The price of re-establishing perfect, almost perfect or public monitoring in games with arbitrary monitoring

TL;DR

This paper explores how to transform arbitrary game monitoring structures into more ideal forms using communication theory techniques, aiming to minimize signaling costs while improving observation quality.

Contribution

It introduces a framework connecting game monitoring with Shannon theory, enabling the transformation of monitoring structures via a mediator with minimal signaling costs.

Findings

Established conditions for transforming monitoring structures

Applied graph coloring, source coding, and channel coding techniques

Demonstrated framework with a wireless power control game

Abstract

This paper establishes a connection between the notion of observation (or monitoring) structure in game theory and the one of communication channels in Shannon theory. One of the objectives is to know under which conditions an arbitrary monitoring structure can be transformed into a more pertinent monitoring structure. To this end, a mediator is added to the game. The objective of the mediator is to choose a signalling scheme that allows the players to have perfect, almost perfect or public monitoring and all of this, at a minimum cost in terms of signalling. Graph coloring, source coding, and channel coding are exploited to deal with these issues. A wireless power control game is used to illustrate these notions but the applicability of the provided results and, more importantly, the framework of transforming monitoring structures go much beyond this example.