Folk Theorem with a Continuum of Public Signals

Failure of gradualism under imperfect monitoring

“…However they depart from the Green and Porter [9] model by restricting attention to a finite set of actions. More recently Ishii [11] proves the folk theorem with a finite numbers of actions and a continuum of signals, and generalizes the full rank condition of Fudenberg et al [7].…”

“…We follow the model of Lockwood and Thomas [12] and add the assumption that actions are not perfectly monitored. We start with the properties of the stage game, which has the structure of a Prisoner's Dilemma with continuous actions: Players choose a level of contribution (for example to a public project) in R + .…”

“…The main insight from the literature on irreversibility (see for example Marx and Matthews [13] and Lockwood and Thomas [12]) is that cooperation has to occur gradually over time. This is because with irreversibility threats to return to a non-cooperative outcome are no longer feasible and instead punishments must consist in the withdrawal of future increases in cooperation, which implies gradualism.…”

“…In this paper we consider a repeated Prisoner's Dilemma with continuous actions in which actions are irreversible, as in Lockwood and Thomas [12], and introduce imperfect public monitoring in the model. Actions are interpreted as total contributions to a public project and irreversibility implies that past contributions are not refundable.…”

“…They construct an approximately efficient subgame-perfect equilibrium when there is little discounting. Lockwood and Thomas [12] study a similar setting, with no extra benefit, and characterize the efficient symmetric equilibrium path for any discount factor by means of a second-order difference equation. Gale [8] introduces the notion of monotone games with positive spillovers, a more general setting, and studies the case without discounting.…”