Every time the agent is facing a new choice, he polls his neighbors and gets some information. This succession of information can be used in different ways.
One way is to forget the information obtained at previous time steps and recompute at the next time step the utility function from the same initial priors. In this case the priors are not updated.
Another possibility is to memorize all the information
acquired at each time step by using as priors for
, 
and 
the posteriors
derived from equation 2 at the previous time step.
We call this choice maximum updating.
But 
increases in time as the total number of
polled opinions. The importance of the risk aversion parameter
is then rapidly decreasing. Furthermore,
agents using maximum updating would give the same importance
to old and new information and would tend to be overconfident
because the variance of the utility probability distribution
is constantly decreased. An image of such an agent would
be an obstinate old man that does not care any more about the present situation
and refers only to the old times. Maximum updating is thus fairly
insensitive to the variable changes in time and
does not fit well with dynamical processes.
An intermediate possibility is to decrease the relative importance
of older information. This is simply achieved by limiting the 
to a maximum value of 
. To see why
choosing an 
is equivalent to a short term memory,
let us suppose that several iterations have been made with
, in a neighborhood where the fraction 
of purchasers have not changed.
By iterating the utility expression (2) towards the past one obtains:
where l is the time difference between the past step and the present.
Utilities from the past are then
discounted by a factor 
at each time step, and since 
,
this corresponds to a decay time for memory of
. In other words limiting 
to
is somehow equivalent to limit the averaging process to the
most recent information.
The prior updating process is only performed on the internal
representation of the agents. It does not apply to the information
transmitted between the agents, when the main source
of uncertainty is the polling process itself. In equation 1,
always represent the initial average utility
of brand i. It is, of course, a constant of the simulation.