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Weighted position value for Network games

Author

Listed:
  • Niharika Kakoty
  • Surajit Borkotokey
  • Rajnish Kumar
  • Abhijit Bora
Abstract
In Network games under cooperative framework, the position value is a link based allocation rule. It is obtained from the Shapley value of an associated cooperative game where the links of the network are considered players. The Shapley value of each of the links is then divided equally among the players who form those links. The inherent assumption is that the value is indifferent to the weights of the players in the network. Depending on how much central a player is in the network, or the ability of making links with other players etc., for example, players can be considered to have weights. Thus, in such situations, dividing the Shapley value equally among the players can be an over-simplistic notion. We propose a generalised version of the position value: the weighted position value that allocates the Shapley shares proportional to the players' weights. These weights of the players are exogenously given. We provide two axiomatic characterizations of our value. Finally, a bidding mechanism is formulated to show that any sub-game perfect equilibrium (SPE) of this mechanism coincides with the weighted position value.

Suggested Citation

  • Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2023. "Weighted position value for Network games," Papers 2308.03494, arXiv.org.
    • Handle: RePEc:arx:papers:2308.03494
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    References listed on IDEAS

    as
    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.
    2. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    3. Ghintran, Amandine, 2013. "Weighted position values," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 157-163.
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    8. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
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    10. Jean-François Caulier & Alexandre Skoda & Emily Tanimura, 2017. "Allocation Rules for Networks Inspired by Cooperative Game-Theory," Revue d'économie politique, Dalloz, vol. 127(4), pages 517-558.
    11. Jean-François Caulier & Alexandre Skoda & Emily Tanimura, 2017. "Allocation Rules for Networks Inspired by Cooperative Game-Theory," Post-Print hal-03225796, HAL.
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    13. Jean-François Caulier & Alexandre Skoda & Emily Tanimura, 2017. "Allocation Rules for Networks Inspired by Cooperative Game-Theory," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03225796, HAL.
    14. Marco Slikker, 2005. "Link Monotonic Allocation Schemes," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 473-489.
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