We examine the classic "Beer-Quiche" game from Cho and Kreps (1987), and relax the assumption that the order placed by the sender is completely observable. Under the optimal degree of transparency, the receiver achieves a higher payoff than with full transparency. Partial obfuscation of the sender's choice encourages separation: committing to a less informative signal about the sender's choice affects the endogenous information generation process such that the receiver thereby secures himself more information.
We study (costless) information transmission from a job applicant to an employer who must decide whether to hire him and, if so, which position to give him. We construct equilibrium payoffs requiring at least two signaling steps, or even that no deadline be imposed on the (plain) conversation. The set of communication equilibrium payoffs (achieved with the help of a communication device) is larger than the set of equilibrium payoffs of the plain conversation game but coincides with the set of correlated equilibrium payoffs. We compare three common dispute resolution processes – negotiation, mediation, and arbitration – in the framework of Crawford and Sobel [V. Crawford, J. Sobel, Strategic information transmission, Econometrica 50 (6) (1982) 1431–1451]. Under negotiation, the two parties engage in (possibly arbitrarily long) face-to-face cheap talk. Under mediation, the parties communicate with a neutral third party who makes a non-binding recommendation. Under arbitration, the two parties commit to conform to the third party recommendation. We characterize and compare the optimal mediation and arbitration procedures. Both mediators and arbitrators should optimally filter information, but mediators should also add noise to it. We find that unmediated negotiation performs as well as mediation if and only if the degree of conflict between the parties is low. In the Crawford-Sobel (uniform, quadratic utility) cheap-talk model, we consider a simple mediation scheme (a communication device) in which the informed agent reports one of N possible elements of a partition to the mediator and then the mediator suggests one of N actions to the uninformed decision-maker according to the probability distribution of the device. We show that such a simple mediated equilibrium cannot improve upon the unmediated N-partition Crawford-Sobel equilibrium when the preference divergence parameter (bias) is small. This paper investigates communication between an informed expert and an uninformed principal via a strategic mediator. We demonstrate that, for any bias in the parties' preferences, there exists a strategic mediator that provides the highest expected payoff to the principal, as if the players had communicated through an optimal non-strategic mediator.