A new era of theoretical computer science addresses fundamental problems about auctions, networks, and human behavior.

http://www.maths.lse.ac.uk/Personal/stengel/TEXTE/agt-stengel.pdf

Algorithmic Game Theory

Besides attracting a billion dollar economy, Bitcoin revolutionized the field of digital currencies and influenced many adjacent areas. This also induced significant scientific interest. In this survey, we unroll and structure the manyfold results and research directions. We start by introducing the Bitcoin protocol and its building blocks. From there we continue to explore the design space by discussing existing contributions and results. In the process, we deduce the fundamental structures and insights at the core of the Bitcoin protocol and its applications. As we show and discuss, many key ideas are likewise applicable in various other fields, so that their impact reaches far beyond Bitcoin itself.

Bitcoin and Beyond: A Technical Survey on Decentralized Digital Currencies

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Combinatorial Auctions

Bitcoin is the first and most popular decentralized cryptocurrency to date. In this work, we extract and analyze the core of the Bitcoin protocol, which we term the Bitcoin backbone, and prove two of its fundamental properties which we call common prefix and chain quality in the static setting where the number of players remains fixed. Our proofs hinge on appropriate and novel assumptions on the “hashing power” of the adversary relative to network synchronicity; we show our results to be tight under high synchronization.

https://courses.cs.washington.edu/courses/cse454/15wi/papers/bitcoin-765.pdf

The Bitcoin Backbone Protocol: Analysis and Applications

Bitcoin is a digital currency that unlike traditional currencies does not rely on a centralized authority. Instead Bitcoin relies on a network of volunteers that collectively implement a replicated ledger and verify transactions. In this paper we analyze how Bitcoin uses a multi-hop broadcast to propagate transactions and blocks through the network to update the ledger replicas. We then use the gathered information to verify the conjecture that the propagation delay in the network is the primary cause for blockchain forks. Blockchain forks should be avoided as they are symptomatic for inconsistencies among the replicas in the network. We then show what can be achieved by pushing the current protocol to its limit with unilateral changes to the client's behavior.

Information propagation in the Bitcoin network

Many large decentralized systems rely on information propagation to ensure their proper function. We examine a common scenario in which only participants that are aware of the information can compete for some reward, and thus informed participants have an incentive not to propagate information to others. One recent example in which such tension arises is the 2009 DARPA Network Challenge (finding red balloons). We focus on another prominent example: Bitcoin, a decentralized electronic currency system.Bitcoin represents a radical new approach to monetary systems. It has been getting a large amount of public attention over the last year, both in policy discussions and in the popular press. Its cryptographic fundamentals have largely held up even as its usage has become increasingly widespread. We find, however, that it exhibits a fundamental problem of a different nature, based on how its incentives are structured. We propose a modification to the protocol that can eliminate this problem.Bitcoin relies on a peer-to-peer network to track transactions that are performed with the currency. For this purpose, every transaction a node learns about should be transmitted to its neighbors in the network. As the protocol is currently defined and implemented, it does not provide an incentive for nodes to broadcast transactions they are aware of. In fact, it provides an incentive not to do so. Our solution is to augment the protocol with a scheme that rewards information propagation. Since clones are easy to create in the Bitcoin system, an important feature of our scheme is Sybil-proofness.We show that our proposed scheme succeeds in setting the correct incentives, that it is Sybil-proof, and that it requires only a small payment overhead, all this is achieved with iterated elimination of dominated strategies. We complement this result by showing that there are no reward schemes in which information propagation and no self-cloning is a dominant strategy.

/pdf/on-bitcoin-and-red-balloons-3r9qolagic.pdf

On bitcoin and red balloons

We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items $m$ and in the number of bidders n, even though the "input size" is exponential in m. The first algorithm provides an O(log m) approximation. The second algorithm provides an O(√ m) approximation in the weaker model of value oracles. This algorithm is also incentive compatible. The third algorithm provides an improved 2-approximation for the more restricted case of "XOS bidders", a class which strictly contains submodular bidders. We also prove lower bounds on the possible approximations achievable for these classes of bidders. These bounds are not tight and we leave the gaps as open problems.

/pdf/approximation-algorithms-for-combinatorial-auctions-with-26ozt3w6bl.pdf

Approximation algorithms for combinatorial auctions with complement-free bidders

We explore the allocation problem in combinatorial auctions with submodular bidders We provide an e/e-1 approximation algorithm for this problem Moreover, our algorithm applies to the more general class of XOS bidders By presenting a matching unconditional lower bound in the communication model, we prove that the upper bound is tight for the XOS classOur algorithm improves upon the previously known 2-approximation algorithm In fact, we also exhibit another algorithm which obtains an approximation ratio better than 2 for submodular bidders, even in the value queries modelThroughout the paper we highlight interesting connections between combinatorial auctions with XOS and submodular bidders and various other combinatorial optimization problems In particular, we discuss coverage problems and online problems

An improved approximation algorithm for combinatorial auctions with submodular bidders

We study multi-unit auctions where the bidders have a budget constraint, a situation very common in practice that has received very little attention in the auction theory literature. Our main result is an impossibility: there are no incentive-compatible auctions that always produce a Pareto-optimal allocation. We also obtain some surprising positive results for certain special cases.

https://www.cs.huji.ac.il/~noam/focs-budget.pdf

Shahar Dobzinski

Papers

On bitcoin and red balloons

Approximation algorithms for combinatorial auctions with complement-free bidders

An improved approximation algorithm for combinatorial auctions with submodular bidders

Multi-unit Auctions with Budget Limits

Multi-unit auctions with budget limits