10,012 research outputs found
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
Self-Organizing Traffic at a Malfunctioning Intersection
Traffic signals and traffic flow models have been studied extensively in the past and have provided valuable insights on the design of signalling systems, congestion control, and punitive policies. This paper takes a slightly different tack and describes what happens at an intersection where the traffic signals are malfunctioning and stuck in some configuration. By modelling individual vehicles as agents, we were able to replicate the surprisingly organized traffic flow that we observed at a real malfunctioning intersection in urban India. Counter-intuitively, the very lawlessness that normally causes jams was causing traffic to flow smoothly at this intersection. We situate this research in the context of other research on emergent complex phenomena in traffic, and suggest further lines of research that could benefit from the analysis and modelling of rule-breaking behaviour.Self-Organizing Systems, Complex Systems, Traffic, Emergent Behaviour, Agent-Based Modelling, Rule-Breaking
On the Connectivity of Unions of Random Graphs
Graph-theoretic tools and techniques have seen wide use in the multi-agent
systems literature, and the unpredictable nature of some multi-agent
communications has been successfully modeled using random communication graphs.
Across both network control and network optimization, a common assumption is
that the union of agents' communication graphs is connected across any finite
interval of some prescribed length, and some convergence results explicitly
depend upon this length. Despite the prevalence of this assumption and the
prevalence of random graphs in studying multi-agent systems, to the best of our
knowledge, there has not been a study dedicated to determining how many random
graphs must be in a union before it is connected. To address this point, this
paper solves two related problems. The first bounds the number of random graphs
required in a union before its expected algebraic connectivity exceeds the
minimum needed for connectedness. The second bounds the probability that a
union of random graphs is connected. The random graph model used is the
Erd\H{o}s-R\'enyi model, and, in solving these problems, we also bound the
expectation and variance of the algebraic connectivity of unions of such
graphs. Numerical results for several use cases are given to supplement the
theoretical developments made.Comment: 16 pages, 3 tables; accepted to 2017 IEEE Conference on Decision and
Control (CDC
Network models of innovation and knowledge diffusion
Much of modern micro-economics is built from the starting point of the perfectly competitive market. In this model there are an infinite number of agents — buyers and sellers, none of whom has the power to influence the price by his actions. The good is well-defined, indeed it is perfectly standardized. And any interactions agents have is mediated by the market. That is, all transactions are anonymous, in the sense that the identities of buyer and seller are unimportant. Effectively, the seller sells “to the market” and the buyer buys “from the market”. This follows from the standardization of the good, and the fact that the market imposes a very strong discipline on prices. Implicit here is one (or both) of two assumptions. Either all agents are identical in every relevant respect, apart, possibly, from the prices they ask or offer; or every agent knows every relevant detail about every other agent. If the former, then obviously my only concern as a buyer is the prices asked by the population of sellers since in every other way they are identical. If the latter, then each seller has a unique good, and again what I am concerned with is the price of it. In either case, we see that prices capture all relevant information and are enough for every agent to make all the decisions he needs to make....economics of technology ;
Ultrafast Consensus in Small-World Networks
In this paper, we demonstrate a phase transition phenomenon in algebraic connectivity of small-world networks. Algebraic connectivity of a graph is the second smallest eigenvalue of its Laplacian matrix and a measure of speed of solving consensus problems in networks. We demonstrate that it is possible to dramatically increase the algebraic connectivity of a regular complex network by 1000 times or more without adding new links or nodes to the network. This implies that a consensus problem can be solved incredibly fast on certain small-world networks giving rise to a network design algorithm for ultra fast information networks. Our study relies on a procedure called "random rewiring" due to Watts & Strogatz (Nature, 1998). Extensive numerical results are provided to support our claims and conjectures. We prove that the mean of the bulk Laplacian spectrum of a complex network remains invariant under random rewiring. The same property only asymptotically holds for scale-free networks. A relationship between increasing the algebraic connectivity of complex networks and robustness to link and node failures is also shown. This is an alternative approach to the use of percolation theory for analysis of network robustness. We also show some connections between our conjectures and certain open problems in the theory of random matrices
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