# Preferential attachment graphs with co-existing types of different fitnesses

## TL;DR

This paper extends preferential attachment models to include competing types with different fitnesses, revealing various limiting behaviors and conditions under which one type dominates or coexists.

## Contribution

It introduces models with multiple fitness types in preferential attachment graphs and analyzes their asymptotic behaviors based on model parameters.

## Key findings

- Different limiting behaviors depending on model parameters.
- Existence of parameter regimes where both types can dominate.
- Conditions under which one type is favored or coexists.

## Abstract

We extend the work of Antunovi\'{c}, Mossel and R\'{a}cz on competing types in preferential attachment models to include cases where the types have different fitnesses, which may be either multiplicative or additive. We will show that, depending on the values of the parameters of the models, there are different possible limiting behaviours depending on the zeros of a certain function. In particular we will show the existence of choices of the parameters where one type is favoured both by having higher fitness and by the type attachment mechanism, but the other type has a positive probability of dominating the network in the limit.