AF: Small: Duality-based tools for simple vs. optimal mechanism design and applications to cryptocurrency

传统上，我们认为算法是“处理输入”以“产生输出”。例如，想象一家公司试图在员工中分配各种资源：它可能会向每个员工询问每种资源如何影响他们的生产力（“投入”），并以最大化总产量的方式分配资源（“产出”）。当每个用户都有相同的目标（最大化公司的生产力）时，传统的算法范式完美地捕捉了公司的目标。如果我们希望对云计算服务进行建模，在其用户之间分配各种资源，该怎么办？现在，单个用户的目标（最大化他们自己的生产力）与服务的目标不一致。因此，用户可以操纵所部署的任何算法以提高他们自己的生产力，这可能是以他人的生产力为代价的。为这些领域设计适当的解决方案不可避免地需要机制设计，这需要使用算法和博弈论工具。作为该项目的一部分，PI正在开发一门新的本科课程“经济学和计算”，以便为下一代计算机科学家提供严格推理与其系统交互的用户的动机的能力。许多先前的工作规定了在实践中无法使用的非常复杂的机制，激励PI和其他人的先前工作来研究简单机制的理论特性。该项目的主要研究重点是通过严格的理论基础，大大扩展我们对如何适当部署简单机制的理解。作为该项目的一部分，PI将继续提供有关用于获得这些新结果的特定方法的讲座和教程，称为“对偶理论”。“该项目的第二个重点是应用这些理论基础来解决比特币（一种新兴的加密货币）中出现的加密货币激励问题。虽然比特币在很大程度上仍然不受传统安全漏洞的影响，但已经发现了许多激励问题，如果不妥善解决，可能会破坏其未来的安全性。作为该项目的一部分，PI将通过教程帮助扩大其他机制设计师在这一方向的参与。更详细地说，该项目的主要研究重点旨在回答以下问题：“设置的哪些属性使简单的机制适当或不适当？或“量化，一个机制需要有多”复杂“才能”接近"最优？“这种方法的主要技术成分是PI和合著者最近开发的一种新的二元框架。第二个重点是在激励兼容的加密货币协议方面取得进展：激励所有用户认真遵守协议，即使他们拒绝这样做也不会被发现。虽然PI的重点将放在这样一个协议的理论基础上，但任何发现都将通过实验（模拟）或经验（数据）研究来跟进。

Traditionally, we think of algorithms as "processing an input" in order to "produce an output." For example, imagine a firm trying to allocate various resources among its employees: It might solicit from each employee how each resource affects their productivity (the "input"), and allocate the resources in a way to maximize the total production (the "output"). When each user has the same goal (maximize the firm's productivity), the traditional algorithmic paradigm perfectly captures the firm's objective. What if instead we wish to model a cloud computing service allocating various resources among its users? Now, the goals of the individual users (maximize their own productivity) are misaligned with that of the service. Therefore, users may manipulate whatever algorithm is deployed in order to improve their own productivity, possibly at the cost of others'. Properly designing solutions for such domains inevitably requires mechanism design, which makes use of both algorithmic and game theoretic tools. As part of this project, the PI is developing a new undergraduate course "Economics and Computation" in order to provide the next generation of computer scientists with the ability to reason rigorously about the incentives of users who interact with their systems. Much prior work prescribes wildly complex mechanisms which are unusable in practice, motivating prior work of the PI and others to investigate the theoretical properties of simple mechanisms. The main research focus of this project is to greatly expand our understanding of how to appropriately deploy simple mechanisms, via a rigorous theoretical foundation. As part of this project, the PI will continue giving talks and tutorials about the specific approach used to obtain these new results, referred to as a "duality theory." A secondary focus of this project is to apply these theoretical foundations to resolve cryptocurrency incentive issues arising within Bitcoin, an emerging cryptocurrency. While Bitcoin has remained largely immune to traditional security breaches, numerous incentive issues have been discovered which could undermine its future security if not properly addressed. As part of this project, the PI will help broaden participation by other mechanism designers in this direction via tutorials. In a little more detail, the main research focus of this project aims to answer questions such as "what properties of a setting make simple mechanisms appropriate or inappropriate?" or "Quantitatively, how 'complex' does a mechanism need to be in order to be 'close' to optimal?" The main technical ingredient in this approach is a novel duality framework recently developed by the PI and co-authors. The secondary focus aims specifically to make progress towards an incentive compatible cryptocurrency protocol: one where all users are incentivized to follow the protocol in earnest, even when their refusal to do so goes undetected. While the PI's focus will be on the theoretical foundations of such a protocol, any findings will be followed up by experimental (simulations) or empirical (data) research as well.