Essays on auctions, mechanism design, and repeated games

Chapter 1 revisits the classic mechanism design question of when buyers with private information in an auction setting can expect to receive economic rents. It is well known that under standard assumptions, the seller can fully extract rent for generic prior distributions over the valuations of the buyers. However, a crucial assumption underlying this result is that the buyers are not able to acquire any additional information about each other. This assumption can be seen as a special case of a general model where buyers have access to some information acquisition technology. We provide necessary and sufficient conditions on the information acquisition technology for the seller to be able to guarantee full rent extraction. Chapter 2 studies auctions when there is ambiguity over the joint information structures generating the valuations and signals of players. We analyse how two standard auction effects interact with ambiguity. First, a ‘competition effect’ arises when different beliefs about the correlation between bidders’ valuations imply different likelihoods of facing competitive bids. Second, a ‘winner’s value effect’ arises when different beliefs imply different inferences about the winner’s value. In private value auctions, only the first effect exists, and the distribution of bids first order stochastically dominates the distribution of bids in the absence of ambiguity. In common value auctions both effects exist, and the seller’s revenue decreases with ambiguity. Chapter 3 characterises the equilibrium payoff set of a repeated game with local interaction and local monitoring. A Nash threats folk theorem holds without any restrictions on the network structure when players are arbitrarily patient, i.e. any feasible payoff above the Nash equilibrium point can be approximated arbitrarily well in sequential equilibrium. When players discount the future, the folk theorem cannot hold unless further restrictions are made either on payoffs or the network structure.