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This paper establishes a connection between the notion of observation (ormonitoring) structure in game theory and the one of communication channels inShannon theory. One of the objectives is to know under which conditions anarbitrary monitoring structure can be transformed into a more pertinentmonitoring structure. To this end, a mediator is added to the game. Theobjective of the mediator is to choose a signalling scheme that allows theplayers to have perfect, almost perfect or public monitoring and all of this,at a minimum cost in terms of signalling. Graph coloring, source coding, andchannel coding are exploited to deal with these issues. A wireless powercontrol game is used to illustrate these notions but the applicability of theprovided results and, more importantly, the framework of transformingmonitoring structures go much beyond this example.

The price of re-establishing perfect, almost perfect or public monitoring in games with arbitrary monitoring