Estimating Product Cannibalisation in Wholesale using Multivariate Hawkes Processes with Inhibition

TL;DR

This paper models product cannibalisation in wholesale markets using a multivariate Hawkes process with inhibition, addressing stability and implementation challenges within a Bayesian framework to better understand competitive effects.

Contribution

It introduces a novel Hawkes process with inhibition for modeling cannibalisation, along with new stability conditions and a Bayesian reparametrisation for dimension-independent inference.

Findings

Effective modeling of product cannibalisation dynamics.

New stability conditions for Hawkes processes with inhibition.

Bayesian framework enables scalable inference.

Abstract

Product cannibalisation in the marketplace refers to the decrease in the sales of one product due to competition from another product. We examine this phenomenon in a wholesale data set provided by an international company. We use a multivariate Hawkes process where each product is represented by a dimension, with cross-inhibition effects that model product cannibalisation. To implement the Hawkes process with inhibition we resolve challenges regarding the integration of the intensity function and introduce a new, stronger conditions for stability as existing conditions are unnecessarily strict under inhibition. We conduct our analysis in a Bayesian framework, for which we design a dimension-independent prior on the cross-inhibition based on a reparametrisation.