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arXiv · 1409.4091

On Gradient like Properties of Population games, Learning models and Self Reinforced Processes

Michel Benaim
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Abstract

We consider ordinary differential equations on the unit simplex of $\RR^n$ that naturally occur in population games, models of learning and self reinforced random processes. Generalizing and relying on an idea introduced in \cite{DF11}, we provide conditions ensuring that these dynamics are gradient like and satisfy a suitable "angle condition". This is used to prove that omega limit sets and chain transitive sets (under certain smoothness assumptions) consist of equilibria; and that, in the real analytic case, every trajectory converges toward an equilibrium. In the reversible case, the dynamics are shown to be $C^1$ close to a gradient vector field. Properties of equilibria -with a special emphasis on potential games - and structural stability questions are also considered.

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Michel Benaim. 2014-09-14. On Gradient like Properties of Population games, Learning models and Self Reinforced Processes. https://arxiv.org/abs/1409.4091

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