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We study a variant of the principal-agent problem in which the principal does not directly observe the outcomes; rather, she gets a signal related to the agent’s action, according to a variable information structure. We provide simple necessary and sufficient conditions for implementability of an action and a utility profile by some information structure and the corresponding optimal contract — for a riskneutral or risk-averse agent, with or without the limited liability assumption. It turns out that the set of implementable utility profiles is characterized by simple thresholds on the utilities. 

The literature on strategic communication originated with the influential cheap talk model, which precedes the Bayesian persuasion model by three decades. This model describes an interaction between two agents: sender and receiver. The sender knows some state of the world which the receiver does not know, and tries to influence the receiver’s action by communicating a cheap talk message to the receiver. This paper initiates the algorithmic study of cheap talk in a finite environment (i.e., a finite number of states and receiver’s possible actions). We first prove that approximating the sender-optimal or the welfare-maximizing cheap talk equilibrium up to a certain additive constant or multiplicative factor is NP-hard. Fortunately, we identify three naturally-restricted cases that admit efficient algorithms for finding a sender-optimal equilibrium. These include a state-independent sender’s utility structure, a constant number of states or a receiver having only two actions.