Cooperative Game Theory: Shapley Value and Coalitional Analysis

Cooperative game theory provides the formal mathematical foundation for understanding how rational agents collaborate and divide the gains of their teamwork. In this text-based course, you will develop a clear, structured understanding of coalitional game models, solution concepts, and allocation fairness rules without getting lost in overly abstract proofs.\n\nWhat you'll learn:\n- Understand fundamental terminology, characteristic functions, and the distinction between transferable utility (TU) and non-transferable utility (NTU) games.\n- Analyze stability and grand coalition feasibility using the mathematical concept of the Core.\n- Apply the Bondareva-Shapley theorem to determine whether a cooperative game has a non-empty core.\n- Calculate the Shapley value using axiomatic foundations and marginal contribution analysis.\n- Explore linear solution concepts and their modern extensions in algorithmic fair division and model interpretability.\n- Practice structured payoff allocations through step-by-step written exercises and worked problem sets.\n\nThe reading begins with core definitions and basic game setups before moving methodically through stability theorems, classical solution concepts, and practical allocation methods. This course is created for beginners, students, and professionals in economics, mathematics, and computing who want to build a solid theoretical foundation without any specialized prerequisites beyond basic algebra. Start reading to master the mathematics of cooperative decision-making and fair value distribution.