A gentle introduction to strategic networks formation

  • if nobody wants to sewer a link included in G
  • if one player wants to include a link, the other player does not want (otherwise it should be included!)
  • 𝙘 < 𝛅-𝛅², cost to form a link is very low so the complete network is efficient
  • 𝛅-𝛅²<𝙘<𝛅+(n-2)*𝛅²/2, the cost is medium and the star network is efficient
  • 𝛅+(n-2)*𝛅²/2<𝙘, the cost is high so the empty network is efficient
  • for a low cost 𝙘 < 𝛅-𝛅², complete network is pairwise stable
  • for a medium/low cost 𝛅-𝛅²< 𝙘 < 𝛅, star network is pairwise stable (but other networks can be pairwise stable too)
  • for a medium/high cost 𝛅 < 𝙘 < 𝛅 + (n-2)𝛅²/2, the cost does not justify bringing only one person in the network with the link so forming links tends to bring in more people to get indirect benefits to compensate cost. Additionally, every agent forms a link only with agents bringing other connection with them. This is actually the case where a star network is efficient but not pairwise stable.
  • 𝛅 + (n-2)𝛅²/2< 𝙘, the empty network is pairwise stable

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Juna Salviati

Juna Salviati

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Full-time Human-computer interpreter. Opinions are my own.