An evolutionary game model for behavioral gambit of loyalists: Global awareness and risk-aversion

TL;DR

This paper models a three-agent class evolutionary game incorporating risk-loving and risk-averse behaviors, analyzing phase transitions influenced by global awareness and network topology.

Contribution

It introduces a novel risk-aversion strategy into a minority game, linking global awareness to payoff dynamics and phase transitions on various network structures.

Findings

Risk-aversion behavior affects phase transition points.

Global awareness influences the prevalence of indifferent agents.

Network topology impacts the dynamics and phase diagram.

Abstract

We study the phase diagram of a minority game where three classes of agents are present. Two types of agents play a risk-loving game that we model by the standard Snowdrift Game. The behaviour of the third type of agents is coded by {\em indifference} w.r.t. the game at all: their dynamics is designed to account for risk-aversion as an innovative behavioral gambit. From this point of view, the choice of this solitary strategy is enhanced when innovation starts, while is depressed when it becomes the majority option. This implies that the payoff matrix of the game becomes dependent on the global awareness of the agents measured by the relevance of the population of the indifferent players. The resulting dynamics is non-trivial with different kinds of phase transition depending on a few model parameters. The phase diagram is studied on regular as well as complex networks.