The development of modellings and analytical tools to structurise and study the allocation of resources through noble user competitions become essential, especially considering the increased degree of heterogeneity in application and service demands that will be cornerstone in future communication systems. Stochastic asymmetric Blotto games appear promising to modelling such problems, and devising their Nash equilibrium (NE) strategies by anticipating the potential outcomes of user competitions. In this regard, this paper approaches the generic energy efficiency problem with a new stochastic asymmetric Blotto game paradigm to enable the derivation of joint optimal bandwidth and transmit power allocations by setting multiple users to compete in multiple auction-like contests for their individual resource demands. The proposed modelling innovates by abstracting the notion of fairness from centrally-imposed to distributed-competitive, where each user’s pay-off probability is expressed as quantitative bidding metric, so as, all users’ actions can be interdependent, i.e., each user attains its utility given the allocations of other users, which eliminates the chance of low-valued carriers not being claimed by any user, and, in principle, enables the full utilisation of wireless resources. We also contribute by resolving the allocation problem with low complexity using new mathematical techniques based on Charnes-Cooper transformation, which eliminate the additional coefficients and multipliers that typically appear during optimisation analysis, and derive the joint optimal strategy as a set of linear single-variable functions for each user. We prove that our strategy converges towards a unique, monotonous and scalable NE, and examine its optimality, positivity and feasibility properties in detail. Simulation comparisons with relevant studies confirm the superiority of our approach in terms of higher energy efficiency performance, fairness index and quality-of-service provision.

中文翻译：

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用于无线资源分配策略的随机非对称 Blotto 博弈方法

开发建模和分析工具以通过高尚的用户竞争来构建和研究资源分配变得至关重要，特别是考虑到应用和服务需求的异质性程度增加，这将成为未来通信系统的基石。随机非对称 Blotto 游戏似乎有望对此类问题进行建模，并通过预测用户竞争的潜在结果来设计其纳什均衡 (NE) 策略。在这方面，本文使用一种新的随机非对称 Blotto 博弈范式来解决通用能源效率问题，通过设置多个用户在多个类似拍卖的竞赛中竞争其各自的资源需求，从而推导出联合最优带宽和传输功率分配。所提出的建模创新通过将公平的概念从集中强加到分布式竞争进行抽象，其中每个用户的支付概率表示为定量竞标度量，因此所有用户的行为可以相互依赖，即每个用户获得其给定其他用户分配的效用，这消除了任何用户不认领低价值载波的机会，并且原则上可以充分利用无线资源。我们还通过使用基于 Charnes-Cooper 变换的新数学技术解决低复杂度的分配问题做出贡献，这些技术消除了优化分析过程中通常出现的额外系数和乘数，并将联合最优策略推导出为一组线性单变量每个用户的功能。我们证明我们的策略收敛于一个独特的、单调的和可扩展的 NE，并详细检查其最优性、积极性和可行性属性。与相关研究的模拟比较证实了我们的方法在更高的能效性能、公平指数和服务质量方面的优越性。