Replicator dynamics for the game theoretic selection models based on state

TL;DR

This paper integrates classical replicator dynamics with a state-based approach, allowing individuals to change states or roles, and applies it to evolutionary game models like Hawk-Dove with role transitions.

Contribution

It introduces a novel framework combining replicator dynamics with state transitions, extending evolutionary game theory to include role and state changes in populations.

Findings

The new model generalizes demographic game models like Hawk-Dove.

Role changes influence population dynamics and feedback mechanisms.

Application to Owner-Intruder game demonstrates complex state-driven interactions.

Abstract

The paper contains the attempt to integration of the classical evolutionary game theory based on replicator dynamics and the state based approach of Houston and Mcnamara. In the new approach, individuals have different heritable strategies, however the individuals carrying the same strategy can differ on the state, role or situation in which they act. Thus, the classical replicator dynamics is completed by the additional subsystem of differential equations describing the dynamics of transitions between different states. In effect the interactions described by game structure, in addition to the demographic payoffs (constituted by births and deaths) can lead to the change of state of the competing individuals. The special cases of the new framework of stage structured models where the state changes describe developmental steps or aging are derived. New approach is illustrated by the example of Owner-Intruder game with explicit dynamics of the role changes. New model is the generalization of the demographic version of the Hawk-Dove game, the difference is that opponents in the game are drawn from two separate subpopulations consisting of Owners and Intruders. Intruders check random nest sites, and play the Hawk-Dove game with the Owner if they are occupied. Interesting feedback mechanism is produced by fluxes of individuals between subpopulations. Owners produce newborns which become Intruders, since they should find a free nest site to reproduce.