A game of information

2026-06-14

AI Summary

This study addresses an adversarial communication scenario in which two transmitters, operating over a noisy channel, strategically select signal-to-noise ratios to induce opposing inferences at a common receiver. The problem is formulated as a two-player infinite game and, for the first time, recast as a continuous game defined over the unit square. By integrating tools from both game theory and information theory, the authors derive a complete characterization of the Nash equilibrium. Furthermore, they propose three generalized formulations that extend the core model, thereby establishing a foundational theoretical framework and an analytically tractable approach for studying adversarial information transmission.

Abstract

A game of information concerns two players transmitting messages that are obscured by noise. A receiver digests the combination of the two information sources and makes an assessment rationally. The aim of the players is to generate opposing assessments for the receiver by choosing signal-to-noise ratios of their information. It is shown that this problem can be reduced into an elementary infinite game on the square, thus admitting a complete equilibrium solution. Three generalisations of the game are proposed.

Problem

• information game
• signal-to-noise ratio
• opposing assessments
• noisy communication
• receiver evaluation

Innovation

• information game
• signal-to-noise ratio
• infinite game
• equilibrium solution
• game theory