  In this paper, we study the conjunction of possibility measures when they are
interpreted as coherent upper probabilities, that is, as upper bounds for some
set of probability measures. We identify conditions under which the minimum of
two possibility measures remains a possibility measure. We provide graphical
way to check these conditions, by means of a zero-sum game formulation of the
problem. This also gives us a nice way to adjust the initial possibility
measures so their minimum is guaranteed to be a possibility measure. Finally,
we identify conditions under which the minimum of two possibility measures is a
coherent upper probability, or in other words, conditions under which the
minimum of two possibility measures is an exact upper bound for the
intersection of the credal sets of those two possibility measures.
