235 research outputs found
Finding Nash Equilibrium Point of Nonlinear Non-cooperative
Abstract In this paper a coevolutionary algorithm is developed to find the Nash Equilibrium (NE
Cooperative Coevolution for Non-Separable Large-Scale Black-Box Optimization: Convergence Analyses and Distributed Accelerations
Given the ubiquity of non-separable optimization problems in real worlds, in
this paper we analyze and extend the large-scale version of the well-known
cooperative coevolution (CC), a divide-and-conquer optimization framework, on
non-separable functions. First, we reveal empirical reasons of why
decomposition-based methods are preferred or not in practice on some
non-separable large-scale problems, which have not been clearly pointed out in
many previous CC papers. Then, we formalize CC to a continuous game model via
simplification, but without losing its essential property. Different from
previous evolutionary game theory for CC, our new model provides a much simpler
but useful viewpoint to analyze its convergence, since only the pure Nash
equilibrium concept is needed and more general fitness landscapes can be
explicitly considered. Based on convergence analyses, we propose a hierarchical
decomposition strategy for better generalization, as for any decomposition
there is a risk of getting trapped into a suboptimal Nash equilibrium. Finally,
we use powerful distributed computing to accelerate it under the multi-level
learning framework, which combines the fine-tuning ability from decomposition
with the invariance property of CMA-ES. Experiments on a set of
high-dimensional functions validate both its search performance and scalability
(w.r.t. CPU cores) on a clustering computing platform with 400 CPU cores
Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
Evolutionary game dynamics is one of the most fruitful frameworks for
studying evolution in different disciplines, from Biology to Economics. Within
this context, the approach of choice for many researchers is the so-called
replicator equation, that describes mathematically the idea that those
individuals performing better have more offspring and thus their frequency in
the population grows. While very many interesting results have been obtained
with this equation in the three decades elapsed since it was first proposed, it
is important to realize the limits of its applicability. One particularly
relevant issue in this respect is that of non-mean-field effects, that may
arise from temporal fluctuations or from spatial correlations, both neglected
in the replicator equation. This review discusses these temporal and spatial
effects focusing on the non-trivial modifications they induce when compared to
the outcome of replicator dynamics. Alongside this question, the hypothesis of
linearity and its relation to the choice of the rule for strategy update is
also analyzed. The discussion is presented in terms of the emergence of
cooperation, as one of the current key problems in Biology and in other
disciplines.Comment: Review, 48 pages, 26 figure
Attribute Equilibrium Dominance Reduction Accelerator (DCCAEDR) Based on Distributed Coevolutionary Cloud and Its Application in Medical Records
© 2013 IEEE. Aimed at the tremendous challenge of attribute reduction for big data mining and knowledge discovery, we propose a new attribute equilibrium dominance reduction accelerator (DCCAEDR) based on the distributed coevolutionary cloud model. First, the framework of N-populations distributed coevolutionary MapReduce model is designed to divide the entire population into N subpopulations, sharing the reward of different subpopulations' solutions under a MapReduce cloud mechanism. Because the adaptive balancing between exploration and exploitation can be achieved in a better way, the reduction performance is guaranteed to be the same as those using the whole independent data set. Second, a novel Nash equilibrium dominance strategy of elitists under the N bounded rationality regions is adopted to assist the subpopulations necessary to attain the stable status of Nash equilibrium dominance. This further enhances the accelerator's robustness against complex noise on big data. Third, the approximation parallelism mechanism based on MapReduce is constructed to implement rule reduction by accelerating the computation of attribute equivalence classes. Consequently, the entire attribute reduction set with the equilibrium dominance solution can be achieved. Extensive simulation results have been used to illustrate the effectiveness and robustness of the proposed DCCAEDR accelerator for attribute reduction on big data. Furthermore, the DCCAEDR is applied to solve attribute reduction for traditional Chinese medical records and to segment cortical surfaces of the neonatal brain 3-D-MRI records, and the DCCAEDR shows the superior competitive results, when compared with the representative algorithms
An evolutionary algorithmic approach to determine the Nash equilibrium in a duopoly with nonlinearities and constraints
This paper presents an algorithmic approach to obtain the Nash Equilibrium in a duopoly. Analytical solutions to duopolistic competition draw on principles of game theory and require simplifying assumptions such as symmetrical payoff functions, linear demand and linear cost. Such assumptions can reduce the practical use of duopolistic models. In contrast, we use an evolutionary algorithmic approach (EAA) to determine the Nash equilibrium values. This approach has the advantage that it can deal with and find optimum values for duopolistic competition modelled using non-linear functions. In the paper we gradually build up the competitive situation by considering non-linear demand functions, non-linear cost functions, production and environmental constraints, and production in discrete bands. We employ particle swarm optimization with composite particles (PSOCP), a variant of particle swarm optimization, as the evolutionary algorithm. Through the paper we explicitly demonstrate how EAA can solve games with constrained payoff functions that cannot be dealt with by traditional analytical methods. We solve several benchmark problems from the literature and compare the results obtained from EAA with those obtained analytically, demonstrating the resilience and rigor of our EAA solution approach
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
Co-optimization: a generalization of coevolution
Many problems encountered in computer science are best stated in terms of interactions amongst individuals. For example, many problems are most naturally phrased in terms of finding a candidate solution which performs best against a set of test cases. In such situations, methods are needed to find candidate solutions which are expected to perform best over all test cases. Coevolution holds the promise of addressing such problems by employing principles from biological evolution, where populations of candidate solutions and test cases are evolved over time to produce higher quality solutions...This thesis presents a generalization of coevolution to co-optimization, where optimization techniques that do not rely on evolutionary principles may be used. Instead of introducing a new addition to coevolution in order to make it better suited for a particular class of problems, this thesis suggests removing the evolutionary model in favor of a technique better suited for that class of problems --Abstract, page iii
Nonlinear eco-evolutionary games with global environmental fluctuations and local environmental feedbacks
Environmental changes play a critical role in determining the evolution of
social dilemmas in many natural or social systems. Generally, the environmental
changes include two prominent aspects: the global time-dependent fluctuations
and the local strategy-dependent feedbacks. However, the impacts of these two
types of environmental changes have only been studied separately, a complete
picture of the environmental effects exerted by the combination of these two
aspects remains unclear. Here we develop a theoretical framework that
integrates group strategic behaviors with their general dynamic environments,
where the global environmental fluctuations are associated with a nonlinear
factor in public goods game and the local environmental feedbacks are described
by the `eco-evolutionary game'. We show how the coupled dynamics of local
game-environment evolution differs in static and dynamic global environments.
In particular, we find the emergence of cyclic evolutions of group cooperation
and local environment, which forms an interior irregular loop in the phase
plane, depending on the relative changing speed of both global and local
environments compared to the strategic change. Our results provide important
insights toward how diverse evolutionary outcomes could emerge from the
nonlinear interactions between strategies and the changing environments
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