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Social Choice and Welfare

Erschienen in:

16.05.2022 | Original Paper

The Burning Coalition Bargaining Model

verfasst von: Marco Rogna

Erschienen in: Social Choice and Welfare | Ausgabe 3/2022

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Abstract

The paper presents a coalitional bargaining model, the Burning Coalition Bargaining Model, having a peculiar type of partial breakdown. In fact, in this model, the rejection of a proposal causes the possibility of the proposed coalition to vanish, rather than triggering the end of all negotiations or the exclusion of some players from the game, as already proposed in the literature. Under this type of partial breakdown and adopting a standard rejecter-proposes protocol, 0-normalized, 3-players games are examined for extreme values of the breakdown probability. When such probability is equal to one, efficiency is more difficult to obtain than in models adopting discounting and the first mover advantage is strongly diminished. Furthermore, when an efficient outcome is attained, the final distribution of payoffs reflects the strength of players in the game, with strength being represented by belonging to more valuable coalitions. The same feature is retained when considering a probability of breakdown approaching zero.

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Along the paper it will be adopted the following terminological convention: multi-player bargaining indicates a bargaining situation entailing more than two players where only one coalition, namely, the coalition with all players can be formed; coalitional bargaining, instead, assumes both the presence of more than two players and the possibility to form coalitions that are subsets of the set of all players; two players bargaining is self-explanatory.

Note that the Egalitarian Solution is also known as the Equal Split (Hart and Mas-Colell 1996) or the Equal Division (van den Brink 2007) allocation.

Note that such assumption is present both in Hart and Mas-Colell (1996) and Calvo and Gutiérrez-López (2016).

We adopt the convention for which \(n = |N|\).

As in Chatterjee et al. (1993), Okada (1996), Compte and Jehiel (2010) and in most of coalitional bargaining models, the order of responders is inconsequential, therefore it could be left to the proposer to choose it. However, given its irrelevance, a predefined order seems the easiest solution.

In our 3-players case with zero normalized characteristic function, the possibility of continuing to bargain is, however, inconsequential.

Note that, in the rest of the paper, since we will always assume 0–normalized games, the subscript 0 will be omitted.

Note that, in Theorem 2 of Hart and Mas-Colell (1996), \(\rho \), the corresponding of \(\alpha \), tend to 1 instead of zero, since \(\rho \) indicates the probability of the game continuing without any breakdown taking place, whereas \(\alpha \) indicates the opposite.

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Titel: The Burning Coalition Bargaining Model
verfasst von: Marco Rogna
Publikationsdatum: 16.05.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 3/2022
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-022-01409-3

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