This paper by Roger B. Myerson introduces the concept of cooperation graphs to analyze cooperation structures in games. The author proposes a procedure to make a game's cooperation structure endogenously dependent on player choices, using bilateral cooperation links represented by graph theory. The paper defines a cooperation graph and explores its applications in characteristic function games and a new form called "graph function games." Key contributions include: 1. **Definition of Cooperation Graphs**: Introduces the concept of a cooperation graph to describe more complex cooperation structures than traditional coalitions. 2. **Endogenous Cooperation Structures**: Proposes a method to make the cooperation structure endogenous, where players' choices influence the formation of cooperation links. 3. **Fair Allocation Rules**: Develops a unique and stable allocation rule that satisfies an equity criterion (equal gains from cooperation) and is closely related to the Shapley value. 4. **Graph Function Games**: Extends the theory to games without transferable utility and introduces a new game form called graph function games, which generalizes characteristic function games. The paper also includes proofs and examples to illustrate the concepts and results, providing a comprehensive framework for analyzing cooperative behavior in games.This paper by Roger B. Myerson introduces the concept of cooperation graphs to analyze cooperation structures in games. The author proposes a procedure to make a game's cooperation structure endogenously dependent on player choices, using bilateral cooperation links represented by graph theory. The paper defines a cooperation graph and explores its applications in characteristic function games and a new form called "graph function games." Key contributions include: 1. **Definition of Cooperation Graphs**: Introduces the concept of a cooperation graph to describe more complex cooperation structures than traditional coalitions. 2. **Endogenous Cooperation Structures**: Proposes a method to make the cooperation structure endogenous, where players' choices influence the formation of cooperation links. 3. **Fair Allocation Rules**: Develops a unique and stable allocation rule that satisfies an equity criterion (equal gains from cooperation) and is closely related to the Shapley value. 4. **Graph Function Games**: Extends the theory to games without transferable utility and introduces a new game form called graph function games, which generalizes characteristic function games. The paper also includes proofs and examples to illustrate the concepts and results, providing a comprehensive framework for analyzing cooperative behavior in games.