TY - JOUR
T1 - On the Convergence of Piecewise Linear Strategic Interaction Dynamics on Networks
AU - Gharesifard, Bahman
AU - Touri, Behrouz
AU - Basar, Tamer
AU - Shamma, Jeff S.
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2015/9/11
Y1 - 2015/9/11
N2 - We prove that the piecewise linear best-response dynamical systems of strategic interactions are asymptotically convergent to their set of equilibria on any weighted undirected graph. We study various features of these dynamical systems, including the uniqueness and abundance properties of the set of equilibria and the emergence of unstable equilibria. We also introduce the novel notions of social equivalence and social dominance on directed graphs, and demonstrate some of their interesting implications, including their correspondence to consensus and chromatic number of partite graphs. Examples illustrate our results.
AB - We prove that the piecewise linear best-response dynamical systems of strategic interactions are asymptotically convergent to their set of equilibria on any weighted undirected graph. We study various features of these dynamical systems, including the uniqueness and abundance properties of the set of equilibria and the emergence of unstable equilibria. We also introduce the novel notions of social equivalence and social dominance on directed graphs, and demonstrate some of their interesting implications, including their correspondence to consensus and chromatic number of partite graphs. Examples illustrate our results.
UR - http://hdl.handle.net/10754/584223
UR - http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7258336
UR - http://www.scopus.com/inward/record.url?scp=84973346018&partnerID=8YFLogxK
U2 - 10.1109/TAC.2015.2477975
DO - 10.1109/TAC.2015.2477975
M3 - Article
SN - 0018-9286
VL - 61
SP - 1682
EP - 1687
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 6
ER -