Interval Scheduling Games

2026-01-21

AI Summary

This study addresses a colored interval scheduling game in multi-agent settings, where each player controls multiple jobs of the same color and machines must be configured with colors to cover these jobs, leading to conflicting objectives. Players select processing intervals for their jobs to maximize their own covered weight, while the machine configures colors to maximize total covered weight. The work extends the classical interval scheduling problem to a multi-player game-theoretic framework, distinguishing between single- and multi-job scenarios, and systematically analyzes the existence, computational complexity, and efficiency loss of Nash equilibria. It proves that, given fixed player strategies, the machine’s scheduling problem is solvable in polynomial time, and fully characterizes the conditions for equilibrium existence, its computational hardness, and the resulting social welfare efficiency.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We consider a game-theoretic variant of an interval scheduling problem. Every job is associated with a length, a weight, and a color. Each player controls all the jobs of a specific color, and needs to decide on a processing interval for each of its jobs. Jobs of the same color can be processed simultaneously by the machine. A job is covered if the machine is configured to its color during its whole processing interval. The goal of the machine is to maximize the sum of weights of all covered jobs, and the goal of each player is to place its jobs such that the sum of weights of covered jobs from its color is maximized. The study of this game is motivated by several applications like antenna scheduling for wireless networks. We first show that given a strategy profile of the players, the machine scheduling problem can be solved in polynomial time. We then study the game from the players'point of view. We analyze the existence of Nash equilibria, its computation, and inefficiency. We distinguish between instances of the classical interval scheduling problem, in which every player controls a single job, and instances in which color sets may include multiple jobs.

Problem

• interval scheduling
• game theory
• Nash equilibrium
• resource allocation
• scheduling games

Innovation

• interval scheduling
• game theory
• Nash equilibrium
• polynomial-time algorithm
• resource allocation