Transforming Monitoring Structures with Resilient Encoders. Application to Repeated Games

TL;DR

This paper explores how an encoder can improve monitoring in dynamic games with arbitrary structures by compressing action profiles, even with unknown distributions and side information, enhancing game equilibrium analysis.

Contribution

It introduces a novel encoder design framework for arbitrary monitoring structures, accounting for unknown distributions and side information, with applications to repeated games.

Findings

Designed a source encoder for arbitrary monitoring with unknown distributions.

Achieved perfect monitoring in repeated prisoner's dilemma using the proposed encoding.

Provided a new information compression constraint for game-theoretic applications.

Abstract

An important feature of a dynamic game is its monitoring structure namely, what the players effectively see from the played actions. We consider games with arbitrary monitoring structures. One of the purposes of this paper is to know to what extent an encoder, who perfectly observes the played actions and sends a complementary public signal to the players, can establish perfect monitoring for all the players. To reach this goal, the main technical problem to be solved at the encoder is to design a source encoder which compresses the action profile in the most concise manner possible. A special feature of this encoder is that the multi-dimensional signal (namely, the action profiles) to be encoded is assumed to comprise a component whose probability distribution is not known to the encoder and the decoder has a side information (the private signals received by the players when the encoder is off). This new framework appears to be both of game-theoretical and information-theoretical interest. In particular, it is useful for designing certain types of encoders that are resilient to single deviations and provide an equilibrium utility region in the proposed setting; it provides a new type of constraints to compress an information source (i.e., a random variable). Regarding the first aspect, we apply the derived result to the repeated prisoner's dilemma.