A discrete mathematical approach to secure multi-agent negotiation systems in e-commerce environments
Pranabananda Rathpranabandada.rath@kls.ac.inDepartment of ManagementSchool of LawKIIT Deemed to be UniversityBhubaneshwar, Odisha, 751027, IndiaView full profile → , *Ankit GargCorresponding authorankit@akgim.edu.inDepartment of ManagementAjay Kumar Garg Institute of ManagementGhaziabad, Uttar Pradesh, 201015, IndiaView full profile → , Sarjue PanditaDr.sarjue@akgim.edu.inDepartment of ManagementAjay Kumar Garg Institute of ManagementGhaziabad, Uttar Pradesh, 201015, IndiaView full profile → , Sanghamitra Dassanghamirta@akgim.edu.inDepartment of ManagementAjay Kumar Garg Institute of ManagementGhaziabad, Uttar Pradesh, 201015, IndiaView full profile → , Anikataniketposwal25@gmail.comDepartment of ManagementInstitute of Technology and ScienceMohan Nagar, Ghaziabad, Uttar Pradesh, 201007, IndiaView full profile → , Vishal Guptaguptavishal@akgec.ac.inDepartment of Applied ScienceAjay Kumar Garg Engineering CollegeGhaziabad, Uttar Pradesh, 201015, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Dec 2025
- Published Online:
- 06 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JSMS-1683
- Pages:
- 893–905
Abstract
Complex multi-agent negotiation systems with high security, efficiency, and trust requirements have been developed in response to the rapid development of e-commerce platforms. Strong security measures for ensuring data integrity and confidentiality in distributed environments are absent in conventional negotiation models. This paper attempts to use graph theory, game theory, and cryptographic protocols in a blockchain environment to develop a discrete mathematical framework for secure multi-agent negotiation systems. Edges in a weighted graph are used to represent negotiation interactions with utility functions, while agents are represented as vertices in the graph. For optimal decision-making by multiple conflicting agents, a game theory approach using Nash equilibrium is used. Hash function validation of blockchain is used for ensuring security, and numerical analysis is used to test a new secure multi-agent negotiation algorithm (SMANA).
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References
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