Three essays on bargaining and cheap talk

It is generally impossible to design an ex post efficient mechanism for bilateral trading when the traders' valuations for an object of trade are private, there are no outside subsidies and the traders can refuse to carry out a transaction if they expect to lose money. The first two essays focus on the problem of bilateral bargaining with multiple objects and private valuations, where efficiency loss can occur not only due to the failure to reach an agreement to trade when positive gains from trade exist, but also due to the failure to fully realize potential gains from trade because of selecting an ex post inefficient object (not the one with the largest spread between the traders' valuations). The problem is studied for general, as well as for the special class of trading mechanisms (k-double auctions), and also for simple and rich trading environments and under different assumptions about the information structure of the game. It is proposed to distinguish between fully ex post efficient mechanisms and the mechanisms, which are ex post efficient with respect to the object selection (given that trade occurs, the traders always select the best object, but trade does not always occur when gains from trade exist). In simple trading environments, the second best mechanism is always ex post efficient with respect to the object selection. For rich trading environments, the necessary conditions for the second-best mechanism to be ex post efficient with respect to the object selection are formulated. When the information structure is such that the optimal choice of the object depends on the private information of only one of the traders, it is always possible to design a mechanism that is ex post efficient with respect to the object selection.; The third essay develops an epistemic framework for the Sender-Receiver Cheap Talk Games that is used to formulate sufficient epistemic conditions for credible neologism (Farrell, 1985) and credible announcement (Matthews et al., 1991). It is shown that the players' knowledge of their opponents' rationality must be bounded in order for them to accept a message as credible neologism or as credible announcement.