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Theory and Decision

Erschienen in:

30.09.2016

Subgame perfect equilibrium in a bargaining model with deterministic procedures

verfasst von: Liang Mao

Erschienen in: Theory and Decision | Ausgabe 4/2017

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Abstract

Two players, A and B, bargain to divide a perfectly divisible pie. In a bargaining model with constant discount factors, \(\delta _A\) and \(\delta _B\), we extend Rubinstein (Econometrica 50:97–110, 1982)’s alternating offers procedure to more general deterministic procedures, so that any player in any period can be the proposer. We show that each bargaining game with a deterministic procedure has a unique subgame perfect equilibrium (SPE) payoff outcome, which is efficient. Conversely, each efficient division of the pie can be supported as an SPE outcome by some procedure if \(\delta _A+\delta _B\ge 1\), while almost no division can ever be supported in SPE if \(\delta _A+\delta _B < 1\).

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For any t, the subgame that starts from period \(t+2\) has exactly the same structure as that which starts from period t.

See, among others, Nash (1953), Binmore et al. (1986), Ju and Wettstein (2009).

See, for example, Fershtman (1990), Anesi and Seidmann (2014).

For example, see Binmore et al. (1986) and Binmore (1987) for some discussions on how the subgame perfect equilibrium outcomes can be affected by players’ time preference.

In this paper, a payoff outcome \((u_A,u_B)\) where \(u_i\ge 0\) is said to be efficient if \(u_A+u_B=1\).

Suppose \(\omega =A^{n_1}B^{n_2}\cdots \), then according to Lemma 3 and Theorem 1, \(x=\theta (\omega )=z_{r(\omega )}\ge z_1=1-\delta _B^{n_1}\ge 1-\delta _B\) if \(r(\omega )\ge 1\); \(x=\theta (\omega )=1>1-\delta _B\) if \(r(\omega )= 0\).

See, for example, Fudenberg and Tirole (1991, section 4.2).

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Titel: Subgame perfect equilibrium in a bargaining model with deterministic procedures
verfasst von: Liang Mao
Publikationsdatum: 30.09.2016
Verlag: Springer US
Erschienen in: Theory and Decision / Ausgabe 4/2017
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-016-9577-5

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