Abstract
We investigate a strategic bargaining approach to resolve queueing conflicts. Given a situation where players with different waiting costs have to form a queue in order to be served, they firstly compete with each other for a specific position in the queue. The winner can decide to take up the position or sell it to the others. In the former case, the rest of the players proceed to compete for the remaining positions in the same manner, whereas in the latter case, the seller proposes a queue with corresponding payments to the others which can be accepted or rejected. Depending on which position players are going to compete for, the subgame perfect equilibrium outcome of the corresponding mechanism coincides with the payoff vector assigned by either the maximal transfer rule or the minimal transfer rule, while an efficient queue is always formed in equilibrium.
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Notes
- 1.
A game v satisfies zero monotonicity if there are no negative externalities when a single player joins a coalition. That is, for all S ⊂ N and all i ∉ S, v(S ∪{ i}) ≥ v(S) + v({i}).
- 2.
A game v satisfies super-additivity if there are no negative externalities when two disjoint coalitions are merged together. That is, for all S, T ⊂ N such that S ∩ T = ∅, v(S ∪ T) ≥ v(S) + v(T).
- 3.
- 4.
Indeed this option makes the choice of taking up the first position at stage F-2 strategically redundant. Yet it seems natural and logical for the winner to have the right to take up the position without proceeding to the next stage.
- 5.
Note that the position of player i may not be | T | + 1 if there is a player j ∈ S with θ j  = θ i . Since the choice of an efficient queue has no effect on v P (S ∪{ i}) − v P (S), we can take an efficient queue σ ∗ with \(\sigma _{i}^{{\ast}} = \vert T\vert + 1\).
- 6.
A value ϕ satisfies the balanced contributions property if \(\phi _{i}(v) -\phi _{i}(v\vert _{N\setminus \{j\}}) =\phi _{j}(v) -\phi _{j}(v\vert _{N\setminus \{i\}})\) for all v ∈ Γ N and all i, j ∈ N. Section 4.4 investigates the implication of this property in the context of queueing.
- 7.
Note that the position of player i may not be | T | + 1 if there is a player j ∈ S with θ j  = θ i . Since the choice of an efficient queue has no effect on v O (S ∪{ i}) − v O (S), we can take an efficient queue σ ∗ with \(\sigma _{i}^{{\ast}} = \vert T\vert + 1\).
- 8.
Note that the possibility of taking up the position and leaving the game is not a part of the Pérez-Castrillo and Wettstein’s (2001) mechanism which implements the Shapley value for TU games.
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Chun, Y. (2016). A Noncooperative Approach. In: Fair Queueing. Studies in Choice and Welfare. Springer, Cham. https://doi.org/10.1007/978-3-319-33771-5_9
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DOI: https://doi.org/10.1007/978-3-319-33771-5_9
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