Effort Estimation in Insourcing Agile Software Development by a Game Theoretical Framework

Introduction: Effort estimation (EE) is crucial for agile software development to cope with delivery times. Although companies prefer insourcing development with mature teams to avoid uncertainty, determining EE remains challenging since agents strategically interact in a top-down or bottom-up relationship. Objective: We analyze insourcing EE by modeling the scrum master and a mature team's interaction as a sequential game of complete information considering three scenarios in a Scrum environment. Such scenarios assume different leadership styles and relationships between the scrum master and the development team. Methodology: We model such strategic behavior by a gametheoretic framework to find the optimal solution to maximize every iteration's results. In the basic game, the scrum master leads by providing resources while the development team follows striving. In the first variation of the game, agents exchange their roles as leader or follower, and in the second variation, the scrum master acts at different stages as a leader and then as a follower. Results: We provide a closed-form solution to compute resources and effort based on environmental factors. By assuming Cobb-Douglas production functions and quadratic costs functions, a unique sub-game Perfect Nash equilibrium exists in the basis game and its first variation. In contrast, multiple equilibria arise in the second game variation. The main results show that equilibrium effort is independent of the interaction's structure, and agents get their largest benefit at equilibrium when they are followers. Conclusion: The analysis of EE through the lenses of game theory revealed that leadership style assumes a reformulating role in achieving sprint goals.