The Repeated Prisoner’s Dilemma in a Network

Imperfect private monitoring in an infinitely repeated discounted Prisoner’s Dilemma played on a communication network is studied. Players observe their direct neighbors’ behavior only, but communicate strategically the repeated game’s history throughout the network. The delay in receiving this information requires the players to be more patient to sustain the same level of cooperation as in a complete network, although a Folk Theorem obtains when the players are patient enough. All equilibria under exogenously imposed truth-telling extend to strategic communication, and additional ones arise due to richer communication. There are equilibria in which a player lies. The flow of information is related with network centrality measures.Repeated Game, Prisoner’s Dilemma, Imperfect Private Monitoring, Network, Strategic Communication, Centrality

Repeated Games with Voluntary Information Purchase

We consider discounted repeated games in which players can voluntarily purchase information about the opponents’ actions at past stages. Information about a stage can be bought at a fixed but arbitrary cost. Opponents cannot observe the information purchase by a player. For our main result, we make the usual assumption that the dimension of the set FIR of feasible and individually rational payoff vectors is equal to the number of players. We show that, if there are at least three players and each player has at least four actions, then every payoff vector in the interior of the set FIR can be achieved by a Nash equilibrium of the discounted repeated game if the discount factor is sufficiently close to 1. Therefore, nearly efficient payoffs can be achieved even if the cost of monitoring is high. We show that the same result holds if there are at least four players and at least three actions for each player. Finally, we indicate how the construction can be extended to sequential equilibrium.mathematical economics;

Repeated Games Played in a Network

Delayed perfect monitoring in an infinitely repeated discounted game is modelled by letting the players form a connected and undirected network. Players observe their immediate neighbors' behavior only, but communicate over time the repeated game's history truthfully throughout the network. The Folk Theorem extends to this setup, although for a range of discount factors strictly below 1, the set of sequential equilibria and the corresponding payoff set may be reduced. A general class of games is analyzed without imposing restrictions on the dimensionality of the payoff space. This and the bilateral communication structure allow for limited results under strategic communication only. As a by-product this model produces a network result; namely, the level of cooperation in this setup depends on the network's diameter, and not on its clustering coefficient as in other models.Repeated Game, Network, Delayed Perfect Monitoring, Communication

Repeated Games Played in a Network

Delayed perfect monitoring in an infinitely repeated discounted game is modelled by allocating the players to a connected and undirected network. Players observe their immediate neighbors’ behavior only, but communicate over time the repeated game’s history truthfully throughout the network. The Folk Theorem extends to this setup, although for a range of discount factors strictly below 1, the set of sequential equilibria and the corresponding payoff set may be reduced. A general class of games is analyzed without imposing restrictions on the dimensionality of the payoff space. Due to this and the bilateral communication structure, truthful communication arises endogenously only under additional conditions. The model also produces a network result; namely, the level of cooperation in this setup depends on the network’s diameter, and not on its clustering coefficient as in other models.Repeated Game, Delayed Perfect Monitoring, Network, Communication

The folk theorem for repeated games with observation costs

This paper studies repeated games with private monitoring where players make optimal decisions with respect to costly monitoring activities, just as they do with respect to stage-game actions. We consider the case where each player can observe other players' current-period actions accurately only if he incurs a certain level of disutility. In every period, players decide whether to monitor other players and whom to monitor. We show that the folk theorem holds for any finite stage game that satisfies the standard full dimensionality condition and for any level of observation costs. The theorem also holds under general structures of costless private signals and does not require explicit communication among the players. Therefore, tacit collusion can attain efficient outcomes in general repeated games with private monitoring if perfect private monitoring is merely feasible, however costly it may be

Repeated games played in a network

Delayed perfect monitoring in an infinitely repeated discounted game is modelled by letting the players form a connected and undirected network. Players observe their immediate neighbors' behavior only, but communicate over time the repeated game's history truthfully throughout the network. The Folk Theorem extends to this setup, although for a range of discount factors strictly below 1, the set of sequential equilibria and the corresponding payoff set may be reduced. A general class of games is analyzed without imposing restrictions on the dimensionality of the payoff space. This and the bilateral communication structure allow for limited results under strategic communication only. As a by-product this model produces a network result; namely, the level of cooperation in this setup depends on the network's diameter, and not on its clustering coefficient as in other models

Giving Gossips Their Due: Information Provision in Games with Private Monitoring

The ability of a long-lived seller to maintain and profit from a good reputation may induce her to provide high quality or effort despite short-run incentives to the contrary. This incentive remains in place with private monitoring, provided that buyers share their information. However, this assumption is unrealistic in environments where information sharing is costly or the beneficiaries of a buyer’s sharing are strangers. I study a simple mechanism that induces costly information provision, and may explain such behavior in environments where the incentives are not overt. Agents who possess information may share it with the community and acquire a reputation for gossiping. Reputations function in tandem: sellers provide high effort because they face agents with reputations for information sharing, and expect the outcome of their dealings will be made public, while information holders share their information as a reputation for doing so results in higher effort from sellers.reputation, moral hazard, information sharing, mechanism design