A Game Theoretic Approach to Hyperbolic Consensus Problems

TL;DR

This paper applies conservation laws and game theory to develop and analyze strategies for multi-player consensus problems, providing theoretical foundations and numerical validation.

Contribution

It introduces a novel game theoretic framework for hyperbolic consensus problems using conservation laws, with well-posedness results and non-anticipative strategies.

Findings

Established well-posedness for the consensus game model

Developed a rigorous analytic definition of strategies

Validated strategies through numerical simulations

Abstract

We introduce the use of conservation laws to develop strategies in multi-player consensus games. First, basic well posedness results provide a reliable analytic setting. Then, a general non anticipative strategy is proposed through its rigorous analytic definitions and then tested by means of numerical integrations.