TY  - GEN
AB  - We extend the analysis of van Damme (1987, Section 7.5) of the famous
smoothing demand in Nash (1953) as an argument for the singular stability of the
symmetric Nash bargaining solution among all Pareto efficient equilibria of the Nash
demand game. Van Damme's analysis provides a clean mathematical framework where
he substantiates Nash's conjecture by two fundamental theorems in which he proves
that the Nash solution is among all Nash equilibria of the Nash demand game the only
one that is *H*-essential. We show by generalizing this analysis that for any asymmetric
Nash bargaining solution a similar stability property can be established that we call
$H_{\alpha}$-essentiality. A special case of our result for α = 1/2 is $H_{1/2}$-essentiality that
coincides with van Damme's *H*-essentiality. Our analysis deprives the symmetric
Nash solution equilibrium of Nash's demand game of its exposed position and fortifies
our conviction that, in contrast to the predominant view in the related literature, the
only structural diffeerence between the asymmetric Nash solutions and the symmetric
one is that the latter one is symmetric.
While our proofs are mathematically straightforward given the analysis of van Damme
(1987), our results change drastically the prevalent interpretation of Nash's smoothing
of his demand game and dilute its conceptual importance.
DA  - 2020
KW  - 2-person bargaining games
KW  - α-symmetric Nash solution
KW  - Nash demand game
KW  - Nash soothing of games
KW  - $H_{\alpha}$-essential Nash equilibrium
LA  - eng
PY  - 2020
SN  - 0931-6558
SP  - 17-
TI  - Nash Smoothing on the Test Bench: $H_{\alpha}$  -Essential Equilibria
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29412682
Y2  - 2024-11-22T01:31:12
ER  -