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Continuous-time integral dynamics for monotone aggregative games with coupling constraints
We consider continuous-time equilibrium seeking in monotone aggregative ...
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Continuous-time Discounted Mirror-Descent Dynamics in Monotone Concave Games
In this paper, we consider concave continuous-kernel games characterized...
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Online Monotone Games
Algorithmic game theory (AGT) focuses on the design and analysis of algo...
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On the Exponential Rate of Convergence of Fictitious Play in Potential Games
The paper studies fictitious play (FP) learning dynamics in continuous t...
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Nonsmooth Aggregative Games with Coupling Constraints and Infinitely Many Classes of Players
After defining a pure-action profile in a nonatomic aggregative game, wh...
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A Tight and Unified Analysis of Extragradient for a Whole Spectrum of Differentiable Games
We consider differentiable games: multi-objective minimization problems,...
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Zero-sum risk-sensitive continuous-time stochastic games with unbounded payoff and transition rates and Borel spaces
We study a finite-horizon two-person zero-sum risk-sensitive stochastic ...
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Continuous-Time Convergence Rates in Potential and Monotone Games
In this paper, we provide exponential rates of convergence to the Nash equilibrium of continuous-time game dynamics such as mirror descent (MD) and actor-critic (AC) in N-player continuous games that are either potential games or monotone games but possibly potential-free. In the first part of this paper, under the assumption the game admits a relatively strongly concave potential, we show that MD and AC converge in 𝒪(e^-β t). In the second part of this paper, using relative concavity, we provide a novel relative characterization of monotone games and show that MD and its discounted version converge with 𝒪(e^-β t) in relatively strongly and relatively hypo-monotone games. Moreover, these rates extend their known convergence conditions and also improve the results in the potential game setup. Simulations are performed which empirically back up our results.
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