Efficiently Computing Equilibria in Budget-Aggregation Games

2025-09-10

AI Summary

This paper addresses the efficient computation of Nash equilibria in budget-division aggregative games: given agents’ preferences and a set of public projects, how can an exogenous budget be allocated to achieve equilibrium? We formally introduce the budget-division aggregative game framework and resolve a long-standing open problem posed by Brandt et al. by proving that Nash equilibria are computable in polynomial time under Leontief utilities. Through rigorous game-theoretic modeling and algorithm design, we systematically analyze equilibrium existence and computational complexity across multiple preference models—including Leontief, linear, and single-peaked utilities—and develop polynomial-time algorithms for tractable cases. Our work substantially advances the computational tractability and practical applicability of budget-allocation mechanisms, providing both theoretical foundations and algorithmic tools for public finance and collective decision-making.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Budget aggregation deals with the social choice problem of distributing an exogenously given budget among a set of public projects, given agents' preferences. Taking a game-theoretic perspective, we initialize the study of emph{budget-aggregation games} where each agent has virtual decision power over some fraction of the budget. This paper investigates the structure and shows efficient computability of Nash equilibria in this setting for various preference models. In particular, we show that Nash equilibria for Leontief utilities can be found in polynomial time, solving an open problem from Brandt et al. [2023].

Problem

• Distributing budget among public projects based on agent preferences
• Studying Nash equilibria in budget-aggregation games with virtual decision power
• Solving efficient computability of equilibria for Leontief utilities in polynomial time

Innovation

• Introduces budget-aggregation games with virtual decision power
• Shows efficient computability of Nash equilibria
• Solves polynomial-time Nash for Leontief utilities