it with the time parameter. This proportion is expressed in the following form:where represents the speed at which sponsors content for each subscriber. We notice that when , and when , .

The temporal analysis of the number of sponsored content can be performed in the networks; we consider as a discount factor, so that a monetary unit in years is worth monetary units of today. with a profit at time can predict this profit over a period ranging from as the average of the discounted revenue in this period as follows:

Similarly, we have

3. Game Analysis

Let denote the noncooperative QoC price QoS game (NQPQG), where is the index set identifying the CPs, is the content access price strategy set of , is the QoS strategy set of , and is the QoC strategy set of . We assume that the strategy spaces , , and of each are compact and convex sets with maximum and minimum constraints; for any given , we consider as strategy spaces the closed intervals , , and . Let the price vector , QoS vector , and QoC vector .

Let denote the noncooperative price QoS game (NPQG), where is the set of the ISPs, is the price strategy set of , and is the QoS strategy set of . We assume that the strategy spaces and of each are compact and convex sets with maximum and minimum constraints; for any given , we consider as strategy spaces the closed intervals and . Let the price vector and QoS vector .

3.1. Price Game

A NPQG in network access price is defined for fixed as .

Definition 1. A price vector is a Nash equilibrium of the NPQPG if

Theorem 1. For each , the game admits a unique Nash equilibrium.

Appendix A gives a proof of the above theorem.

3.2. QoS Game

A NPQG in QoS is defined for fixed as .

Definition 2. A QoS vector is a Nash equilibrium of the NPQG if

Theorem 2. For each , the game admits a unique Nash equilibrium.

Appendix B gives a proof of the above theorem.

3.3. Price Game

A NQPQG in price is defined for fixed and as .

Definition 3. A price vector is a Nash equilibrium of the NQPQG if

Theorem 3. For each and , the game admits a unique Nash equilibrium.

Appendix C gives a proof of the above theorem.

3.4. QoC Game

A NQPQG in QoC is defined for a fixed and as .

Definition 4. A QoC vector is a Nash equilibrium of the NQPQG if

Theorem 4. For each and , the game admits a unique Nash equilibrium.

Appendix D gives a proof of the above theorem.

3.5. QoS Game

A NQPQG in QoS is defined for a fixed and as .

Definition 5. A QoS vector is a Nash equilibrium of the NQPQG if

Theorem 5. For each and , the game admits a unique Nash equilibrium.

Appendix E gives a proof of the above theorem.

3.6. Learning Nash Equilibrium

In this section, based on our previous analysis, we introduce two distributed and iterative learning processes that convergence toward the Nash equilibrium point. In this algorithm, each provider observes the policy taken by its competitors in previous rounds and inputs them in its decision process to update its policy. Therefore, the best response and Nash seeking algorithms will converge to the unique equilibrium point.

The best response (BR) algorithm is known to reach equilibria for S-modular games, by exploiting the monotonicity of the best response functions. Each player fixes its desirable strategies to maximize its profit. Then, each player can observe the policy taken by its competitors in previous rounds and input them in its decision process to update its policy. Then, it becomes natural to accept the Nash equilibrium as the attractive point of the game. Yet, the best response algorithm requires perfect rationality and complete information, which is not practical for real-world applications and may increase the signaling load as well. Therefore, we propose an adaptive distributed learning framework to discover equilibria for the activation game based on the “Nash seeking algorithm” (NSA) with stochastic state-dependent payoffs for continuous actions.

The equilibrium-learning framework is an iterative process. At each iteration , the player I chooses its policy and obtains from the environment the realization of its payoff. The improvement of the strategy is based on the current observation of the realized payoff and previously chosen strategies. Hence, we say players learn to play an equilibrium if after a given number of iterations; the strategy profile converges to an equilibrium strategy.

The proposed learning framework has the following parameters: is the perturbation phase, is the growth rate, is the perturbation amplitude, and is the perturbation frequency. This procedure is repeated for the window T.

Algorithms 1 and 2 summarize the best response learning and Nash seeking algorithm steps that each player has to perform to discover its Nash equilibrium strategy.

(1)	Initialize vectors randomly;
(2)	For each , at time instant compute:
	(i) .
(3)	If , , then STOP.
(4)	Else, and go to step (2).

(1)	Data
	(i) : perturbation phase;
	(ii) : perturbation amplitude;
	(iii) : perturbation phase;
	(iv) : the growth rate;
(2)	Result. Equilibrium
(3)	Initialize vectors and randomly;
(4)	Learning Pattern. For each iteration :
(5)	Observes the payoff and estimates using
	(v) ;
(6)	Update using the following rules
	(vi) ;

such as(i) denotes a CP or ISP(ii) refers to or (iii) refers to the vector price , vector price , vector , vector , or vector (iv) refers to the policy profile price, QoS, or QoC

4. Numerical Investigations

In this section, we study the telecommunication network numerically as a noncooperative game while considering the expressions of the utility functions and using the best response algorithm. We consider a network scenario that includes two ISPs and two CPs.

Figures 1–5 show the convergence toward Nash equilibrium price, Nash equilibrium QoS, and Nash equilibrium QoC of all providers. Figures 1–5 demonstrate the existence and uniqueness of a Nash equilibrium point at which no providers can profitably deviate given the strategies of another opponent. So, our model ensures the existence of an equilibrium for keeping the economy stable and achieving economic growth.

(a)

(b)

(a)

(b)

(a)

(b)

(a)

(b)

(a)

(b)

Table 1 gives a comparison between the two algorithms proposed for the learning of the numerical results; we notice that the algorithm of best response gives the same results as the Nash seeking algorithm but in fewer iterations and in a very small time compared with a Nash seeking algorithm.

The effect of the parameter on the QoS and the QoC is shown in Figures 6 and 7. The QoS and the QoC of the proposed model are growing as increases. When increases, the demand of end-users increases, and then, the revenue of CPs increases. As a result, the CPs increase their QoS and QoC to attract more end-users.

Figures 8–10 represent the impact of sponsoring price on the content access price, the QoS, and the QoC of the two CPs. As the sponsoring price increases, the content access price increases, the QoC decreases, and the QoS decreases. When the sponsoring price is low, the CP invests more to offer better QoS, better QoC, and low content access price to induce increased demand from end-users. On the other hand, when the sponsoring price is high, the CP increases their content access price and decreases their QoS and QoC to compensate the increase in the sponsoring price.

The impact of sponsoring price on the network access price and QoS of the two ISPs is illustrated in Figures 11 and 12. Figures 11 and 12 show that the network access price decreases and the QoS increases when sponsoring price increases. The reason is that as sponsoring price increases, the revenue of sponsoring increases, which leads to a rise in the income of the ISPs. Therefore, the ISPs decrease their network access price and invest for more bandwidth to increase their QoS to attract more end-users.

Figures 13 and 14 show the influence of sponsoring content speed , respectively, on network access price and QoS equilibrium. From the two figures, we notice that when the speed of sponsoring content increases, the number of sponsored content increases and then the revenue of ISPs increases. Therefore, the ISP needs to lower the price and improve the QoS to induce increased demand from end-users.

We plot in Figures 15–17, respectively, the interplay of the speed of sponsoring content on the content access price, the QoC, and the QoS at Nash equilibrium, for both CPs that we consider in this example. On the one hand, we note that the equilibrium content access price for both CPs is increasing with respect to the speed of sponsored content. On the other hand, we indicate that the equilibrium QoS and QoC for all CPs is decreasing with the speed of sponsored content. When the speed of sponsoring content is low, the CPs invest more to offer better QoS, QoC, and an attractive content access price. However, as the speed of sponsoring content increases, the CPs choose to raise their content access price and decrease their QoS and QoC to compensate the rise in the sponsoring price.

5. Conclusion

In this paper, we study the data sponsoring problem with time constraint in the Internet market with multiple ISPs, multiple CPs, and a set of end-users. The interaction among ISPs and among CPs is investigated by using the noncooperative game. Then, we have proved the existence and uniqueness of the Nash equilibrium. This result is significant because it implies that a stable solution with suitable economic incentives in collaborative data sponsoring is feasible in the Internet paradigm. In addition, we describe a learning mechanism that allows each provider to discover accurately and rapidly its equilibrium policies. At last, we have presented a numerical investigation to validate the proposed approach, and we found that the sponsoring content has a negative effect on the strategies of CPs and positive one on the strategies of ISPs and to motivate the CPs to sponsor more content to reduce the cost of sponsorship in a long term.

Appendix

A. Proof of Theorem 1

The second derivative of the utility function is

The second derivative of the utility function is negative, and then the utility function is thus concave, which ensures existence of a Nash equilibrium in the game .

The authors use the following proposition that holds for a concave game [40]. If a concave game satisfies the dominance solvability conditionthen the game admits a unique Nash equilibrium point.

The mixed partial is written as follows:

Then,

Thus, the game admits a unique Nash equilibrium point.

B. Proof of Theorem 2

The second derivative of the utility function is

The second derivative of the utility function is negative, and then the utility function is thus concave, which ensures existence of a Nash equilibrium in the game .

In order to prove uniqueness, the authors follow [41] and define the weighted sum of user utility functions.

The pseudogradient of (B.2) is given as follows:

The Jacobian matrix J of the pseudogradient (with respect to q) is written as follows:

Thus, is a diagonal matrix with negative diagonal elements. This implies that is negative definite. Henceforth, is also negative definite, and according to Theorem 6 in [41], the weighted sum of the utility functions is diagonally strictly concave. Thus, the game admits a unique Nash equilibrium point.

C. Proof of Theorem 3

The second derivative of the utility function is

Then, the second derivative of the utility function is negative, and then the utility function is thus concave, which ensures existence of a Nash equilibrium in the game .

The authors use the following proposition that holds for a concave game [40]. If a concave game satisfies the dominance solvability conditionthen the game admits a unique Nash equilibrium point.

The mixed partial is written as follows:

Then,

Thus, the game admits a unique Nash equilibrium point.

D. Proof of Theorem 4

The second derivative of the utility function is

The second derivative of the utility function is negative, and then the utility function is thus concave, which ensures existence of a Nash equilibrium in the game .

The authors use the following proposition that holds for a concave game [40]. If a concave game satisfies the dominance solvability conditionthen the game admits a unique Nash equilibrium point.

The mixed partial is written as follows:

Then,

Thus, the game admits a unique Nash equilibrium point.

E. Proof of Theorem 5

The second derivative of the utility function is

The second derivative of the utility function is negative, and then the utility function is thus concave, which ensures existence of a Nash equilibrium in the game .

The authors use the following proposition that holds for a concave game [40]. If a concave game satisfies the dominance solvability conditionthen the game admits a unique Nash equilibrium point.

The mixed partial is written as follows:

Then,

Thus, the game admits a unique Nash equilibrium point.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest regarding the publication of this paper.

References

S. Sen, C. Joe-Wong, S. Ha, and M. Chiang, “A survey of smart data pricing: Past proposals, current plans, and future trends,” ACM, vol. 46, no. 2, pp. 1–37.
View at: Google Scholar
H. Pang, L. Gao, and L. Sun, “Joint optimization of data sponsoring and edge caching for mobile video delivery,,” in Proceedings of the 2016 IEEE Global Communications Conference (GLOBECOM), pp. 1–7, IEEE, Washington, DC, USA, March 2016.
View at: Google Scholar
Z. Xiong, S. Feng, D. Niyato, P. Wang, and Y. Zhang, “Competition and cooperation analysis for data sponsored market: a network effects model,,” in Proceedings of the 2018 IEEE Wireless Communications and Networking Conference (WCNC), pp. 1–6, IEEE, Barcelona, Spain, April 2018.
View at: Google Scholar
D. telecoms: Data monetisation strategies will help telcos capture emerging markets. [Online]. Available: https://www.developingtelecoms.com/tech/customer-management/7297-data-monetisation-strategies-will-help-telcos-capture-emerging-markets.html.
Z. Xiong, J. Zhao, D. Niyato, P. Wang, and Y. Zhang, “Design of contract-based sponsorship scheme in stackelberg game for sponsored content market,” in Proceedings of the 2019 IEEE Global Communications Conference (GLOBECOM), pp. 1–6, IEEE, Waikoloa, HI, USA, December 2019.
View at: Google Scholar
Y. Zhao, H. Su, L. Zhang, D. Wang, and K. Xu, “Variety matters: a new model for the wireless data market under sponsored data plans,” in Proceedings of the International Symposium on Quality of Service, pp. 1–10, ACM, Phoenix, ARI, USA, June 2019.
View at: Google Scholar
S. Kim, “Novel data sponsoring control scheme based on the dual-leader stackelberg game model,” Mobile Information Systems, vol. 2019, Article ID 1231574, 10 pages, 2019.
View at: Publisher Site | Google Scholar
Z. Xiong, S. Feng, D. Niyato, P. Wang, A. Leshem, and Y. Zhang, “Game theoretic analysis for joint sponsored and edge caching content service market,,” in Proceedings of the 2018 IEEE Global Communications Conference (GLOBECOM), pp. 1–7, IEEE, Abu Dhabi, UAE, December 2018.
View at: Google Scholar
Z. Xiong, S. Feng, D. Niyato, P. Wang, A. Leshem, and Z. Han, “Joint sponsored and edge caching content service market: a game-theoretic approach,” IEEE Transactions on Wireless Communications, vol. 18, no. 2, pp. 1166–1181.
View at: Google Scholar
A. Satybaldy and C. Joo, “Content sponsoring with inter-ISP transit cost,” Game Theory for Networking Applications, Springer International Publishing, Berlin, Germany, pp. 57–68.
View at: Google Scholar
C. Joe-Wong, S. Sen, and S. Ha, “Sponsoring mobile data: analyzing the impact on internet stakeholders,” IEEE/ACM Transactions on Networking’s, vol. 26, no. 3, pp. 1179–1192.
View at: Google Scholar
Z. Xiong, S. Feng, D. Niyato, P. Wang, and Y. Zhang, “Economic analysis of network effects on sponsored content: a hierarchical game theoretic approach,” in Proceedings of the GLOBECOM 2017-2017 IEEE Global Communications Conference, pp. 1–6, IEEE, Singapore, December 2017.
View at: Google Scholar
R. T. Ma, “Subsidization competition: vitalizing the neutral internet,,” in Proceedings of the 10th ACM International on Conference on Emerging Networking Experiments and Technologies, pp. 283–294, Sydney, Australia, December 2014.
View at: Google Scholar
L. Zhang, W. Wu, and D. Wang, “Time-dependent sponsored data plan for wireless data traffic market,” in Proceedings of the IEEE INFOCOM 2016-The 35th Annual IEEE International Conference on Computer Communications, pp. 1–9, IEEE, San Francisco, CA, USA, April 2016.
View at: Google Scholar
Y. Zhang and M. Guizani, Game Theory for Wireless Communications and Networking, CRC Press, Boca Raton, FL, USA, 2011.
H. Garmani, M. Baslam, and M. Jourhmane, “Analysis of competition between CPs fronting advertisers,” International Journal of Informatics and Communication Technology (IJ-ICT), vol. 117, pp. 53–66.
View at: Google Scholar
M. Outanoute, H. Garmani, M. Baslam, R. El Ayachi, and B. Bouikhalene, “A non-cooperative game analysis of competition between content providers in the internet market,” International Journal of Business Data Communications and Networking, vol. 15, no. 1, pp. 88–104.
View at: Google Scholar
D. Papies, F. Eggers, and N. Wlömert, “Music for free? How free ad-funded downloads affect consumer choice,” Journal of the Academy of Marketing Science, vol. 39, no. 5, pp. 777–794, 2011.
View at: Publisher Site | Google Scholar
S. Handouf and E. Sabir, “Strategic availability and cost-effective UAV-based flying access networks: S-modular game analysis,” Mobile Information Systems, vol. 2019, Article ID 4897171, 11 pages, 2019.
View at: Publisher Site | Google Scholar
M. Baslam, L. Echabbi, R. El-Azouzi, and E. Sabir, “Joint price and QoS market share game with adversarial service providers and migrating customers,” in Proceedings of the Game Theory for Networks: 2nd International ICST Conference, GAMENETS 2011, Shanghai, China, April 2011.
View at: Google Scholar
M. El Amrani, H. Garmani, M. Baslam, B. Minaoui, and R. El Ayachi, “Cournot game of ISP under net neutrality,” International Journal of Control and Automation, vol. 11, no. 7, p. 16, 2018.
View at: Google Scholar
B. Gu, X. Yang, Z. Lin, W. Hu, M. Alazab, and R. Kharel, “Multi-agent actor-critic network-based incentive mechanism for mobile crowdsensing in industrial systems,” IEEE Transactions on Industrial Informatics, vol. 99, 2020.
View at: Google Scholar
R. Jain and R. Kannan, Eds.in Revised Selected Papers, pp. 642–657, Springer, Berlin, Heidelberg, 2012.
D. Ait Omar, H. Garmani, M. El Amrani, M. Baslam, and M. Fakir, “A customer confusion environment in telecommunication networks: analysis and policy impact,” International Journal of Cooperative Information Systems, vol. 28, no. 2, Article ID 1930002, 2019.
View at: Google Scholar
S. Shakkottai and R. Srikant, “Economics of network pricing with multiple ISPs,” IEEE/ACM Transactions On Networking, vol. 14, no. 6, pp. 1233–1245, 2006.
View at: Publisher Site | Google Scholar
A. A. Lazar, A. Orda, and D. E. Pendarakis, “Virtual path bandwidth allocation in multiuser networks,” IEEE/ACM Transactions on Networking, vol. 5, no. 6, pp. 861–871, 1997.
View at: Publisher Site | Google Scholar
Z. Zhou, B. Wang, B. Gu et al., “Time-dependent pricing for bandwidth slicing under information asymmetry and price discrimination,” IEEE Transactions on Communications, vol. 99, 2020.
View at: Google Scholar
E. E. Tsiropoulou, T. Kastrinogiannis, and S. Papavassiliou, “Uplink power control in qos-aware multi-service cdma wireless networks,” Journal of Communications, vol. 4, no. 9, pp. 654–668, 2009.
View at: Publisher Site | Google Scholar
E. E. Tsiropoulou, P. Vamvakas, and S. Papavassiliou, “Energy efficient uplink joint resource allocation non-cooperative game with pricing,” in Proceedings of the 2012 IEEE Wireless Communications and Networking Conference (WCNC), pp. 2352–2356, Sydney, Australia, May 2012.
View at: Google Scholar
T. Roughgarden, Selfish Routing and the Price of Anarchy, vol. 174, MIT press Cambridge, Cambridge, MA, USA, 2005.
H. Garmani, M. Baslam, and M. Jourhmane, “Caching games between ISP in information centric network,” International Journal of Control and Automation, vol. 11, no. 4, pp. 125–142, 2018.
View at: Google Scholar
S. Roy, C. Ellis, S. Shiva, D. Dasgupta, V. Shandilya, and Q. Wu, “A survey of game theory as applied to network security,” in Proceedings of the 2010 43rd Hawaii International Conference on System Sciences, pp. 1–10, IEEE, Honolulu, HI, USA, January 2010.
View at: Google Scholar
D. A. Omar, H. Garmani, M. El Amrani, M. Baslam, and M. Fakir, “Analysis of bargaining game policy in the internet content distribution chain,” International Journal of Mobile Computing and Multimedia Communications, vol. 10, no. 3, pp. 47–73, 2019.
View at: Google Scholar
H. Garmani, M. El Amrani, M. Baslam, R. El Ayachi, and M. Jourhmane, “A stackelberg game-based approach for interactions among internet service providers and content providers,” NETNOMICS: Economic Research and Electronic Networking, vol. 20, no. 2, pp. 101–128, 2019.
View at: Google Scholar
H. Garmani, D. Ait Omar, M. El Amrani, M. Baslam, and M. Jourhmane, “Towards a predictive analysis of UAV-based flying base station decisions,” International Journal of Business Data Communications and Networking, vol. 16, no. 2, pp. 20–52, 2020.
View at: Google Scholar
D. A. Omar, M. El Amrani, and M. Baslam, “Analysis of a dynamics duopoly game with two content providers,” Chaos Solitons & Fractals, vol. 131, Article ID 109466, 2020.
View at: Google Scholar
H. Garmani, D. A. Omar, M. El Amrani, M. Baslam, and M. Jourhmane, “A dynamic duopoly game with content providers’ bounded rationality,” International Journal of Bifurcation and Chaos, vol. 30, no. 7, Article ID 2050095, 2020.
View at: Google Scholar
H. Garmani, D. Ait Omar, M. Baslam, and M. El Kamili, “UAV-based ubiquitous network access: a game theoretic analysis,” in Proceedings of the 2019 IEEE Global Communications Conference (GLOBECOM), pp. 1–6, IEEE, Waikoloa, HI, USA, December 2019.
View at: Google Scholar
H. Garmani, M. Outanoute, M. Baslam, and M. Jourhmane, “New competition-based approach for caching popular content in ICN,” in Networked Systems, A. Podelski and F. Taïani, Eds., vol. 11028, pp. 286–300, Springer International Publishing, Berlin, Germany, 2018.
View at: Google Scholar
S. Lasaulce, M. Debbah, and E. Altman, “Methodologies for analyzing equilibria in wireless games,” IEEE Signal Processing Magazine, vol. 26, no. 5, pp. 41–52, 2009.
View at: Publisher Site | Google Scholar
J. B. Rosen, “Existence and uniqueness of equilibrium points for concave N-person games,” Econometrica, vol. 33, no. 3, pp. 520–534, 1965.
View at: Publisher Site | Google Scholar

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Copyright © 2021 Mohamed El Amrani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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