Optimizing Social Welfare for Network Bargaining Games in the Face of Instability, Greed and Idealism

Abstract

Stable and balanced outcomes of network bargaining games have been investigated recently, but the existence of such outcomes requires that the linear program relaxation of a certain maximum matching problem have integral optimal solution. We propose an alternative model for network bargaining games in which each edge acts as a player, who proposes how to split the weight of the edge among the two incident nodes. Based on the proposals made by all edges, a selection process will return a set of accepted proposals, subject to node capacities. An edge receives a commission if its proposal is accepted. The social welfare can be measured by the weight of the matching returned. The node users exhibit two characteristics of human nature: greed and idealism. We define these notions formally and show that the distributed protocol by Kanoria et al. can be modified to be run by the edge players such that the configuration of proposals will converge to a pure Nash Equilibrium, without the integrality gap assumption. Moreover, after the nodes have made their greedy and idealistic choices, the remaining ambiguous choices can be resolved in a way such that there exists a Nash Equilibrium that will not hurt the social welfare too much.

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Notes

  1. 1.

    In case x + y < wij the remaining amount is lost and not gained by anyone.

  2. 2.

    The actual gain of an agent could be scaled according to the weight we, but this will not affect the Nash Equilibrium.

  3. 3.

    As a side note, we remark that our results implies that under the unique integral LP optimum assumption, there will be no ambiguous edges left.

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Correspondence to T.-H. Hubert Chan.

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The conference version of the paper has appeared in the European Symposium on Algorithms 2012. This research was partially funded by Hong Kong RGC under the contract 17202715.

This work was done while the author was at the University of Hong Kong.

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Chan, TH.H., Chen, F. & Ning, L. Optimizing Social Welfare for Network Bargaining Games in the Face of Instability, Greed and Idealism. Theory Comput Syst 64, 999–1027 (2020). https://doi.org/10.1007/s00224-019-09958-4

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Keywords

  • Network bargaining game
  • Nash equilibrium
  • Optimizing social welfare
  • Unstable outcome
  • Greed and idealism