Polarized Population Under Imitation Dynamics in Complex Networks

Abstract

Evolutionary game theory is applied in a variety of settings, ranging from economics to socio-technical networks. The core concept in evolutionary game theory is evolutionary dynamics, which determines the composition of strategies in the population at steady state. Most evolutionary dynamics are modeled to descriptively showcase the utility derived from interactions between random pairs of players in well-mixed populations, or random pairs of neighbors in structured populations. In real-life social and socio-technical networks, it is more appropriate to evaluate a player’s utility as a collection of interactions with its neighbors. To understand this; in practice, people form opinions by means of observation and imitation, by not just one friend, but a collection of friends. This paper displays a variation of the pairwise imitation dynamics where players imitate the most well-off neighbor. This process is memory-less i.e., players only use the outcome of the current game to determine their strategies in subsequent games. Empirical results demonstrate that in real-life social networks, this imitation dynamic leads to a polarized population with games that have multiple pure strategy Nash equilibria such as the Stag-Hunt game and anti-coordination games like Hawk-Dove, where an "undecided" population indefinitely swings between two strategies.