General Properties of Long-Run Supergames

Abstract

Repeated games, Signals, Folk theorem,

Limit Equilibrium Payoffs in Stochastic Games

“…These results have been generalized in many ways to games with imperfectly observed actions (see e.g. Abreu et al [1], Fudenberg and Levine [5], Fudenberg, Levine and Maskin [6], Fudenberg et al [7], Lehrer [12,13,14], or Renault and Tomala [18,19]), but a full overview of that literature is beyond the scope of the present paper.…”

An achievable rate region for the broadcast wiretap channel with asymmetric side information

“…The fourth term (24) is lower bounded by the following quantity: −n(max[I(U 1 , U 2 ; S 1 , S 2 ) − I(U 1 , U 2 ; Z), 0] + 4ε). From the condition (16) and the definition of the sub-bins we have:…”

“…Therefore, in dynamic games with imperfect monitoring/observation, players observe the actions taken by other players through channels also called "signalling structure". An important challenge is to characterize the set of equilibrium utilities for a long-run game with imperfect monitoring; even in the case of repeated games, the problem of finding this set is still open [16]. This problem is closely related to the characterization of achievable rate regions for a class of channel models containing the one we investigate in this paper.…”

“…The reader is referred to the paper of Renault and Tomala [16] for more details about the model of repeated games with signals.…”

“…One of the messages of the present work is that, conversely, multiuser channels can be used to understand (dynamic) games with arbitrary observation structures and utility functions. This contributes to strengthen the links between Shannon theory and game theory and gives more momentum to some works in this direction such as [1] [16].…”