Evolutionary Game Theory

Evolutionary game theory developed as a means to predict the
expected distribution of individual behaviors in a biological system with a
single species that evolves under natural selection. It has long since expanded
beyond its biological roots and its initial emphasis on models based
on symmetric games with a finite set of pure strategies where payoffs result
from random one-time interactions between pairs of individuals (i.e. on matrix
games). The theory has been extended in many directions (including
non-random, multi-player or asymmetric interactions, and games with continuous
strategy (or trait) spaces) and has become increasingly important
for analyzing human and/or social behavior as well. This chapter initially
summarizes features of matrix games before showing how the theory changes
when the two-player game has a continuum of traits or interactions become
asymmetric. It’s focus is on the connection between static game-theoretic
solution concepts (e.g. ESS, CSS, NIS) and stable evolutionary outcomes
for deterministic evolutionary game dynamics (e.g. the replicator equation,
adaptive dynamics).