We consider a double-auction mechanism, which was recently proposed in the context of rate allocation in mobile data-offloading markets; our mechanism is also applicable to the problem of bandwidth allocation in network slicing markets. Network operators ( users ) derive benefit from offloading their traffic to third party WiFi or femtocell networks ( link-suppliers ). Link-suppliers experience costs for the additional capacity that they provide. Users and link-suppliers (collectively referred to as agents ) have their pay-offs and cost functions as private knowledge. A network-manager decomposes the problem into a network problem (with surrogate pay-offs and surrogate cost functions) and agent problems (one per agent). The surrogate pay-offs and cost functions are modulated by the agents’ bids. Agents’ payoffs and costs are then determined by the allocations and prices set by the network-manager. Under this design, so long as the agents do not anticipate the effect of their actions on the prices set by the network-manager (i.e., price-taking agents), a competitive equilibrium exists as a solution to the network and agent problems, and this equilibrium optimizes the sum utility of all agents. However, this design fails when the agents (including the link-supplier) are all strategic ( price-anticipating ). Specifically, the presence of a strategic link-supplier drives the system to an undesirable equilibrium with zero participation resulting in an efficiency loss of 100%. This is in stark contrast to an earlier setting where the users alone are strategic but the link-supplier is not − the efficiency loss is known to be at most 34%. The paper then proposes the following Stackelberg game modification with asymmetric information structures for link-supplier and users in order to alleviate the efficiency-loss problem: the network-manager first announces the allocation and payment functions; he then invites the link-supplier to announce its bid, following which the users are invited to respond with their bids. The resulting Stackelberg games’ efficiency losses can be characterized in terms of the link-supplier’s cost function when the users’ pay-off functions are linear. Specifically, when the link-supplier’s cost function is quadratic, the worst case efficiency loss is 25%. Further, the loss in efficiency improves for polynomial cost functions of higher degree. For non-linear utility functions (e.g., $\alpha $ -fair and $\log $ utilities), we demonstrate the efficacy of the proposed mechanism via. a detailed numerical study.

中文翻译：

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资源交易市场的双重拍卖机制

我们考虑了一种双重拍卖机制，该机制最近在移动数据卸载市场的费率分配背景下提出；我们的机制也适用于网络切片市场中的带宽分配问题。网络运营商（ 用户 ）从将流量卸载到第三方 WiFi 或毫微微蜂窝网络中获益（ 链接供应商 ）。链路供应商会因他们提供的额外容量而产生成本。用户和链接供应商（统称为代理商 ) 将其收益和成本函数作为私有知识。一种网络管理员将问题分解为网络问题（具有代理支付和代理成本函数）和代理问题（每个代理一个）。代理支付和成本函数由代理的出价调节。然后，代理的收益和成本由网络管理员设定的分配和价格决定。在这种设计下，只要代理没有预料到他们的行为对网络管理员设定的价格的影响（即，价格接受代理），竞争均衡作为网络和代理问题的解决方案存在，并且该均衡优化了所有代理的总和效用。然而，当代理（包括链接供应商）都是战略性的（ 价格预期 ）。具体而言，战略链接供应商的存在将系统推向不希望的平衡，零参与导致 100% 的效率损失。这与早期的设置形成鲜明对比，在早期设置中，只有用户是战略性的，而链接供应商不是——已知效率损失最多为 34%。然后，为了缓解效率损失问题，论文提出了以下具有非对称信息结构的链供应商和用户的 Stackelberg 博弈修正：网络管理者首先宣布分配和支付功能；然后，他邀请链接供应商宣布其出价，然后邀请用户以他们的出价做出回应。当用户的支付函数是线性的时，由此产生的 Stackelberg 游戏的效率损失可以用链接供应商的成本函数来表征。具体而言，当链路供应商的成本函数为二次方时，最坏情况下的效率损失为 25%。此外，对于更高阶的多项式成本函数，效率损失有所改善。对于非线性效用函数（例如， $\alpha $ -公平和 $\log $ 实用程序），我们证明了所提出的机制的有效性通过。详细的数值研究。