  This paper provides a source coding theorem for multi-dimensional information
signals when, at a given instant, the distribution associated with one
arbitrary component of the signal to be compressed is not known and a side
information is available at the destination. This new framework appears to be
both of information-theoretical and game-theoretical interest: it provides a
new type of constraints to compress an information source; it is useful for
designing certain types of mediators in games and characterize utility regions
for games with signals. Regarding the latter aspect, we apply the derived
source coding theorem to the prisoner's dilemma and the battle of the sexes.
