  The original Hegselmann-Krause (HK) model is composed of a finite number of
agents characterized by their opinion, a number in $[0,1]$. An agent updates
its opinion via taking the average opinion of its neighbors whose opinion
differs by at most $\epsilon$ for $\epsilon>0$ a confidence bound. An agent is
absolutely stubborn if it does not change its opinion while update, and
absolutely open-minded if its update is the average opinion of its neighbors.
There are two types of HK models--the synchronous HK model and the asynchronous
HK model. The paper is about a variant of the HK dynamics, called the mixed
model, where each agent can choose its degree of stubbornness and mix its
opinion with the average opinion of its neighbors at all times. The mixed model
reduces to the synchronous HK model if all agents are absolutely open-minded
all the time, and the asynchronous HK model if only one uniformly randomly
selected agent is absolutely open-minded and the others are absolutely stubborn
at all times. In \cite{mhk}, we discuss the mixed model deterministically.
Point out some properties of the synchronous HK model, such as finite-time
convergence, do not hold for the mixed model. In this topic, we study the mixed
model nondeterministically. List some properties of the asynchronous model
which do not hold for the mixed model. Then, study circumstances under which
the asymptotic stability holds.
