Publication type: Article in scientific journal
Type of review: Peer review (publication)
Title: On the relationship between uniqueness and stability in sum-aggregative, symmetric and general differentiable games
Authors: Hefti, Andreas
DOI: 10.1016/j.mathsocsci.2016.02.008
Published in: Mathematical Social Sciences
Volume(Issue): 80
Pages: 83
Pages to: 96
Issue Date: 2016
Publisher / Ed. Institution: Elsevier
ISSN: 0165-4896
Language: English
Subject (DDC): 510: Mathematics
Abstract: This article explores the relationship between uniqueness and stability in differentiable regular games, with a major focus on the important classes of sum-aggregative, two-player and symmetric games. We consider three types of popular dynamics, continuous-time gradient dynamics as well as continuous- and discrete-time best-reply dynamics, and include aggregate-taking behavior as a non-strategic behavioral variant. We show that while in general games stability conditions are only sufficient for uniqueness, they are likely to be necessary as well in models with sum-aggregative or symmetric payoff functions. In particular, a unique equilibrium always verifies the stability conditions of all dynamics if strategies are equilibrium complements, and this also holds for both continuous-time dynamics if strategies are equilibrium substitutes with bounded slopes. These findings extend to the case of aggregate-taking equilibria. We further analyze the stability relations between the various dynamics, and demonstrate that the restrictive nature of the discrete dynamics originates from simultaneity of adjustments. Asynchronous decisions or heterogeneous forward thinking may stabilize the adjustment process.
Fulltext version: Published version
License (according to publishing contract): Licence according to publishing contract
Departement: School of Management and Law
Organisational Unit: Center for Energy and Environment (CEE)
Appears in collections:Publikationen School of Management and Law

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