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Generic Regularity of Stationary Equilibrium Points in a Class of Bargaining Games
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Generic Regularity of Stationary Equilibrium Points in
a Class of Bargaining Games
1
by
Tasos Kalandrakis
Preliminary Draft. Comments Welcomed.
Abstract:
For a class of n-player (n
≥ 2) sequential bargaining games with prob-
abilistic recognition and general agreement rules, we characterize stationary subgame per-fect (SSP) equilibria as solutions to systems of equations and establish their existence viaBrouwer’s fixed point theorem. Using this characterization we show that when utility overagreements is strictly concave and satisfies certain smoothness conditions, there is a finitenumber of pure strategy SSP (PSSP) equilibrium points for almost all discount factors ordelay costs. When the space of agreements is one-dimensional, all equilibria are PSSP. Thesame is true for oligarchic voting rules (which include unanimity) for which, in addition, weshow that (generically) the number of equilibria is odd and equilibrium correspondence islower-hemicontinuous. Thus, for discounted unanimity games our results constitute a natu-ral analogue to the uniqueness finding of Merlo and Wilson, 1995, in cases when bargainingdoes not emulate the division of a cake, as is typical in political environments with ideologicalagreement spaces.
Keywords:
Local Uniqueness of Equilibrium, Regularity, Sequential Bargaining.
Correspondence Address:
Department of Political Science, Yale University, PO
Box 208301, New Haven, CT 06520-8301. E-mail: ## email not listed ##.
1
Prepared for delivery at the annual meeting of the American Political Science Association, Philadelphia
Mariott Hotel, Philadelphia, PA.
1
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| | Authors: Kalandrakis, Anastassios. |
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|
.
Generic Regularity of Stationary Equilibrium Points in
a Class of Bargaining Games
1
by
Tasos Kalandrakis
Preliminary Draft. Comments Welcomed.
Abstract:
For a class of n-player (n
≥ 2) sequential bargaining games with prob-
abilistic recognition and general agreement rules, we characterize stationary subgame per-
fect (SSP) equilibria as solutions to systems of equations and establish their existence via
Brouwer’s fixed point theorem. Using this characterization we show that when utility over
agreements is strictly concave and satisfies certain smoothness conditions, there is a finite
number of pure strategy SSP (PSSP) equilibrium points for almost all discount factors or
delay costs. When the space of agreements is one-dimensional, all equilibria are PSSP. The
same is true for oligarchic voting rules (which include unanimity) for which, in addition, we
show that (generically) the number of equilibria is odd and equilibrium correspondence is
lower-hemicontinuous. Thus, for discounted unanimity games our results constitute a natu-
ral analogue to the uniqueness finding of Merlo and Wilson, 1995, in cases when bargaining
does not emulate the division of a cake, as is typical in political environments with ideological
agreement spaces.
Keywords:
Local Uniqueness of Equilibrium, Regularity, Sequential Bargaining.
Correspondence Address:
Department of Political Science, Yale University, PO
Box 208301, New Haven, CT 06520-8301. E-mail: ## email not listed ##.
1
Prepared for delivery at the annual meeting of the American Political Science Association, Philadelphia
Mariott Hotel, Philadelphia, PA.
1
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