Elephant random walk with attributed steps and extractions of random sizes
Sooraj M, Moumanti Podder, Archi Roy

TL;DR
This paper models a market with customers choosing between two products based on sampled past customer choices and satisfaction, analyzing the resulting stochastic process as a variant of the elephant random walk.
Contribution
It introduces a novel market model linked to elephant random walk dynamics, analyzing convergence properties of the sales performance ratio.
Findings
Almost sure convergence of sales ratio S_n/n.
Distributional convergence depends on the regime.
The model captures complex customer choice dynamics.
Abstract
We study a model of market economics wherein the -st customer, for each , with being a prespecified positive integer, draws a sample of (random) size , either with replacement or without, from the customers of the past. Each sampled customer is queried as to which of the two products, A and B, available in the oligopolistic market, they chose, and whether they are satisfied or not with their choice. The -st customer now employs a stochastic rule, based on the information collected from the sampled customers, to decide which of the two products to buy. The probability that a customer is satisfied with the product they have purchased equals when the product is A, and when it is B, independent of all else. The resulting stochastic process may be represented as a variant of the celebrated elephant random walk, with the relative…
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