Mentors and Recombinators: Multi-Dimensional Social Learning

TL;DR

This paper introduces recombinator dynamics for multi-dimensional social learning in strategic games, analyzing how agents learn and combine different strategic dimensions from mentors, revealing new stable states and behaviors.

Contribution

It proposes a novel family of dynamics parameterized by recombination rate, extending traditional replicator dynamics to multi-dimensional learning scenarios.

Findings

Characterization of stationary states under recombinator dynamics

Identification of stable states and their properties

Prediction of novel behaviors in strategic applications

Abstract

We study games in which the set of strategies is multi-dimensional, and new agents might learn various strategic dimensions from different mentors. We introduce a new family of dynamics, the recombinator dynamics, which is characterised by a single parameter, the recombination rate r in [0,1]. The case of r = 0 coincides with the standard replicator dynamics. The opposite case of r = 1 corresponds to a setup in which each new agent learns each new strategic dimension from a different mentor, and combines these dimensions into her adopted strategy. We fully characterise stationary states and stable states under these dynamics, and we show that they predict novel behaviour in various applications.