A game-theoretical approach to Islamic law disputes
Authors: Doğan Burak , Ertemel Sinan 
Published: September 2023

Purpose
This study aims to analyze notable distribution dispute cases from Islamic law history. The authors will assess these alongside resolutions proposed by historical authorities, some of which evolved into established Islamic case law. In addition, the authors intend to apply classic fair division rules to these cases, providing alternative solutions. Using a game-theoretical approach, the authors plan to compare Islamic solutions with traditional division rules through axiomatic analysis. The goal of this study is to systematically explore the unique principles underpinning Islamic distributions.

Design/methodology/approach
In this study, the authors collate Islamic inheritance law disputes involving conflicting claims, unresolvable by primary Islamic law sources, from historical and modern texts. The authors formally model these as claims problems, surplus-sharing problems and adapted claims problems. Concurrently, the authors gather the proposed solutions and historical backgrounds offered by the era’s authorities and jurists. These solutions are axiomatically generalized into rules, while the axioms characterizing distribution rules are checked if they are aligned with Islamic norms and values. This approach facilitates a comparison between Islamic distributions and classic division rules.

Findings
The 'Awl and Radd doctrines, used in Islamic inheritance law, are axiomatically equivalent to the Proportional Rule, a prevalent non-Jewish division rule. These doctrines present solutions impervious to manipulation by legal heirs through rights transfer, unlike other possible distributions. Ibn 'Abbas' solution for Awliyya cases uses sequential priorities and diverges uniquely from classic fair division rules in the literature. In addition, it is established that Abu Yusuf's (b. 729) distribution for a legal dispute is axiomatically identical to Abraham ibn Ezra's (b. 1089) division rule.

Research limitations/implications
There is a noticeable dearth of comprehensive studies investigating contentious disputes concerning resource claims within Islamic law. Many of these studies are lacking in-depth analyses of diverse cases, casting doubts on their reliability. As a result, a robust focus is needed on case collection prior to any analytical process. Future research should concentrate on collating instances of fair division problems throughout Islamic history, as well as separately collecting methods of Islamic sharing. This procedure may lead to the characterization of various Islamic regulations, thereby emphasizing distinct Islamic principles. In forthcoming studies, conducting an exhaustive axiomatic evaluation of the cases and proposed resolutions is imperative.

Practical implications
This research illuminates existing knowledge gaps, setting a course for novel research trajectories. It underlines the fair division literature’s oversight of disputes within Islamic law, despite the plentiful existence of contentious cases. The research underscores the relevance of cooperative game theory as a tool for dissecting Islamic legal disputes. By accounting for unique Islamic norms and principles, this study lays a foundation for a nuanced comprehension of the dynamics and outcomes of legal disputes. By integrating an interdisciplinary approach, this research strives to bridge the gap between game theory and Islamic law.

Social implications
Beyond addressing a significant research lacuna, this study carries extensive societal implications. By shedding light on enduring debates within Islamic law, it encourages a rejuvenated understanding of the evolution and interpretation of legal disputes. The axiomatic disparities between rulers’ and jurists’ methods provide invaluable insights within the Islamic context, bolstering the understanding of sociocultural dynamics that influence legal decision-making. This research has the potential to shape legal discourse, guide policymaking and spur scholarly, juristic and societal dialogue. Consequently, it may foster a more comprehensive and enlightened approach toward the resolution of legal disputes in Islamic law.

Originality/value
To the best of the authors’ knowledge, this study is the first to examine Islamic law’s historical legal disputes from a game-theoretical standpoint. Existing studies rarely collect distribution disputes systematically, and none scrutinize the axiomatic rationales underlying authorities’ and jurists’ distributions, opting instead to focus on historical backgrounds. While the fair division literature extensively examines disputes, it often overlooks those originating from Islamic law, which presents a rich source of disputes that can be modeled as fair division problems. This research makes a distinct contribution by incorporating disputes from Islamic law into the existing body of cooperative game theory literature.