Passivity analysis of higher order evolutionary dynamics and population games

@article{Mabrok2016PassivityAO,
  title={Passivity analysis of higher order evolutionary dynamics and population games},
  author={Mohamed A. Mabrok and Jeff S. Shamma},
  journal={2016 IEEE 55th Conference on Decision and Control (CDC)},
  year={2016},
  pages={6129-6134}
}
  • M. Mabrok, J. Shamma
  • Published 16 September 2016
  • Mathematics, Computer Science
  • 2016 IEEE 55th Conference on Decision and Control (CDC)
Evolutionary dynamics describe how the population composition changes in response to the fitness levels, resulting in a closed-loop feedback system. Recent work established a connection between passivity theory and certain classes of population games, namely so-called “stable games”. In particular, it was shown that a combination of stable games and (an analogue of) passive evolutionary dynamics results in stable convergence to Nash equilibrium. This paper considers the converse question of… 
Gains in evolutionary dynamics A unifying approach to dynamic stability of contractive games and ESS∗
TLDR
It is discussed that the idea of reconstructing evolutionary dynamics from optimization with switching costs and focusing on net revision gains for stability is promising for further applications to more complex situations.
Passivity and Evolutionary Game Dynamics
TLDR
This paper defines a notion of passivity using the state-space representation of the models and explains how the main results can be used to establish a connection between passivity and stability of equilibrium in population games.
Gains in evolutionary dynamics: a unifying approach to stability for contractive games and ESS
TLDR
The idea of reconstructing evolutionary dynamics from optimization with switching costs and focusing on net revision gains for stability is promising for further applications to more complex situations.
Higher-Order Game Dynamics in Population Games and Reinforcement Learning
TLDR
Higher-Order Game Dynamics in Population Games and Reinforcement Learning Bolin Gao Master of Applied Science Graduate Department of Electrical and Computer Engineering University of Toronto 2017 is able to leverage a host of powerful tools from convex analysis, monotone operator theory, and Lyapunov theory to systematically design higher-order game dynamics with guaranteed convergence in large classes of games.
Nash equilibrium seeking in potential games with double-integrator agents
  • F. Fabiani, A. Caiti
  • Computer Science, Mathematics
    2019 18th European Control Conference (ECC)
  • 2019
TLDR
This paper shows the equivalence between a constrained, multi-agent control problem, modeled within the port-Hamiltonian framework, and an exact potential game, and a network of double-integrator agents, which can be represented as a graph.
On Passivity, Reinforcement Learning, and Higher Order Learning in Multiagent Finite Games
  • Bolin Gao, L. Pavel
  • Computer Science, Mathematics
    IEEE Transactions on Automatic Control
  • 2021
TLDR
It is shown that convergence to a Nash distribution can be attained in a broader class of games than previously considered in the literature—namely, in games characterized by the monotonicity property of their (negative) payoff vectors.
A Passivity-Based Approach to Nash Equilibrium Seeking Over Networks
TLDR
This paper proposes an augmented gradient-play dynamics with correction, in which players communicate locally only with their neighbors to compute an estimate of the other players’ actions, and exploits incremental passivity properties and shows that a synchronizing, distributed Laplacian feedback can be designed using relative estimates of the neighbors.
Robust Hybrid Systems for Control, Learning, and Optimization in Networked Dynamical Systems
TLDR
This dissertation proposes a step-by-step approach to the design of different types of discrete-time, continuous- time, hybrid, and stochastic controllers for different type of applications, extending and generalizing different results in the literature in the area of extremum seeking control, sampled-data extremization, robust synchronization, and Stochastic learning in networked systems.
On Passivity and Reinforcement Learning in Finite Games
  • Bolin Gao, L. Pavel
  • Computer Science
    2018 IEEE Conference on Decision and Control (CDC)
  • 2018
TLDR
This work considers an exponentially-discounted reinforcement learning scheme, and shows that convergence can be guaranteed for the class of games characterized by the monotonicity property of their (negative) payoff.
Positive Invariance of Subset of Positive Externalities
TLDR
It is shown that only a certain subset of the subset of positive externalities can be a positively invariant set of the pseudo-gradient dynamics.
...
1
2
...

References

SHOWING 1-10 OF 44 REFERENCES
Population games, stable games, and passivity
  • Michael J. Fox, J. Shamma
  • Computer Science, Mathematics
    2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
  • 2012
TLDR
This work shows that stable games can be formulated as passive input-output systems, and identifies passivity of a learning dynamic as a sufficient condition for global convergence in stable games.
Evolutionary game dynamics
Evolutionary game dynamics is the application of population dynamical methods to game theory. It has been introduced by evolutionary biologists, anticipated in part by classical game theorists. In
Anticipatory Learning in General Evolutionary Games
TLDR
It is shown that the notion of "anticipatory" learning, or, using more traditional feedback control terminology ,"lead compensation", can be used to enable convergence through a simple modification of existing learning models, is broadly applicable to a variety of evolutionary game models.
Stable games and their dynamics
TLDR
It is proved that the set of Nash equilibria of a stable game is globally asymptotically stable under a wide range of evolutionary dynamics.
Evolutionary Games and Population Dynamics
TLDR
In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities.
Higher order game dynamics
TLDR
This paper shows that strictly dominated strategies become extinct in n-th order payoff-monotonic dynamics n orders as fast as in the corresponding first order dynamics; furthermore, in stark contrast to first order, weakly dominated strategies also become extinct for n⩾2.
Population Games And Evolutionary Dynamics
  • W. Sandholm
  • Mathematics, Computer Science
    Economic learning and social evolution
  • 2010
TLDR
The text first considers population games, which provide a simple, powerful model for studying strategic interactions among large numbers of anonymous agents, and studies the dynamics of behavior in these games, providing foundations for two distinct approaches to aggregate behavior dynamics.
Chaos in learning a simple two-person game
TLDR
That chaos can occur in learning a simple game indicates one should use caution in assuming real people will learn to play a game according to a Nash equilibrium strategy, as it provides an important self-consistency condition for determining when players will learning to behave as though they were fully rational.
Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria
TLDR
A form of "dynamic" fictitious and gradient play strategy update mechanisms that use derivative action in processing opponent actions and, in some cases, can lead to behavior converging to Nash equilibria in previously nonconvergent situations are introduced.
A general class of adaptative strategies
We exhibit and characterize an entire class of simple adaptive strategies, in the repeated play of a game, having the Hannan-consistency property: In the long-run, the player is guaranteed an average
...
1
2
3
4
5
...