  In two player bi-matrix games with partial monitoring, actions played are not
observed, only some messages are received. Those games satisfy a crucial
property of usual bi-matrix games: there are only a finite number of required
(mixed) best replies. This is very helpful while investigating sets of Nash
equilibria: for instance, in some cases, it allows to relate it to the set of
equilibria of some auxiliary game with full monitoring. In the general case,
the Lemke-Howson algorithm is extended and, under some genericity assumption,
its output are Nash equilibria of the original game. As a by product, we obtain
an oddness property on their number.
