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Implementing Efficient Graphs in Connection Networks

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  • Ruben Juarez

    (Department of Economics, University of Hawaii at Manoa)

  • Rajnish Kumar

    (Department of Economics, Louisiana State University)

Abstract

We consider the problem of sharing the cost of a network that meets the connection demands of a set of agents. The agents simultaneously choose paths in the network connecting their demand nodes. A mechanism splits the total cost of the network formed among the participants. We introduce two new properties of implementation. The first property, Pareto Nash Implementation (PNI), requires that the ecient outcome always be implemented in a Nash equilibrium and that the efficient outcome Pareto dominates any other Nash equilibrium. The average cost mechanism (AC) and other asymmetric variations are the only rules that meet PNI. These mechanisms are also characterized under Strong Nash Implementation. The second property, Weakly Pareto Nash Implementation (WPNI), requires that the least inefficient equilibrium Pareto dominates any other equilibrium. The egalitarian mechanism (EG), a variation of AC that meets individual rationality, and other asymmetric mechanisms are the only rules that meet WPNI and Individual Rationality. PNI and WPNI provide the first economic justification of the Price of Stability (PoS), a seemingly natural measure in the computer science literature but one not easily embraced in economics. EG minimizes the PoS across all individually rational mechanisms.

Suggested Citation

  • Ruben Juarez & Rajnish Kumar, 2012. "Implementing Efficient Graphs in Connection Networks," Working Papers 201203, University of Hawaii at Manoa, Department of Economics.
    • Handle: RePEc:hai:wpaper:201203
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    File URL: http://www.economics.hawaii.edu/research/workingpapers/WP_12-3.pdf
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    Cited by:

    1. Ruben Juarez & Michael Wu, 2019. "Routing-Proofness in Congestion-Prone Networks," Games, MDPI, vol. 10(2), pages 1-18, April.
    2. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    3. Ruben Juarez & Kohei Nitta, 2017. "Profit-Sharing and Implementation of Efficient Outcomes," Working Papers 201702, University of Hawaii at Manoa, Department of Economics.
    4. Han, Lining & Juarez, Ruben, 2018. "Free intermediation in resource transmission," Games and Economic Behavior, Elsevier, vol. 111(C), pages 75-84.
    5. Jens Leth Hougaard & Mich Tvede, 2020. "Implementation of Optimal Connection Networks," IFRO Working Paper 2020/06, University of Copenhagen, Department of Food and Resource Economics.
    6. Hougaard, Jens Leth & Tvede, Mich, 2022. "Trouble comes in threes: Core stability in minimum cost connection networks," European Journal of Operational Research, Elsevier, vol. 297(1), pages 319-324.
    7. Ruben Juarez & Kohei Nitta & Miguel Vargas, 2020. "Profit-sharing and efficient time allocation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 817-846, October.
    8. Jung S. You & Ruben Juarez, 2021. "Incentive-compatible simple mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1569-1589, June.
    9. Bhardwaj, Bhavook & Kumar, Rajnish & Ortega, Josué, 2020. "Fairness and efficiency in cake-cutting with single-peaked preferences," Economics Letters, Elsevier, vol. 190(C).
    10. Hougaard, Jens Leth & Tvede, Mich, 2015. "Minimum cost connection networks: Truth-telling and implementation," Journal of Economic Theory, Elsevier, vol. 157(C), pages 76-99.
    11. Jens Leth Hougaard & Mich Tvede, 2020. "Trouble Comes in Threes: Core stability in Minimum Cost Connection Networks," IFRO Working Paper 2020/07, University of Copenhagen, Department of Food and Resource Economics.
    12. Juarez, Ruben & Nitta, Kohei & Vargas, Miguel, 2021. "Coalitional efficient profit-sharing," Economics Letters, Elsevier, vol. 204(C).
    13. Andreas Darmann & Christian Klamler & Ulrich Pferschy, 2015. "Sharing the Cost of a Path," Studies in Microeconomics, , vol. 3(1), pages 1-12, June.
    14. Kristal K. Trejo & Ruben Juarez & Julio B. Clempner & Alexander S. Poznyak, 2023. "Non-Cooperative Bargaining with Unsophisticated Agents," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 937-974, March.
    15. Sinan Ertemel & Rajnish Kumar, 2018. "Proportional rules for state contingent claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 229-246, March.
    16. María Gómez-Rúa & Juan Vidal-Puga, 2017. "A monotonic and merge-proof rule in minimum cost spanning tree situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 813-826, March.
    17. Jens Leth Hougaard & Mich Tvede, 2010. "Strategyproof Nash Equilibria in Minimum Cost Spanning Tree Models," MSAP Working Paper Series 01_2010, University of Copenhagen, Department of Food and Resource Economics.
    18. Julio R. Fernández & Inés Gallego & Andrés Jiménez-Losada & Manuel Ordóñez, 2022. "Cost-allocation problems for fuzzy agents in a fixed-tree network," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 531-551, December.
    19. Ruben Juarez & Jung S. You, 2019. "Optimality of the uniform rule under single-peaked preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 27-36, May.
    20. Hougaard, Jens Leth & Tvede, Mich, 2012. "Truth-telling and Nash equilibria in minimum cost spanning tree models," European Journal of Operational Research, Elsevier, vol. 222(3), pages 566-570.

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    More about this item

    Keywords

    Cost-sharing; Implementation; Average Cost; Egalitarian Mechanism;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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