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Register a new userMechanism Design and Blockchains
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Added by
Jan Christoph Schlegel
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Game theory is often used as a tool to analyze decentralized systems and their properties, in particular, blockchains. In this note, we take the opposite view. We argue that blockchains can and should be used to implement economic mechanisms because they can help to overcome problems that occur if trust in the mechanism designer cannot be assumed. Mechanism design deals with the allocation of resources to agents, often by extracting private information from them. Some mechanisms are immune to early information disclosure, while others may heavily depend on it. Some mechanisms have to randomize to achieve fairness and efficiency. Both issues, information disclosure, and randomness require trust in the mechanism designer. If there is no trust, mechanisms can be manipulated. We claim that mechanisms that use randomness or sequential information disclosure are much harder, if not impossible, to audit. Therefore, centralized implementation is often not a good solution. We consider some of the most frequently used mechanisms in practice and identify circumstances under which manipulation is possible. We propose a decentralized implementation of such mechanisms, that can be, in practical terms, realized by blockchain technology. Moreover, we argue in which environments a decentralized implementation of a mechanism brings a significant advantage.
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We pose and study a fundamental algorithmic problem which we term mixture selection, arising as a building block in a number of game-theoretic applications: Given a function $g$ from the $n$-dimensional hypercube to the bounded interval $[-1,1]$, and an $n times m$ matrix $A$ with bounded entries, maximize $g(Ax)$ over $x$ in the $m$-dimensional simplex. This problem arises naturally when one seeks to design a lottery over items for sale in an auction, or craft the posterior beliefs for agents in a Bayesian game through the provision of information (a.k.a. signaling). We present an approximation algorithm for this problem when $g$ simultaneously satisfies two smoothness properties: Lipschitz continuity with respect to the $L^infty$ norm, and noise stability. The latter notion, which we define and cater to our setting, controls the degree to which low-probability errors in the inputs of $g$ can impact its output. When $g$ is both $O(1)$-Lipschitz continuous and $O(1)$-stable, we obtain an (additive) PTAS for mixture selection. We also show that neither assumption suffices by itself for an additive PTAS, and both assumptions together do not suffice for an additive FPTAS. We apply our algorithm to different game-theoretic applications from mechanism design and optimal signaling. We make progress on a number of open problems suggested in prior work by easily reducing them to mixture selection: we resolve an important special case of the small-menu lottery design problem posed by Dughmi, Han, and Nisan; we resolve the problem of revenue-maximizing signaling in Bayesian second-price auctions posed by Emek et al. and Miltersen and Sheffet; we design a quasipolynomial-time approximation scheme for the optimal signaling problem in normal form games suggested by Dughmi; and we design an approximation algorithm for the optimal signaling problem in the voting model of Alonso and C^{a}mara.
We study Bayesian automated mechanism design in unstructured dynamic environments, where a principal repeatedly interacts with an agent, and takes actions based on the strategic agents report of the current state of the world. Both the principal and the agent can have arbitrary and potentially different valuations for the actions taken, possibly also depending on the actual state of the world. Moreover, at any time, the state of the world may evolve arbitrarily depending on the action taken by the principal. The goal is to compute an optimal mechanism which maximizes the principals utility in the face of the self-interested strategic agent. We give an efficient algorithm for computing optimal mechanisms, with or without payments, under different individual-rationality constraints, when the time horizon is constant. Our algorithm is based on a sophisticated linear program formulation, which can be customized in various ways to accommodate richer constraints. For environments with large time horizons, we show that the principals optimal utility is hard to approximate within a certain constant factor, complementing our algorithmic result. We further consider a special case of the problem where the agent is myopic, and give a refined efficient algorithm whose time complexity scales linearly in the time horizon. Moreover, we show that memoryless mechanisms do not provide a good solution for our problem, in terms of both optimality and computational tractability. These results paint a relatively complete picture for automated dynamic mechanism design in unstructured environments. Finally, we present experimental results where our algorithms are applied to synthetic dynamic environments with different characteristics, which not only serve as a proof of concept for our algorithms, but also exhibit intriguing phenomena in dynamic mechanism design.
We describe a structured system for distributed mechanism design. It consists of a sequence of layers. The lower layers deal with the operations relevant for distributed computing only, while the upper layers are concerned only with communication among players, including broadcasting and multicasting, and distributed decision making. This yields a highly flexible distributed system whose specific applications are realized as instances of its top layer. This design supports fault-tolerance, prevents manipulations and makes it possible to implement distributed policing. The system is implemented in Java. We illustrate it by discussing a number of implemented examples.
Nearly fifteen years ago, Google unveiled the generalized second price (GSP) auction. By all theoretical accounts including their own [Varian 14], this was the wrong auction --- the Vickrey-Clarke-Groves (VCG) auction would have been the proper choice --- yet GSP has succeeded spectacularly. We give a deep justification for GSPs success: advertisers preferences map to a model we call value maximization, they do not maximize profit as the standard theory would believe. For value maximizers, GSP is the truthful auction [Aggarwal 09]. Moreover, this implies an axiomatization of GSP --- it is an auction whose prices are truthful for value maximizers --- that can be applied much more broadly than the simple model for which GSP was originally designed. In particular, applying it to arbitrary single-parameter domains recovers the folklore definition of GSP. Through the lens of value maximization, GSP metamorphosizes into a powerful auction, sound in its principles and elegant in its simplicity.
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