Fitness-based models and pairwise comparison models of evolutionary games are typically different—even in unstructured populations

Abstract

The modeling of evolutionary game dynamics in finite populations requires microscopic processes that determine how strategies spread. The exact details of these processes are often chosen without much further consideration. Different types of microscopic models, including in particular fitnessbased selection rules and pairwise comparison dynamics, are often used as if they were interchangeable. We challenge this view and investigate how robust these choices on the micro-level really are. We focus on a key macroscopic quantity, the probability for a single mutant to take over a population of wild-type individuals. We show that even in unstructured populations there is only one pair of a fitness-based process and a pairwise comparison process leading to identical outcomes for arbitrary games and for all intensities of selection. This strong restriction is not relaxed even when the class of pairwise comparison processes is broadened. This highlights the perils of making arbitrary choices at the micro-level without regard of the consequences at the macro-level.

Fourier decomposition of payoff matrix for symmetric three-strategy games

“…One can easily evaluate the corresponding coefficients β(n) defined by Eq. (26). The straightforward calculation gives that all these coefficients differ from zero.…”

“…For such a type of payoff there is no direct interactions between the selfish and rational players for the noncooperative games. This type of interaction, however, becomes relevant for the so-called cooperative games when the players are allowed to collaborate with each other, as well as for evolutionary games when the strategy update is based on imitation [26]. The latter situations occur for games where…”

Evolutionary games played by multi-agent system with different memory capacity

“…Why and how cooperation among selfish and rational agents can persist in the presence of cheating and the cruel rule of 'survival of the fittest' driven by natural selection, remains a puzzling, fascinating and broad-ranging unsolved question in evolutionary biology [1][2][3][4][5][6]. Moreover, this interdisciplinary topic has also drawn plenty of attention, interest and research across disciplines, e.g., social sciences, behavioral sciences, psychology, physics, computer science, engineering and so on.…”

Extinction rates in tumor public goods games

“…Without the possibility of spontaneous mutation events, offspring carry the parent strategy. Evolutionary games have also been used extensively to study learning and pairwise comparison-based changes in strategy abundance in populations of potentially erroneous players [10,11,12].Selection in evolutionary games is based on the assumption that payoff translates into Darwinian fitness, which is a measure for an individual's contribution to the pool of offspring in the future. Complex deterministic dynamical systems arise when one considers very large populations of reproducing individuals.…”

“…Without the possibility of spontaneous mutation events, offspring carry the parent strategy. Evolutionary games have also been used extensively to study learning and pairwise comparison-based changes in strategy abundance in populations of potentially erroneous players [10,11,12].…”