标题： 基于Tullock损失性竞赛的资源分割博弈 显示英文标题

标题： Resource-Splitting Games with Tullock-Based Lossy Contests

摘要： 本文介绍了一类新型的多阶段资源分配博弈，该博弈模型模拟了现实世界中的场景，其中盈利能力取决于供给与需求之间的平衡，并且更高的资源投入会导致更大的回报。 我们提出的框架结合了由于玩家参与不足而导致的利润损失的概念，在应用加权公平比例资源分配时，会产生类似Tullock的阶段收益结构的函数形式。 我们探讨了集中式和纳什均衡策略，建立了它们存在性和唯一性的充分条件，并提供了一种迭代的半分布式方法来计算具有任意多玩家的博弈中的纳什均衡。 此外，我们证明了该框架可以推广几种现有模型的实例，包括回溯时间范围和布洛托博弈，并提出了一种半解析方法来计算布洛托设置中的唯一纳什均衡。 我们的研究结果通过一个智能移动性的数值案例研究得到了验证，突显了所提出模型的实际相关性和适用性。 显示英文摘要

摘要： 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.