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A non-cooperative mechanism for the Shapley value of airport problems

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Abstract

In this paper we address the question of how to allocate the total cost of building and maintaining an airport runway among its users based on a non-cooperative approach. We present a non-cooperative bargaining game with a unique Nash equilibrium outcome whose payoffs are the Shapley value of an airport problem. Furthermore, it is shown that all strategy profiles leading to a subgame perfect equilibrium in these games are also coalition-proof.

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Notes

  1. We are assuming that the more efficient runway from a social point of view is the longest one.

  2. The same goes for the mechanism of Dagan et al. (1997).

  3. Two TU games (Nv) and (Nw) are strategically equivalent if there exists \(\alpha \in \mathbb {R}_{++}\) and \(\beta \in \mathbb {R}^N\) such that: \(w(S)=\alpha \cdot v(S)+\beta (S)\) for all \(S\subseteq N\).

  4. In these non-cooperative game there is a continuum of strategy profiles that are Nash equilibria, but all of them leading to the same outcome.

  5. That is, it is assumed that the agents regard lotteries in just this fashion; one lottery is better than another if it has a higher expected payoff. If the agents were not risk neutral, they would not necessarily try to maximize their expected payoff, and consequently the Nash equilibrium outcome could be a different one.

  6. This bilateral problem could also be solved using a fair coin to pick a dictator without the previous stage.

  7. This is the only place where we use that s is an SPE.

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Correspondence to M. J. Albizuri.

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This research has been supported by Spanish Ministerio de Ciencia e Innovación (ECO2012-33618) and by UPV/EHU (UFI11/51 and GIU13/31).

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Albizuri, M.J., Echarri, J.M. & Zarzuelo, J.M. A non-cooperative mechanism for the Shapley value of airport problems. Ann Oper Res 235, 1–11 (2015). https://doi.org/10.1007/s10479-015-1981-7

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