### Jorge Cortés

#### Professor

Distributed convergence to Nash equilibria by adversarial networks
with directed topologies

B. Gharesifard, J. Cortés

Proceedings of the IEEE Conference on Decision and
Control and European Control Conference, Maui, Hawaii,
USA, 2012, pp. 5786-5791

### Abstract

This paper considers a class of strategic scenarios in which two
cooperative groups 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 network. We
consider scenarios where the interaction topology within each
cooperative network is given by a strongly connected and
weight-balanced directed graph. We introduce a provably-correct
distributed dynamics which converges to the set of Nash equilibria
when the objective function is strictly concave-convex,
differentiable, with globally Lipschitz gradient. The technical
approach combines tools from algebraic graph theory, dynamical
systems, convex analysis, and game theory.

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Mechanical and Aerospace Engineering,
University of California, San Diego

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