Characterization of a class of moral-hazard, adverse selection games

Studying a principal-agent game in which the agent alone observes the state of the world and reports it, but the moral hazard is not reducible, shows that, if the principal uses all signals, then no solution exists, i.e. there is no contract that elicits truth-telling and motivates the agent to exert effort. When the principal does not use signals on the state of the world that seem irrelevant, a solution exists in which some of the ex post signals on outcome are not used, even though they obey the informativeness condition of Holmstrom (Bell Journal of Economics, 1979, 10, 74-91).