Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Distributed convergence to Nash equilibria by adversarial
networks with undirected topologies
B. Gharesifard, J. Cortés
Proceedings of the American Control Conference,
Montréal, Canada, 2012, pp. 5881-5886
Abstract
This paper considers a class of strategic scenarios in
which two undirected networks of agents have opposing
objectives with regards to the optimization of a common
objective function. In the resulting zero-sum game,
individual agents collaborate with neighbors in their
respective network and have only partial knowledge of
the state of the agents in the other one. We synthesize
a distributed saddle-point algorithm that is
implementable via local interactions and establish its
convergence to the set of Nash equilibria for a class of
strictly concave-convex and locally Lipschitz objective
functions. Our algorithm synthesis builds on a
continuous-time optimization strategy for finding the
set of minimizers of a sum of convex functions in a
distributed way. As a byproduct, we show that this
strategy can be itself cast as a saddle-point dynamics
and use this fact to establish its asymptotic
convergence properties. The technical approach combines
tools from algebraic graph theory, nonsmooth analysis,
set-valued dynamical systems, and game theory.
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Mechanical and Aerospace Engineering,
University of California, San Diego
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Ph: 1-858-822-7930
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cortes at ucsd.edu
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