TY - JOUR
T1 - Constrained evolutionary games by using a mixture of imitation dynamics
AU - Barreiro-Gomez, Julian
AU - Tembine, Hamidou
N1 - Funding Information:
We gratefully acknowledge support from U.S. Air Force Office of Scientific Research under grant number FA9550-17-1-0259. The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Vijay Gupta under the direction of Editor Christos G. Cassandras.
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/11
Y1 - 2018/11
N2 - Game dynamics have been widely used as learning and computational tool to find evolutionarily stable strategies. Nevertheless, most of the existing evolutionary game dynamics, i.e., the replicator, Smith, projection, Brown–Von Neumann–Nash, Logit and best response dynamics have been analyzed only in the unconstrained case. In this work, we introduce novel evolutionary game dynamics inspired from a combination of imitation dynamics. The proposed approach is able to satisfy both upper- and lower-bound constraints. Moreover, dynamics have asymptotic convergence guarantees to a generalized-evolutionarily stable strategy. We show important features of the proposed game dynamics such as the positive correlation and invariance of the feasible region. Several illustrative examples handling population state constraints are provided.
AB - Game dynamics have been widely used as learning and computational tool to find evolutionarily stable strategies. Nevertheless, most of the existing evolutionary game dynamics, i.e., the replicator, Smith, projection, Brown–Von Neumann–Nash, Logit and best response dynamics have been analyzed only in the unconstrained case. In this work, we introduce novel evolutionary game dynamics inspired from a combination of imitation dynamics. The proposed approach is able to satisfy both upper- and lower-bound constraints. Moreover, dynamics have asymptotic convergence guarantees to a generalized-evolutionarily stable strategy. We show important features of the proposed game dynamics such as the positive correlation and invariance of the feasible region. Several illustrative examples handling population state constraints are provided.
KW - Constrained evolutionary game dynamics
KW - Generalized-Nash equilibrium
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U2 - 10.1016/j.automatica.2018.08.014
DO - 10.1016/j.automatica.2018.08.014
M3 - Article
AN - SCOPUS:85051928908
SN - 0005-1098
VL - 97
SP - 254
EP - 262
JO - Automatica
JF - Automatica
ER -