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On Gradient like Properties of Population games, Learning models and Self Reinforced Processes
Auteur(s)
Date de parution
2014-09-14T19:05:06Z
Résumé
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.
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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Type de publication
preprint
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