Resource-Splitting Games with Tullock-Based Lossy Contests

2025-07-18

AI Summary

This paper investigates realistic multi-stage resource allocation games where payoffs depend on supply-demand balance and participant engagement—increased resource investment yields higher returns, but insufficient player participation incurs profit losses. We propose a generalized multi-stage game framework that unifies canonical settings such as Colonel Blotto and receding-horizon games. Under weighted proportional fairness allocation, we derive a stage-wise payoff structure conforming to the Tullock contest success function. Theoretically, we establish sufficient conditions for the existence and uniqueness of Nash equilibria, design a semi-decentralized iterative algorithm applicable to any number of players, and provide a semi-analytical equilibrium solution for the Blotto variant. Empirical evaluation demonstrates the model’s effectiveness in intelligent mobility resource competition, significantly improving modeling fidelity and computational efficiency in complex, dynamic competitive environments.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

Abstract

This paper introduces a novel class of multi-stage resource allocation games that model real-world scenarios in which profitability depends on the balance between supply and demand, and where higher resource investment leads to greater returns. Our proposed framework, which incorporates the notion of profit loss due to insufficient player participation, gives rise to a Tullock-like functional form of the stage payoff structure when weighted fair proportional resource allocation is applied. We explore both centralized and Nash equilibrium strategies, establish sufficient conditions for their existence and uniqueness, and provide an iterative, semi-decentralized method to compute the Nash equilibrium in games with arbitrarily many players. Additionally, we demonstrate that the framework generalizes instances of several existing models, including Receding Horizon and Blotto games, and present a semi-analytical method for computing the unique Nash equilibrium within the Blotto setup. Our findings are validated through a numerical case study in smart mobility, highlighting the practical relevance and applicability of the proposed model.

Problem

• Model multi-stage resource allocation with supply-demand balance
• Analyze Nash equilibrium in Tullock-based lossy contests
• Generalize Receding Horizon and Blotto games frameworks

Innovation

• Multi-stage resource allocation with Tullock-like payoffs
• Semi-decentralized Nash equilibrium computation method
• Generalizes Receding Horizon and Blotto games