Noncooperative foundations of bargaining power in committees and the Shapley–Shubik index

doi:10.1016/j.geb.2007.09.003

Games and Economic Behavior

Volume 63, Issue 1, May 2008, Pages 341-353

https://doi.org/10.1016/j.geb.2007.09.003 Get rights and content

Abstract

In this paper we explore the noncooperative foundations of the bargaining power that a voting rule gives to each member of a committee that bargains in search of consensus over a set of feasible agreements under a voting rule. Assuming complete information, we model a variety of bargaining protocols and investigate their stationary subgame perfect equilibria. We show how the Shapley–Shubik index and other power indices can be interpreted as measures of ‘bargaining power’ that appear in this light as limit cases.

References (32)

K. Binmore et al.
Noncooperative models of bargaining
H. Eraslan
Uniqueness of stationary equilibrium payoffs in the Baron–Ferejohn model
J. Econ. Theory
(2002)
H. Eraslan et al.
Majority rule in a stochastic model of bargaining
J. Econ. Theory
(2002)
A. Laruelle et al.
Bargaining in committees as an extension of Nash's bargaining theory
J. Econ. Theory
(2007)
M. Montero
Noncooperative bargaining foundations of the nucleolus in majority games
Games Econ. Behav.
(2006)
D. Pérez-Castrillo et al.
Bidding for the surplus: A non-cooperative approach to the Shapley value
J. Econ. Theory
(2001)
J.S. Banks et al.
A bargaining model of collective choice
Amer. Polit. Sci. Rev.
(2000)
J.F. Banzhaf
Weighted voting doesn't work: A mathematical analysis
Rutgers Law Rev.
(1965)
D.P. Baron et al.
Bargaining in legislatures
Amer. Polit. Sci. Rev.
(1989)
K. Binmore
Perfect equilibria in bargaining models

K. Binmore

Game Theory and the Social Contract II, Just Playing

(1998)

K. Binmore

Playing for Real

(2007)

P. Dubey

On the uniqueness of the Shapley value

Int. J. Game Theory

(1975)

P. Dubey et al.

Value theory without efficiency

Math. Operations Res.

(1981)

F. Gul

Bargaining foundations of the Shapley value

Econometrica

(1989)

S. Hart et al.

Bargaining and value

Econometrica

(1996)

Cited by (37)

Pledge-and-review bargaining
2023, Journal of Economic Theory
This paper presents a novel dynamic bargaining game where every party is proposing only its own contribution, before all pledges must be unanimously approved. I show that, with uncertain tolerance for delay, each equilibrium pledge maximizes an asymmetric Nash product. The weights on others' payoffs increase in the uncertainty, but decrease in the correlation of the shocks. The weights vary pledge to pledge, and this implies that the outcome is generically inefficient. The Nash demand game and its mapping to the Nash bargaining solution follow as a limiting case. The model sheds light on the Paris climate change agreement, but it also applies to negotiations between policymakers or business partners that have differentiated responsibilities or expertise.
Multi-lateral strategic bargaining without stationarity
2021, Journal of Mathematical Economics
Citation Excerpt :
This development has also extended to the relation with the cooperative approach. For instance, Laruelle and Valenciano (2008) characterize an extension of Nash’s bargaining solution for voting rules beyond unanimity. In the existence result presented below, all conceivable agreement rules are allowed, and additionally there is no requirement that the agreement rule should remain fixed over time.
This paper establishes existence of subgame perfect equilibrium in pure strategies for a general class of sequential multi-lateral bargaining games, without assuming a stationary setting. The only required hypothesis is that utility functions are continuous on the space of economic outcomes. In particular, no assumption on the space of feasible payoffs is needed. The result covers arbitrary and even time-varying bargaining protocols (acceptance rules), externalities, and other-regarding preferences. As a side result, we clarify the meaning of assumptions on “continuity at infinity.”
Optimal recommendation in two-player bargaining games
2020, Mathematical Social Sciences
This paper extends the traditional two-player noncooperative bargaining game by adding a recommendation stage before the regular bargaining stage. At the recommendation stage, a coordinator recommends a feasible payoff pair to the players. If both players accept the recommendation, the game ends and the recommendation is enforced. Otherwise, the game enters the bargaining stage, where each player is picked as the proposer of any bargaining round according to an exogenous probability characterizing their relative bargaining power, and both players receive their respective reservation payoffs with a certain risk of breakdown if they fail to reach an agreement in this round. We characterize the unique subgame perfect equilibrium outcome of this extended game. The equilibrium recommendation, which will be accepted by both players, is optimal for the coordinator among all acceptable recommendations. A player’s payoff in optimal recommendation increases with her bargaining power. As the risk of breakdown vanishes, the optimal recommendation converges to an asymmetric Nash bargaining solution parameterized by the probability at the bargaining stage.
Bargaining delay under partial breakdowns and externalities
2019, Economics Letters
We consider a noncooperative coalitional bargaining game where partial breakdowns, such as the rejecter of a proposal exiting from the game, take place with a positive probability, and externalities accompany the formation of coalitions. We present an example in which there exists a stationary subgame perfect equilibrium (SSPE) such that a bargaining delay occurs. We also show that under no partial breakdowns or no externalities, delay does not occur in any SSPE.
The Owen and Shapley spatial power indices: A comparison and a generalization
2017, Mathematical Social Sciences
Spatial games take into account the position of any voter in the space. In this class of games, two main indices of political power were defined. The first by Owen (1971) and the second, by Shapley (1977), later on extended in a two-dimensional space by Owen and Shapley (1989). We propose a generalization of Owen index. We show that the method proposed by this later in which players ordering is based on the distance between bliss and political issues points, yields the Shapley index if issues can be any point in the space.
Communication in vertical markets: Experimental evidence
2017, International Journal of Industrial Organization
An upstream monopolist supplying competing downstream firms may fail to monopolize the market because it is unable to commit not to behave opportunistically. We build on previous experimental studies of this well-known commitment problem by introducing communication. Allowing the upstream firm to chat privately with each downstream firm reduces total offered quantity from near the Cournot level (observed in the absence of communication) halfway toward the monopoly level. Allowing all firms to chat together openly results in complete monopolization. Downstream firms obtain such a bargaining advantage from open communication that all of the gains from monopolizing the market accrue to them. A simple structural model of Nash-in-Nash bargaining fits the pattern of shifting surpluses well. Using third-party coders, unsupervised text mining, among other approaches, we uncover features of the rich chat data that are correlated with market outcomes. We conclude with a discussion of the antitrust implications of open communication in vertical markets.

View all citing articles on Scopus

View full text

Noncooperative foundations of bargaining power in committees and the Shapley–Shubik index

Abstract

J. Econ. Theory

J. Econ. Theory

J. Econ. Theory

Games Econ. Behav.

J. Econ. Theory

A bargaining model of collective choice

Amer. Polit. Sci. Rev.

Weighted voting doesn't work: A mathematical analysis

Rutgers Law Rev.

Bargaining in legislatures

Amer. Polit. Sci. Rev.

Perfect equilibria in bargaining models

Game Theory and the Social Contract II, Just Playing

Playing for Real

On the uniqueness of the Shapley value

Int. J. Game Theory

Value theory without efficiency

Math. Operations Res.

Bargaining foundations of the Shapley value

Econometrica

Bargaining and value

Econometrica