Competing with oneself: Introducing self-interaction in a model of competitive learning

TL;DR

This paper extends a competitive learning model by incorporating individuals' own outcomes into their decision-making process, analyzing how this self-interaction influences the system's phase behavior and its relation to cooperative models.

Contribution

It introduces a self-interaction mechanism into an existing competitive learning model and explores its effects on phase diagrams and system dynamics.

Findings

Self-interaction alters phase diagrams systematically.

Different update rules lead to distinct system behaviors.

Connections to cooperative models are discussed.

Abstract

A competitive learning model was introduced in Ref. 1 (A. Mehta and J. M. Luck, Phys. Rev. E 60, 5, 1999), in which the learning is outcome-related. Every individual chooses between a pair of existing strategies or types, guided by a combination of two factors: tendency to conform to the local majority, \em{and} a preference for the type with higher perceived success \em{among its neighbors}, based on their relative outcomes. Here, an extension of the \em{interfacial model} of Ref. 1 is proposed, in which individuals additionally take into account their \em{own} outcomes in arriving at their outcome-based choices. Three possible update rules for handling bulk sites are considered. The corresponding phase diagrams, obtained at coexistence, show systematic departures from the original interfacial model. Possible relationships of these variants with the \em{cooperative model} of Ref. 1 are also touched upon.