  We define the incentive process, a natural generalization of the Moran
process incorporating evolutionary updating mechanisms corresponding to
well-known evolutionary dynamics, such as the logit, projection, and best-reply
dynamics. Fixation probabilities and internal stable states are given for a
variety of incentives, including new closed-forms, as well as results relating
fixation probabilities for members of two one-parameter families of incentive
processes. We show that the behaviors of the incentive process can deviate
significantly from the analogous properties of deterministic evolutionary
dynamics in some ways but are similar in others. For example, while the
fixation probabilities change, their ratio remains constant.
