Strategic tradeoffs in competitor dynamics on adaptive networks

Laurent Hébert-Dufresne,Eric Libby,Pierre-André Noël,Antoine Allard,Jean-Gabriel Young

doi:10.1038/s41598-017-07621-x

Abstract

Recent empirical work highlights the heterogeneity of social competitions such as political campaigns: proponents of some ideologies seek debate and conversation, others create echo chambers. While symmetric and static network structure is typically used as a substrate to study such competitor dynamics, network structure can instead be interpreted as a signature of the competitor strategies, yielding competition dynamics on adaptive networks. Here we demonstrate that tradeoffs between aggressiveness and defensiveness (i.e., targeting adversaries vs. targeting like-minded individuals) creates paradoxical behaviour such as non-transitive dynamics. And while there is an optimal strategy in a two competitor system, three competitor systems have no such solution; the introduction of extreme strategies can easily affect the outcome of a competition, even if the extreme strategies have no chance of winning. Not only are these results reminiscent of classic paradoxical results from evolutionary game theory, but the structure of social networks created by our model can be mapped to particular forms of payoff matrices. Consequently, social structure can act as a measurable metric for social games which in turn allows us to provide a game theoretical perspective on online political debates.

Highlights

Fixed resources drive competition and non-linear dynamics in socio-biological systems[1,2,3,4,5,6,7,8]
Using the directed stochastic block model (SBM) to encode these strategies[15], we extend the MP and voter model (VM) dynamics to an adaptive network structure to study the effects of strategic decisions
We obtain general analytical solutions for the voter model dynamics and investigate specific cases with tradeoffs between aggressiveness and defensiveness. We show that these tradeoffs yield interesting, and even paradoxical, behaviors such as long transient dynamics, sensitive dependence to initial conditions, and non-transitive dynamics. These results are reminiscent of classic voting paradoxes and are known results from evolutionary game theory; the SBM allows us to directly map the social structure created by our model to particular cases of payoff matrices in game theory

Summary

Introduction

Fixed resources drive competition and non-linear dynamics in socio-biological systems[1,2,3,4,5,6,7,8]. Barberá et al studied 150 million tweets on Twitter to determine how often online political discussions were debates as opposed to echo chambers where like-minded people voice a shared opinion[12]. We obtain general analytical solutions for the voter model dynamics and investigate specific cases with tradeoffs between aggressiveness and defensiveness (i.e., targeting adversaries vs targeting like-minded individuals) We show that these tradeoffs yield interesting, and even paradoxical, behaviors such as long transient dynamics, sensitive dependence to initial conditions, and non-transitive dynamics. We show how we can use our model to infer different dynamical regimes from empirical observations of activities on Twitter and interpret the resulting network structure as a signature of competitor strategies

Methods

Results

Conclusion