Adaptive bias for dissensus in nonlinear opinion dynamics with application to evolutionary division of labor games

TL;DR

This paper introduces an adaptive bias mechanism in nonlinear opinion dynamics combined with evolutionary games to control agent group allocations for maximizing collective rewards, validated through theoretical analysis and simulations.

Contribution

It proposes a novel model integrating NOD with evolutionary games and provides conditions for decentralized control of agent distribution.

Findings

Theoretical conditions for opinion control are established.

Simulation confirms effective adaptive bias in division of labor.

Model enhances autonomous task allocation strategies.

Abstract

This paper addresses the problem of adaptively controlling the bias parameter in nonlinear opinion dynamics (NOD) to allocate agents into groups of arbitrary sizes for the purpose of maximizing collective rewards. In previous work, an algorithm based on the coupling of NOD with an multi-objective behavior optimization was successfully deployed as part of a multi-robot system in an autonomous task allocation field experiment. Motivated by the field results, in this paper we propose and analyze a new task allocation model that synthesizes NOD with an evolutionary game framework. We prove sufficient conditions under which it is possible to control the opinion state in the group to a desired allocation of agents between two tasks through an adaptive bias using decentralized feedback. We then verify the theoretical results with a simulation study of a collaborative evolutionary division of labor game.