Repeated games with local monitoring and private communication

I consider repeated games with local monitoring: each player observes his neighbors' moves only. Hence, monitoring is private and imperfect. I assume local and public communication: communication is restricted to neighbors, and each player sends the same message to each of his neighbors at each stage. Both communication and monitoring structures are given by the network. The solution concept is perfect Bayesian equilibrium. In the four-player case, a folk theorem holds if and only if the network is 2-connected. Some examples are given for games with more than four players

Repeated games and networks

The chapter provides an overview of recent results on infinitely repeated games in which monitoring and interactions are local. The chapter surveys Folk Theorems for games with local monitoring, and results characterizing optimal punishments in separable local public goods games. The relationship between the monitoring structure and the equilibrium correspondence is a key topic of enquiry. Results clarify the roles played by contagion, ostracism, and communication in shaping equilibrium outcomes. Understanding how network measures of social cohesion and of information diffusion can affect trust in communities is the main applied aim of the literature.</p

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

Fault Reporting in Partially Known Networks and Folk Theorems

International audienceWe consider a group of players who perform tasks repeatedly. The players are nodes of a communication network and observe their neighbors' actions. Players have partial knowledge of the network and only know their set of neighbors. We study the existence of protocols for fault reporting: whenever a player chooses a faulty action, the communication protocol starts and the output publicly reveals the identity of the faulty player. We consider two setups. In the first one, players do not share authentication keys. We show that existence of a protocol for fault reporting is equivalent to the 2-vertex-connectedness of the network: no single vertex deletion disconnects the graph. In the second setup, we allow players to share authentication keys. We show that existence of a distribution of the keys and of a protocol for fault reporting is equivalent to the 2-edge-connectedness of the network: no single edge deletion disconnects the graph. We give applications to the implementation of socially optimal outcomes in repeated games