  Many multiagent dynamics, including various collective dynamics occurring on
networks, can be modeled as a stochastic process in which the agents in the
system change their state over time in interaction with each other. The
Gillespie algorithms are popular algorithms that exactly simulate such
stochastic multiagent dynamics when each state change is driven by a discrete
event, the dynamics is defined in continuous time, and the stochastic law of
event occurrence is governed by independent Poisson processes. In the first
main part of this volume, we provide a tutorial on the Gillespie algorithms
focusing on simulation of social multiagent dynamics occurring in populations
and networks. We do not assume advanced knowledge of mathematics (or computer
science or physics). We clarify why one should use the continuous-time models
and the Gillespie algorithms in many cases, instead of easier-to-understand
discrete-time models. In the remainder of this volume, we review recent
extensions of the Gillespie algorithms aiming to add more reality to the model
(i.e., non-Poissonian cases) or to speed up the simulations.

Physics and Society;Social and Information Networks