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Aggregate play and welfare in strategic interactions on networks

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  • Chadha, Karan N.
  • Kulkarni, Ankur A.

Abstract

In recent work by Bramoullé and Kranton (2007), a model for the provision of public goods on a network was presented and relations between equilibria of such a game and properties of the network were established. This model was further extended to include games with imperfect substitutability in Bramoullé et al. (2014). The vast multiplicity of equilibria in such games along with the dramatic changes in equilibria with small changes in network structure, makes it challenging for a system planner to estimate the maximum social welfare of such a game or to devise interventions that enhance this welfare. Our main results address this challenge by providing for arbitrary networks, close approximations to the maximum social welfare and the maximum aggregate play in terms of only network characteristics such as the maximum degree and independence number. For the special case when the underlying network is a tree, we derive formulas which use only the number of nodes and their degrees. These results allow a system planner to assess aggregate outcomes and design interventions for the game, directly from the underlying graph structure, without enumerating all equilibria of the game, thereby significantly simplifying the planner’s problem. A part of our results can be viewed as a logical extension of Pandit and Kulkarni (2018) where the maximum weighted aggregate effort of the model in Bramoullé and Kranton (2007) was characterized as the weighted independence number of the graph.

Suggested Citation

  • Chadha, Karan N. & Kulkarni, Ankur A., 2020. "Aggregate play and welfare in strategic interactions on networks," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 72-86.
    • Handle: RePEc:eee:mateco:v:88:y:2020:i:c:p:72-86
    DOI: 10.1016/j.jmateco.2020.02.006
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    References listed on IDEAS

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    1. Yann Bramoull? & Rachel Kranton & Martin D'Amours, 2014. "Strategic Interaction and Networks," American Economic Review, American Economic Association, vol. 104(3), pages 898-930, March.
    2. Pandit, Parthe & Kulkarni, Ankur A., 2018. "Refinement of the equilibrium of public goods games over networks: Efficiency and effort of specialized equilibria," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 125-139.
    3. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
    4. Bramoulle, Yann & Kranton, Rachel, 2007. "Public goods in networks," Journal of Economic Theory, Elsevier, vol. 135(1), pages 478-494, July.
    5. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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    Cited by:

    1. Pathak, Shraddha & Kulkarni, Ankur A., 2025. "A scalable Bayesian persuasion framework for epidemic containment on heterogeneous networks," Journal of Mathematical Economics, Elsevier, vol. 119(C).
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    4. Trivikram Dokka Venkata Satyanaraya & Herve Moulin & Indrajit Ray & Sonali Sen Gupta, 2020. "Equilibrium Design by Coarse Correlation in Quadratic Games," Working Papers 301895429, Lancaster University Management School, Economics Department.

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