Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Learning and innovative elements of strategy adoption rules expand cooperative network topologies

Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated games. Here we show that cooperation remains rather stable by applying the reinforcement learning strategy adoption rule, Q-learning on a variety of random, regular, small-word, scale-free and modular network models in repeated, multi-agent Prisoners Dilemma and Hawk-Dove games. Furthermore, we found that using the above model systems other long-term learning strategy adoption rules also promote cooperation, while introducing a low level of noise (as a model of innovation) to the strategy adoption rules makes the level of cooperation less dependent on the actual network topology. Our results demonstrate that long-term learning and random elements in the strategy adoption rules, when acting together, extend the range of network topologies enabling the development of cooperation at a wider range of costs and temptations. These results suggest that a balanced duo of learning and innovation may help to preserve cooperation during the re-organization of real-world networks, and may play a prominent role in the evolution of self-organizing, complex systems.Comment: 14 pages, 3 Figures + a Supplementary Material with 25 pages, 3 Tables, 12 Figures and 116 reference

A survey on the analysis and control of evolutionary matrix games

In support of the growing interest in how to efficiently influence complex systems of interacting self interested agents, we present this review of fundamental concepts, emerging research, and open problems related to the analysis and control of evolutionary matrix games, with particular emphasis on applications in social, economic, and biological networks. (C) 2018 Elsevier Ltd. All rights reserved

Evolutionary games and spatial periodicity

We establish a theoretical framework to address evolutionary dynamics of spatial games under strong selection. As the selection intensity tends to infinity, strategy competition unfolds in the deterministic way of winners taking all. We rigorously prove that the evolutionary process soon or later either enters a cycle and from then on repeats the cycle periodically, or stabilizes at some state almost everywhere. This conclusion holds for any population graph and a large class of finite games. This framework suffices to reveal the underlying mathematical rationale for the kaleidoscopic cooperation of Nowak and May's pioneering work on spatial games: highly symmetric starting configuration causes a very long transient phase covering a large number of extremely beautiful spatial patterns. For all starting configurations, spatial patterns transit definitely over generations, so cooperators and defectors persist definitely. This framework can be extended to explore games including the snowdrift game, the public goods games (with or without loner, punishment), and repeated games on graphs. Aspiration dynamics can also be fully addressed when players deterministically switch strategy for unmet aspirations by virtue of our framework. Our results have potential implications for exploring the dynamics of a large variety of spatially extended systems in biology and physics.Comment: 35 pages, 10 figures, and supplementary informatio

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

Probabilistic memory-one strategies to dominate the iterated prisoner’s dilemma over networks

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGThe Iterated Prisoner’s Dilemma (IPD) has been a classical game theoretical scenario used to model behaviour interactions among agents. From the famous Axelrod’s tournament, and the successful results obtained by the Tit for Tat strategy, to the introduction of the zerodeterminant strategies in the last decade, the game theory community has been exploring the performance of multiple strategies for years. This article grounds on such previous work, studying probabilistic memory-one strategies (PMO) and using evolutionary game theory, to analyse the criteria to find the most successful set of strategies in networked topologies. The results are nearly deterministic in discrete PMO scenarios. However, results become much more complex when moving to continuous ones, and there is no optimal strategy for a given scenario. Finally, this article describes how, using machine learning and evolutionary techniques; a cluster of agents, playing synchronously and adaptively, is able to dominate the rest of the populatio

Creative Thinking and Modelling for the Decision Support in Water Management

This paper reviews the state of art in knowledge and preferences elicitation techniques. The purpose of the study was to evaluate various cognitive mapping techniques in order to conclude with the identification of the optimal technique for the NetSyMod methodology. Network Analysis – Creative System Modelling (NetSyMod) methodology has been designed for the improvement of decision support systems (DSS) with respect to the environmental problems. In the paper the difference is made between experts and stakeholders knowledge and preference elicitation methods. The suggested technique is very similar to the Nominal Group Techniques (NGT) with the external representation of the analysed problem by means of the Hodgson Hexagons. The evolving methodology is undergoing tests within several EU-funded projects such as: ITAES, IISIM, NostrumDSS.Creative modelling, Cognitive mapping, Preference elicitation techniques, Decision support

Properties of interaction networks underlying the minority game

The minority game is a well-known agent-based model with no explicit interaction among its agents. However, it is known that they interact through the global magnitudes of the model and through their strategies. In this work we have attempted to formalize the implicit interactions among minority game agents as if they were links on a complex network. We have defined the link between two agents by quantifying the similarity between them. This link definition is based on the information of the instance of the game (the set of strategies assigned to each agent at the beginning) without any dynamic information on the game and brings about a static, unweighed and undirected network. We have analyzed the structure of the resulting network for different parameters, such as the number of agents ( N ) and the agent's capacity to process information ( m ) , always taking into account games with two strategies per agent. In the region of crowd effects of the model, the resulting networks structure is a small-world network, whereas in the region where the behavior of the minority game is the same as in a game of random decisions, networks become a random network of Erdos-Renyi. The transition between these two types of networks is slow, without any peculiar feature of the network in the region of the coordination among agents. Finally, we have studied the resulting static networks for the full strategy minority game model, a maximal instance of the minority game in which all possible agents take part in the game. We have explicitly calculated the degree distribution of the full strategy minority game network and, on the basis of this analytical result, we have estimated the degree distribution of the minority game network, which is in accordance with computational results.Fil: Caridi, Délida Inés. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin