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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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    1. Dagan, Nir & Serrano, Roberto & Volij, Oscar, 1997. "A Noncooperative View of Consistent Bankruptcy Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 55-72, January.
    2. Potters, Jos & Sudholter, Peter, 1999. "Airport problems and consistent allocation rules," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 83-102, July.
    3. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    4. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    5. Yeh, Chun-Hsien, 2006. "Reduction-consistency in collective choice problems," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 637-652, September.
    6. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    7. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    8. Orshan, Gooni, 1993. "The Prenucleolus and the Reduced Game Property: Equal Treatment Replaces Anonymity," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 241-248.
    9. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    10. Serrano, Roberto & Vohra, Rajiv, 2002. "Bargaining and Bargaining Sets," Games and Economic Behavior, Elsevier, vol. 39(2), pages 292-308, May.
    11. Chang, Chih & Hu, Cheng-Cheng, 2008. "A non-cooperative interpretation of the f-just rules of bankruptcy problems," Games and Economic Behavior, Elsevier, vol. 63(1), pages 133-144, May.
    12. Serrano, Roberto, 1997. "Reinterpreting the Kernel," Journal of Economic Theory, Elsevier, vol. 77(1), pages 58-80, November.
    13. S.C. Littlechild & G.F. Thompson, 1977. "Aircraft Landing Fees: A Game Theory Approach," Bell Journal of Economics, The RAND Corporation, vol. 8(1), pages 186-204, Spring.
    14. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    15. Lensberg, Terje, 1987. "Stability and Collective Rationality," Econometrica, Econometric Society, vol. 55(4), pages 935-961, July.
    16. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(1), pages 61-80.
    17. Chun, Youngsub, 2002. "The Converse Consistency Principle in Bargaining," Games and Economic Behavior, Elsevier, vol. 40(1), pages 25-43, July.
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    3. 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.
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    7. Alexander Karpov & Semyon Yurkov, 2012. "Generalized bankruptcy problem," HSE Working papers WP BRP 08/FE/2012, National Research University Higher School of Economics.
    8. Moreno-Ternero, Juan D., 2013. "A new analysis of a simple model of fair allocation," Economics Letters, Elsevier, vol. 118(2), pages 393-395.
    9. 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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    11. 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.
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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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