Strategic insights and simulation analysis in coalitional game theory for edge computing coinvestment.

Abstract

This thesis explores the application of cooperative game theory to optimize resource allocation by conducting an in-depth analysis of the academic article ”Coalitional Game Theoretical Approach to Coinvestment with Application to Edge Computing,” focusing on identifying and validating the theoretical properties of the proposed model, exploring implications for software implementation, and proposing extensions to improve its applicability and effectiveness. The referenced article studies how different stakeholders, specifically a Network Owner (who controls the infrastructure) and multiple Service Providers (who use this infrastructure to deliver services), can jointly invest in shared resources, such as computational capacity in Edge Computing. The article proposes a cooperative game theoretical model that determines how stakeholders should allocate resources optimally, share investment costs, and fairly distribute revenues among themselves based on each stakeholder’s contribution. The main analysis is structured in two stages. In the first stage, we examine the original model and identify possible simplifications that significantly reduce its computational complexity, transforming it from a non-deterministic exponential time problem into one deterministic and solvable in linear time. These simplifications will preserve the exact results. Additionally, we highlight constraints that were overlooked in the original formulation, enhancing the theoretical accuracy of the model. Furthermore, we study the risks arising from inaccuracies or incorrect estimates in critical parameters, offering simplified analytical equations that stakeholders can use to quantify and evaluate the potential impact of these errors on their expected outcomes. In the second stage, we propose alternative utility functions specifically designed to address the limitations identified in the original model, particularly its reduced applicability to realistic scenarios. These alternative functions are systematically studied and compared to evaluate their implications for resource allocation and incentive compatibility. Additionally, we introduce model extensions that optimize resource allocation under more realistic conditions; however, these enhancements result in increased computational complexity. Both main stages of this thesis follow a structured approach composed of two complementary parts. The first part is theoretical, involving an analytical study of the model, its parameters, and the derived equations. The second part is practical, providing empirical evidence through numerical simulations and sensitivity analyses. These simulations illustrate theoretical insights and help to evaluate the effects of varying utility function parameters. For the purpose of conducting a systematic study, the model is implemented and the results of the executions are stored and analyzed with standard tools; the programming language is Python, the database is MySQL, and the business intelligence tool is Metabase. This combination of theory and empirical validation clearly demonstrates the practical relevance of game theoretical models and provides a robust framework for assessing parameter impacts in real-world scenarios.