Incentive Processes in Finite Populations

TL;DR

This paper introduces the incentive process, a generalized evolutionary model that extends the Moran process by incorporating various incentive mechanisms, providing new formulas for fixation probabilities and analyzing their behaviors compared to deterministic dynamics.

Contribution

It defines the incentive process, derives new closed-form fixation probabilities, and compares stochastic incentives with deterministic evolutionary dynamics.

Findings

Fixation probabilities are derived for various incentives.

The ratio of fixation probabilities remains constant across incentive processes.

Behavioral deviations from deterministic dynamics are identified.

Abstract

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.