Cooperative bots exhibit nuanced effects on cooperation across strategic frameworks

TL;DR

This study explores how cooperative bots influence human cooperation across various strategic frameworks, revealing their effects depend on population structure and imitation strength, with nuanced impacts in continuous, mixed, and discrete strategies.

Contribution

It extends analysis of cooperative bots to continuous and mixed strategies, showing their varied effects on cooperation in structured and well-mixed populations.

Findings

Cooperative bots enhance cooperation under weak imitation.

They disrupt cooperation in structured populations with discrete and continuous strategies.

They facilitate cooperation with mixed strategies in structured populations.

Abstract

The positive impact of cooperative bots on cooperation within evolutionary game theory is well documented; however, existing studies have predominantly used discrete strategic frameworks, focusing on deterministic actions with a fixed probability of one. This paper extends the investigation to continuous and mixed strategic approaches. Continuous strategies employ intermediate probabilities to convey varying degrees of cooperation and focus on expected payoffs. In contrast, mixed strategies calculate immediate payoffs from actions chosen at a given moment within these probabilities. Using the prisoner's dilemma game, this study examines the effects of cooperative bots on human cooperation within hybrid populations of human players and simple bots, across both well-mixed and structured populations. Our findings reveal that cooperative bots significantly enhance cooperation in both population types across these strategic approaches under weak imitation scenarios, where players are less concerned with material gains. However, under strong imitation scenarios, while cooperative bots do not alter the defective equilibrium in well-mixed populations, they have varied impacts in structured populations across these strategic approaches. Specifically, they disrupt cooperation under discrete and continuous strategies but facilitate it under mixed strategies. These results highlight the nuanced effects of cooperative bots within different strategic frameworks and underscore the need for careful deployment, as their effectiveness is highly sensitive to how humans update their actions and their chosen strategic approach.