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SUMMARY:Individual and network heterogeneity in agent-based models
DTSTART;VALUE=DATE-TIME:20170908T070000Z
DTEND;VALUE=DATE-TIME:20170908T073000Z
DTSTAMP;VALUE=DATE-TIME:20230207T214200Z
UID:indico-contribution-41@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Raul Toral (IFISC)\n\nMost applications of Statistic
al Mechanics methods to agent-based models make assumptions that aim at a
simplification of the mathematical treatment and which are reasonable\, or
well established\, in other applications of the field. Amongst others\, w
e can cite the assumption of the thermodynamic limit and the assumption th
at there is a high degree of homogeneity amongst the agents. This is certa
inly not true in most cases: the number of agents is never close to the Av
ogadro number and the dispersion in the individual features of agents is a
n unavoidable nature of the system. In this talk I will discuss some diffi
culties associated to the existence of such a heterogeneity and the mathem
atical tools that can be used to achieve analytical results. As an example
\, I will consider in detail both network and parametric heterogeneity in
Kirmanâ€™s model for herding behavior in financial markets. Stylized facts
of financial markets (fat tails\, volatility clustering) has been propose
d as an emergent phenomenon of interactions among traders. One of the simp
lest agent-based models capable of reproducing these statistical propertie
s is the one proposed by Kirman. The fundamental aspect of the model is th
at agents change opinion based on the proportion of neighbor agents holdin
g it. The effect of network structure on the results of the model is also
addressed with recent analytical tools known as heterogeneous mean field a
pproximations. This approach suggests that the dynamics in an heterogeneou
s degree network is equivalent to the usual all-to-all approximation with
an effective system size $N_{\\textrm{eff}}=N \\mu_{1}^2/\\mu_{2}$\, where
$\\mu_{k}$ is the *k*-th moment of the degree distribution. This implies
that highly heterogeneous degree networks are characterized by a low effec
tive population number. Intuitively\, only highly connected agents play an
important role in the dynamics and the number of those agents is measured
by this effective population number. Taking into account that most real n
etworks are highly heterogeneous with power-law degree distributions\, one
concludes that the effect finite-size fluctuations is non-trivial and mus
t be studied in detail for each specific type of network.\n\nhttps://zakop
ane.if.uj.edu.pl/event/4/contributions/41/
RELATED-TO:indico-event-4@zakopane.if.uj.edu.pl
URL:https://zakopane.if.uj.edu.pl/event/4/contributions/41/
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