2,851 research outputs found
Continuous Strategy Replicator Dynamics for Multi--Agent Learning
The problem of multi-agent learning and adaptation has attracted a great deal
of attention in recent years. It has been suggested that the dynamics of multi
agent learning can be studied using replicator equations from population
biology. Most existing studies so far have been limited to discrete strategy
spaces with a small number of available actions. In many cases, however, the
choices available to agents are better characterized by continuous spectra.
This paper suggests a generalization of the replicator framework that allows to
study the adaptive dynamics of Q-learning agents with continuous strategy
spaces. Instead of probability vectors, agents strategies are now characterized
by probability measures over continuous variables. As a result, the ordinary
differential equations for the discrete case are replaced by a system of
coupled integral--differential replicator equations that describe the mutual
evolution of individual agent strategies. We derive a set of functional
equations describing the steady state of the replicator dynamics, examine their
solutions for several two-player games, and confirm our analytical results
using simulations.Comment: 12 pages, 15 figures, accepted for publication in JAAMA
Information Geometry and Evolutionary Game Theory
The Shahshahani geometry of evolutionary game theory is realized as the
information geometry of the simplex, deriving from the Fisher information
metric of the manifold of categorical probability distributions. Some essential
concepts in evolutionary game theory are realized information-theoretically.
Results are extended to the Lotka-Volterra equation and to multiple population
systems.Comment: Added reference
Coupled Replicator Equations for the Dynamics of Learning in Multiagent Systems
Starting with a group of reinforcement-learning agents we derive coupled
replicator equations that describe the dynamics of collective learning in
multiagent systems. We show that, although agents model their environment in a
self-interested way without sharing knowledge, a game dynamics emerges
naturally through environment-mediated interactions. An application to
rock-scissors-paper game interactions shows that the collective learning
dynamics exhibits a diversity of competitive and cooperative behaviors. These
include quasiperiodicity, stable limit cycles, intermittency, and deterministic
chaos--behaviors that should be expected in heterogeneous multiagent systems
described by the general replicator equations we derive.Comment: 4 pages, 3 figures,
http://www.santafe.edu/projects/CompMech/papers/credlmas.html; updated
references, corrected typos, changed conten
Evolutionary Game Dynamics for Two Interacting Populations under Environmental Feedback
We study the evolutionary dynamics of games under environmental feedback
using replicator equations for two interacting populations. One key feature is
to consider jointly the co-evolution of the dynamic payoff matrices and the
state of the environment: the payoff matrix varies with the changing
environment and at the same time, the state of the environment is affected
indirectly by the changing payoff matrix through the evolving population
profiles. For such co-evolutionary dynamics, we investigate whether convergence
will take place, and if so, how. In particular, we identify the scenarios where
oscillation offers the best predictions of long-run behavior by using
reversible system theory. The obtained results are useful to describe the
evolution of multi-community societies in which individuals' payoffs and
societal feedback interact.Comment: 7 pages, submitted to a conferenc
Chaotic provinces in the kingdom of the Red Queen
The interplay between parasites and their hosts is found in all kinds of
species and plays an important role in understanding the principles of
evolution and coevolution. Usually, the different genotypes of hosts and
parasites oscillate in their abundances. The well-established theory of
oscillatory Red Queen dynamics proposes an ongoing change in frequencies of the
different types within each species. So far, it is unclear in which way Red
Queen dynamics persists with more than two types of hosts and parasites. In our
analysis, an arbitrary number of types within two species are examined in a
deterministic framework with constant or changing population size. This general
framework allows for analytical solutions for internal fixed points and their
stability. For more than two species, apparently chaotic dynamics has been
reported. Here we show that even for two species, once more than two types are
considered per species, irregular dynamics in their frequencies can be observed
in the long run. The nature of the dynamics depends strongly on the initial
configuration of the system; the usual regular Red Queen oscillations are only
observed in some parts of the parameter region
Evolutionary Poisson Games for Controlling Large Population Behaviors
Emerging applications in engineering such as crowd-sourcing and
(mis)information propagation involve a large population of heterogeneous users
or agents in a complex network who strategically make dynamic decisions. In
this work, we establish an evolutionary Poisson game framework to capture the
random, dynamic and heterogeneous interactions of agents in a holistic fashion,
and design mechanisms to control their behaviors to achieve a system-wide
objective. We use the antivirus protection challenge in cyber security to
motivate the framework, where each user in the network can choose whether or
not to adopt the software. We introduce the notion of evolutionary Poisson
stable equilibrium for the game, and show its existence and uniqueness. Online
algorithms are developed using the techniques of stochastic approximation
coupled with the population dynamics, and they are shown to converge to the
optimal solution of the controller problem. Numerical examples are used to
illustrate and corroborate our results
- …