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Expected Values for Variable Network Games

Author

Listed:
  • Subhadip Chakrabarti
  • Loyimee Gogoi
  • Robert P Gilles
  • Surajit Borkotokey
  • Rajnish Kumar

Abstract

A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting. We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payoff to the players in a variable network game. We establish two axiomatizations of the Expected Myerson Value, originally formulated and proven on the class of communication situations, based on the well-established component balance, equal bargaining power and balanced contributions properties. Furthermore, we extend an established axiomatization of the Position Value based on the balanced link contribution property to the Expected Position Value.

Suggested Citation

  • Subhadip Chakrabarti & Loyimee Gogoi & Robert P Gilles & Surajit Borkotokey & Rajnish Kumar, 2021. "Expected Values for Variable Network Games," Papers 2108.07047, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:2108.07047
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    References listed on IDEAS

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    1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
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    7. Borkotokey, Surajit & Chakrabarti, Subhadip & Gilles, Robert P. & Gogoi, Loyimee & Kumar, Rajnish, 2021. "Probabilistic network values," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 169-180.
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