Related Work Description of the Problem Our Work Game-theoretic aspects of link placement in the WorldWide Web George Kouroupas kouroupa@ aueb .gr Katia Papakonstantinopoulou katia@di. uoa .gr AUEB � Theory Tea November 5, 2010 George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Motivation Web models (important applications, eg. web search, advertising) The role of modern search engines (web structure, scaling) Game-theoretic aspect (users’ behavior: competition for reputation, traffic) PageRank George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Our work A game-theoretic web model that captures the selfish nature of web page authors. Joint work with M. Sideri, E. Koutsoupias, V. Markakis and C. Papadimitriou. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Our work A game-theoretic web model that captures the selfish nature of web page authors. Joint work with M. Sideri, E. Koutsoupias, V. Markakis and C. Papadimitriou. Goals: Explain the evolution of today’s web using graph theory and game theory, and taking into account the modern incentives such as PageRank and advertising, and Study whether it is possible to give the authors incentives to build a web of high total welfare. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Outline 1 Related Work 2 Description of the Problem 3 Our Work George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work (summarized) About PageRank: The effect of new links on Google PageRank [1] Based on graph theory and game theory: Network Formation and the Structure of the Commercial World Wide Web [2] Network Reputation Games [3] (and also: On the alpha-Sensitivity of Nash Equilibria in PageRank-Based Network Reputation Games [4]) Game-Theoretic Aspects of Designing Hyperlink Structures [5] George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work PageRank (definition) The PageRank of page i is: PR ( i ) = 1 − d PR ( j ) � + d N L ( j ) j ∈ B i where N : total number of pages, B i : set of backlinks of i , L ( j ): number of outgoing links of page j , d: damping factor. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work PageRank - Web graph Figure: Example of PageRank computation. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work PageRank as an Incentive on the WWW Figure: The relation between link structure and PageRank. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work: The effect of new links on PageRank K. Avrachenkov and N. Litvak study to what extent a page can control its PageRank . Main Results: Simple conditions that show whether new links bring benefits to a web page and its neighbors, in terms of PageRank. There exists an optimal linking strategy. A web page benefits from links inside its web community. Irrelevant links penalize the web pages and their web communities. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work The web graph The link structure forms communities and raises reputation issues. Thus we can see the web as the outcome (equilibrium) of a game among the web authors. Which game is it? George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work: Formation & Structure of the Commercial WorldWide Web Z. Katona and M. Sarvary study a game in which heterogeneous web pages establish reference and/or purchase advertising links. Main results: George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work: Formation & Structure of the Commercial WorldWide Web Z. Katona and M. Sarvary study a game in which heterogeneous web pages establish reference and/or purchase advertising links. Main results: Their equilibrium structure (indegree/outdegree distributions) matches the empirical structure of the www very well. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work: Formation & Structure of the Commercial WorldWide Web Z. Katona and M. Sarvary study a game in which heterogeneous web pages establish reference and/or purchase advertising links. Main results: Their equilibrium structure (indegree/outdegree distributions) matches the empirical structure of the www very well. Higher content sites: establish more reference links purchase more advertising links ( ⇒ strong positive correlation between a site’s content and the number of its inlinks) sell less advertising links, and at higher prices. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work: Formation & Structure of the Commercial WorldWide Web Z. Katona and M. Sarvary study a game in which heterogeneous web pages establish reference and/or purchase advertising links. Main results: Their equilibrium structure (indegree/outdegree distributions) matches the empirical structure of the www very well. Higher content sites: establish more reference links purchase more advertising links ( ⇒ strong positive correlation between a site’s content and the number of its inlinks) sell less advertising links, and at higher prices. High content sites earn revenue from the sales of content, while low content ones from the sales of traffic. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work: Network Reputation Games J. Hopcroft and D. Sheldon study a game in which authors may place reference links but have no control over their inlinks. They consider PageRank and Hitting time . Main results: Considering hitting time, any directed graph is a Nash eq. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work: Network Reputation Games J. Hopcroft and D. Sheldon study a game in which authors may place reference links but have no control over their inlinks. They consider PageRank and Hitting time . Main results: Considering hitting time, any directed graph is a Nash eq. Considering PageRank, unless the links are delicately balanced, some page can increase its PageRank by replacing all its links with a single one to a carefully chosen page, every equilibrium has a core in which all edges are bidirectional, in a restricted setting, equilibria are characterized by simple properties (mainly edgewise walk-regularity), they demonstrate surprising algebraic properties of equilibria, relating eigenvalues and their multiplicities to graph structure. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work: Game-Theoretic Design of Hyperlink Structures N. Immorlica, K. Jain and M. Mahdian study the design of hyperlink structure among the pages of a web site, in order to maximize the revenue generated from the traffic on the web site. Main results: George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work: Game-Theoretic Design of Hyperlink Structures N. Immorlica, K. Jain and M. Mahdian study the design of hyperlink structure among the pages of a web site, in order to maximize the revenue generated from the traffic on the web site. Main results: Problem equivalent to Markov Decision Processes � optimal link structure: described by a linear program and exist polynomial-time algorithms for finding it. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
Related Work Description of the Problem Our Work Related work: Game-Theoretic Design of Hyperlink Structures N. Immorlica, K. Jain and M. Mahdian study the design of hyperlink structure among the pages of a web site, in order to maximize the revenue generated from the traffic on the web site. Main results: Problem equivalent to Markov Decision Processes � optimal link structure: described by a linear program and exist polynomial-time algorithms for finding it. Using the framework of cooperative game theory , they study whether it is possible to give the authors and coalitions incentive to cooperate and build the optimal hyperlink design. George Kouroupas, Katia Papakonstantinopoulou Game-theoretic aspects of link placement in the WWW
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