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Axiomatic and strategic justifications for the constrained equal benefits rule in the airport problem

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  • Hu, Cheng-Cheng
  • Tsay, Min-Hung
  • Yeh, Chun-Hsien

Abstract

We consider the “airport problem”, which is concerned with sharing the cost of an airstrip among agents who need airstrips of different lengths. We investigate the implications of two properties, Left-endpoint Subtraction (LS) bilateral consistency and LS converse consistency, in the airport problem. First, on the basis of the two properties, we characterize the constrained equal benefits rule, which equalizes agentsʼ benefits subject to no one receiving a subsidy. Second, we introduce a 2-stage extensive form game that exploits LS bilateral consistency and LS converse consistency. We show that there is a unique subgame perfect equilibrium outcome of the game and moreover, it is the allocation chosen by the constrained equal benefits rule.

Suggested Citation

  • Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2012. "Axiomatic and strategic justifications for the constrained equal benefits rule in the airport problem," Games and Economic Behavior, Elsevier, vol. 75(1), pages 185-197.
    • Handle: RePEc:eee:gamebe:v:75:y:2012:i:1:p:185-197
    DOI: 10.1016/j.geb.2011.12.005
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    Citations

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    Cited by:

    1. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    2. Rick K. Acosta-Vega & Encarnaci'on Algaba & Joaqu'in S'anchez-Soriano, 2022. "On proportionality in multi-issue problems with crossed claims," Papers 2202.09877, arXiv.org.
    3. Juan D. Moreno-Ternero & Min-Hung Tsay & Chun-Hsien Yeh, 2020. "A strategic justification of the Talmud rule based on lower and upper bounds," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1045-1057, December.
    4. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez Rodríguez, 2016. "Monotonicity implications for the ranking of rules for airport problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 379-400, December.
    5. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2020. "Allocating extra revenues from broadcasting sports leagues," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 65-73.
    6. Tsay, Min-Hung & Yeh, Chun-Hsien, 2019. "Relations among the central rules in bankruptcy problems: A strategic perspective," Games and Economic Behavior, Elsevier, vol. 113(C), pages 515-532.
    7. Li, Jiawen & Ju, Yuan, 2023. "Divide and choose: An informationally robust strategic approach to bankruptcy problems," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    8. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2018. "A study of the nucleolus in the nested cost-sharing problem: Axiomatic and strategic perspectives," Games and Economic Behavior, Elsevier, vol. 109(C), pages 82-98.
    9. Juan D. Moreno‐Ternero & Min‐Hung Tsay & Chun‐Hsien Yeh, 2022. "Strategic justifications of the TAL family of rules for bankruptcy problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 92-102, March.
    10. Alexander Karpov & Semyon Yurkov, 2012. "Generalized bankruptcy problem," HSE Working papers WP BRP 08/FE/2012, National Research University Higher School of Economics.
    11. Sanchez-Soriano, Joaquin, 2021. "Families of sequential priority rules and random arrival rules with withdrawal limits," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 136-148.
    12. Moreno-Ternero, Juan D., 2013. "A new analysis of a simple model of fair allocation," Economics Letters, Elsevier, vol. 118(2), pages 393-395.
    13. Rick K. Acosta & Encarnación Algaba & Joaquín Sánchez-Soriano, 2022. "Multi-issue bankruptcy problems with crossed claims," Annals of Operations Research, Springer, vol. 318(2), pages 749-772, November.

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    More about this item

    Keywords

    Bilateral consistency; Converse consistency; Constrained equal benefits rule; Subgame perfect equilibrium; Airport problem;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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