Conditions for Altruistic Perversity in Two-Strategy Population Games

TL;DR

This paper investigates the conditions under which altruistic behavior in two-strategy population games can lead to worse societal outcomes, revealing that convex social welfare and large altruistic groups are key factors.

Contribution

It provides a comprehensive analysis of the conditions causing altruistic perversity, linking game properties to altruistic impact in population dynamics.

Findings

Altruistic perversity occurs only with convex social welfare functions.

A sufficiently large altruistic sub-population is necessary for perversity.

The study connects agent interaction properties to societal outcomes.

Abstract

Self-interested behavior from individuals can collectively lead to poor societal outcomes. These outcomes can seemingly be improved through the actions of altruistic agents, which benefit other agents in the system. However, it is known in specific contexts that altruistic agents can actually induce worse outcomes compared to a fully selfish population -- a phenomenon we term altruistic perversity. This paper provides a holistic investigation into the necessary conditions that give rise to altruistic perversity. In particular, we study the class of two-strategy population games where one sub-population is altruistic and the other is selfish. We find that a population game can admit altruistic perversity only if the associated social welfare function is convex and the altruistic population is sufficiently large. Our results are a first step in establishing a connection between properties of nominal agent interactions and the potential impacts from altruistic behaviors.