A Non-Cooperative Game Analysis of Competition between Content Providers in the Internet Market

A Non-Cooperative Game Analysis of Competition between Content Providers in the Internet Market

M'hamed Outanoute (LIRST Laboratory, Sultan Moulay Slimane University, Beni Mellal, Morocco), Hamid Garmani (TIAD Laboratory, Sultan Moulay Slimane University, Beni Mellal, Morocco), Mohamed Baslam (TIAD Laboratory, Sultan Moulay Slimane University, Beni Mellal, Morocco), Rachid El Ayachi (TIAD Laboratory, Sultan Moulay Slimane University, Beni Mellal, Morocco) and Belaid Bouikhalene (LIRST Laboratory, Sultan Moulay Slimane University, Beni Mellal, Morocco)
DOI: 10.4018/IJBDCN.2019010106

Abstract

In internet market, content providers (CPs) continue to play a primordial role in the process of accessing different types of data. Competition in this area is fierce; customers are looking for providers that offer them good content (credibility of content and quality of service) with a reasonable price. In this work, the authors analyze this competition between CPs and the economic influence of their strategies on the market. The authors formulate their problem as a non-cooperative game among multiple CPs for the same market. Through a detailed analysis, the researchers prove uniqueness of a pure Nash Equilibrium (NE). Furthermore, a fully distributed algorithm to converge on the NE point is presented. In order to quantify how efficient the NE point is, a detailed analysis of the Price of Anarchy (PoA) is adopted to ensure the performance of the system at equilibrium. Finally, an extensive numerical study is provided to describe the interactions between CPs and to point out the importance of quality of service (QoS) and credibility of content in the market.
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Introduction

The current internet has enabled numerous distributed applications and services. However, providers generally face many challenges in determining technical and economic solutions to providing services (Wolf et al., 2012). Key challenges are how to price and bill these services and how to establish economic relationships with other providers that are necessary to provide end-to-end services. Equilibrium models for the internet generally assume basic economic relationships and consider price as the only factor that affects users demand (Altman, Caron, & Kesidis, 2010; Laffont, Marcus, Rey, & Tirole, 2003; Zhang, Nabipay, Odlyzko, & Guerin, 2010). However, in new paradigms for the internet and even in the case of supply chain networks, price is not the only factor. Quality of Service (QoS), i.e., the ability to provide different priorities to applications, users, or data flows, comes into play (Hu & Qiang, 2013; Nagurney & Li, 2014; Nagurney, Li, & Nagurney, 2013a; Nagurney, Li, Wolf, & Saberi, 2013b; Nagurney & Wolf, 2014).

The contribution in this work is to expand the study on the internet domain by adding a utility model on income from content providers (CPs). CPs can be social networks, internet search engines, or any other websites. In this framework, a model of competition between CPs is proposed. This model is based on the parameters of price and credibility of content that is used to measure the effectiveness of content provided by the CP. Credibility is a function that depends on the QoS and quality of content (QoC).

Customer behavior is modeled by the function demand that depends on providers policies. The authors use game theory to study the behavior of CPs in the internet. Then they study the impact of CPs decisions on customers and other CPs. The researchers focus their studies on the non-cooperative games in terms of stable solutions, which are the pure strategy Nash Equilibria (NE) of the game. Mixed strategy equilibria are not considered, because the environment requires a concrete strategy rather than a randomized strategy, which would be the result of a mixed strategy. Hence, when using the term Nash equilibrium it means pure strategy exact NE unless mentioned otherwise.

CPs may be faced with the question of “how to choose in what content to specialize” (Altman, 2012). Altman (2012) considers several CPs that are faced with a similar problem and study the impact of their decisions on each other using a game theoretic approach. The author shows that the problem of selecting the content type is equivalent to a congestion game.

Jiménez et al. (2012) have studied game problems involving two types of CPs: one that corresponds to independent CPs, and one that correspond to CPs that have exclusive agreements with Internet Service Providers (ISPs). The cost for the internet users, who are subscribers of some ISP of fetching content from an independent CP or from a CP that has an exclusive agreement with another ISP, was assumed larger than for fetching it from the CP that has an exclusive agreement with their own ISP.

Wu et al. (2011) consider a Stackelberg game, where the CP decides reward first, and after that, the peers decide amount of capacity. The CP rewards the peers based on the amount of upload capacity they contribute. From CP point of view, it aims at minimizing its total cost, i.e., the cost of uploading and the cost of rewarding the peers. The utility of a peer is the reward it receives, minus its cost of upload contribution.

The rest of the paper is organized as follows: in section 2, the problem model is described. In section 3, the model described in latest section is formulated as a non-cooperative game. The authors present numerical results in section 4 and conclude their work in section 5.

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