  This paper studies an instance of zero-sum games in which one player (the
leader) commits to its opponent (the follower) to choose its actions by
sampling a given probability measure (strategy). The actions of the leader are
observed by the follower as the output of an arbitrary channel. In response to
that, the follower chooses its action based on its current information, that
is, the leader's commitment and the corresponding noisy observation of its
action. Within this context, the equilibrium of the game with noisy action
observability is shown to always exist and the necessary conditions for its
uniqueness are identified. Interestingly, the noisy observations have important
impact on the cardinality of the follower's set of best responses. Under
particular conditions, such a set of best responses is proved to be a singleton
almost surely. The proposed model captures any channel noise with a density
with respect to the Lebesgue measure. As an example, the case in which the
channel is described by a Gaussian probability measure is investigated.
