Resource-Splitting Games with Tullock-Based Lossy Contests

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.