875 research outputs found
Adaptive cyclically dominating game on co-evolving networks: Numerical and analytic results
A co-evolving and adaptive Rock (R)-Paper (P)-Scissors (S) game (ARPS) in
which an agent uses one of three cyclically dominating strategies is proposed
and studied numerically and analytically. An agent takes adaptive actions to
achieve a neighborhood to his advantage by rewiring a dissatisfying link with a
probability or switching strategy with a probability . Numerical
results revealed two phases in the steady state. An active phase for
has one connected network of agents using different
strategies who are continually interacting and taking adaptive actions. A
frozen phase for has three separate clusters of agents using
only R, P, and S, respectively with terminated adaptive actions. A mean-field
theory of link densities in co-evolving network is formulated in a general way
that can be readily modified to other co-evolving network problems of multiple
strategies. The analytic results agree with simulation results on ARPS well. We
point out the different probabilities of winning, losing, and drawing a game
among the agents as the origin of the small discrepancy between analytic and
simulation results. As a result of the adaptive actions, agents of higher
degrees are often those being taken advantage of. Agents with a smaller
(larger) degree than the mean degree have a higher (smaller) probability of
winning than losing. The results are useful in future attempts on formulating
more accurate theories.Comment: 17 pages, 4 figure
Error-driven Global Transition in a Competitive Population on a Network
We show, both analytically and numerically, that erroneous data transmission
generates a global transition within a competitive population playing the
Minority Game on a network. This transition, which resembles a phase
transition, is driven by a `temporal symmetry breaking' in the global outcome
series. The phase boundary, which is a function of the network connectivity
and the error probability , is described quantitatively by the
Crowd-Anticrowd theory.Comment: 4 pages, 3 figure
Internal character dictates phase transition dynamics between isolation and cohesive grouping
We show that accounting for internal character among interacting,
heterogeneous entities generates rich phase transition behavior between
isolation and cohesive dynamical grouping. Our analytical and numerical
calculations reveal different critical points arising for different
character-dependent grouping mechanisms. These critical points move in opposite
directions as the population's diversity decreases. Our analytical theory helps
explain why a particular class of universality is so common in the real world,
despite fundamental differences in the underlying entities. Furthermore, it
correctly predicts the non-monotonic temporal variation in connectivity
observed recently in one such system
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