On a Unique Solution of the Stochastic Functional Equation Arising in Gambling Theory and Human Learning Process

Ali Turab,O M Kalthum S K Mohamed,Awad A Bakery,Wajahat Ali,Santosh Kumar

doi:10.1155/2022/1064803

Abstract

The term “learning” is often used to refer to a generally stable behavioral change resulting from practice. However, it is a fundamental biological capacity far more developed in humans than in other living beings. In an animal or human being, the learning phase may often be viewed as a series of choices between multiple possible reactions. Here, we analyze a specific type of human learning process related to gambling in which a subject inserts a poker chip to operate a two-armed bandit device and then presses one of the two keys. Through the use of an electromagnet, one or more poker chips are given to the individual in a container located in the apparatus’s center. If a chip is provided, it is declared a winner; otherwise, it is considered a loser. The goal of this paper is to look at the subject’s actions in such situations and provide a mathematical model that is appropriate for it. The existence of a unique solution to the suggested human learning model is examined using relevant fixed point results.

Highlights

Learning is a fundamental biological capacity that is much more evolved in humans than in any other living being
By considering the work presented in [6, 8, 9] and the above transition operators with their corresponding probabilities and events given in Table 4, we introduce the following functional equation, which can discuss all the aspects of the two-armed bandit model
We have discussed a special type of stochastic process related to the two-armed bandit experiment [15] which plays a vital role in observing the subject’s behavior in a two-choice situation

Summary

Introduction

Learning is a fundamental biological capacity that is much more evolved in humans than in any other living being. The central topic in learning philosophy is how multiple forms of learning take place in a human brain and body since this was explicitly formulated in the discipline of learning psychology, but with additional feedback from other psychological disciplines and the adjacent areas of sociology, pedagogy, and biology, including contemporary brain science. In modern mathematical learning experiments, the researchers concluded that a basic learning experiment was compatible with any stochastic process. It is not a novel concept (for detail, see [1]). The learning method egalitarian essence was a core feature of the developed model

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