Game-Theoretic Aspects of Designing Hyperlink Structures

  • Nicole Immorlica
  • Kamal Jain
  • Mohammad Mahdian
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)


We study the problem of designing the hyperlink structure between the web pages of a web site in order to maximize the revenue generated from the traffic on the web site. We show this problem is equivalent to the well-studied setting of infinite horizon discounted Markov Decision Processes (MDPs). Thus existing results from that literature imply the existence of polynomial-time algorithms for finding the optimal hyperlink structure, as well as a linear program to describe the optimal structure. We use a similar linear program to address our problem (and, by extension all infinite horizon discounted MDPs) from the perspective of cooperative game theory: if each web page is controlled by an autonomous agent, is it possible to give the individuals and coalitions incentive to cooperate and build the optimal hyperlink design? We study this question in the settings of transferrable utility (TU) and non-transferrable utility (NTU) games. In the TU setting, we use linear programming duality to show that the core of the game is non-empty and that the optimal structure is in the core. For the NTU setting, we show that if we allow “mixed” strategies, the core of the game is non-empty, but there are examples that show that the core can be highly inefficient.


Random Walk Cooperative Game Markov Decision Process Total Revenue Cooperative Game Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Badasyan, N., Chakrabarti, S.: Private peering among internet backbone providers. Virginia Tech., mimeo (2003)Google Scholar
  2. 2.
    Bondareva, O.N.: Some applications of linear programming to cooperative games. Problemy Kibernetiki 10, 119–139 (1963)MathSciNetGoogle Scholar
  3. 3.
    Furusawa, T., Konishi, H.: Free trade networks. Yokohama National University and Boston College, mimeo (2002)Google Scholar
  4. 4.
    Granovetter, M.: Getting a job: a study of contacts and careers, 2nd edn. University of Chicago Press (1995)Google Scholar
  5. 5.
    Jackson, M.O.: A survey of models of network formation: Stability and efficiency. In: Demange, G., Wooders, M. (eds.) Group Formation in Economics; Networks, Clubs and Coalitions, ch. 1, pp. 11–57. Cambridge University Press, Cambridge (2004)Google Scholar
  6. 6.
    Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (1994)zbMATHGoogle Scholar
  7. 7.
    Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley-Interscience, Chichester (1994)zbMATHGoogle Scholar
  8. 8.
    Scarf, H.E.: The core of an n-person game. Econometrica 35, 50–69 (1967)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Shapley, L.S.: On balanced sets and cores. Naval Research Logistics Quarterly 14, 453–460 (1967)CrossRefGoogle Scholar
  10. 10.
    von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior, ch. 13, pp. 257–275. John Wiley and Sons, Chichester (1944)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nicole Immorlica
    • 1
  • Kamal Jain
    • 1
  • Mohammad Mahdian
    • 1
  1. 1.Microsoft ResearchRedmond

Personalised recommendations