We study the problem of providing blockchain applications with \emph{economically viable randomness} (EVR), namely, randomness that has significant economic consequences. Applications of EVR include blockchain-based lotteries and gambling. An EVR source guarantees (i) secrecy, assuring that the random bits are kept secret until some predefined condition indicates that they are safe to reveal (e.g., the lottery's ticket sale closes), and (ii) robustness, guaranteeing that the random bits are published once the condition holds. We formalize the EVR problem and solve it on top of an Ethereum-like blockchain abstraction, which supports smart contracts and a transferable native coin. Randomness is generated via a distributed open commit-reveal scheme by game-theoretic agents who strive to maximize their coin holdings. Note that in an economic setting, such agents might profit from breaking secrecy or robustness, and may engage in side agreements (via smart contracts) to this end. Our solution creates an incentive structure that counters such attacks. We prove that following the protocol gives rise to a stable state, called Coalition-Proof Nash Equilibrium, from which no coalition comprised of a subset of the players can agree to deviate. In this stable state, robustness and secrecy are satisfied. Finally, we implement our EVR source over Ethereum.

中文翻译：

---

经济上可行的随机性

我们研究为区块链应用程序提供\emph{经济上可行的随机性}（EVR）的问题，即具有重大经济后果的随机性。EVR 的应用包括基于区块链的彩票和赌博。EVR 源保证 (i) 保密性，确保随机位保密，直到某些预定义条件表明它们可以安全公开（例如，彩票销售结束），以及 (ii) 稳健性，保证随机位是一旦条件成立就发布。我们将 EVR 问题形式化，并在类似以太坊的区块链抽象之上解决它，该抽象支持智能合约和可转让的原生代币。随机性是由致力于最大化其代币持有量的博弈论代理通过分布式开放提交-显示方案生成的。请注意，在经济环境中，此类代理可能会从破坏保密性或稳健性中获利，并且可能为此参与附带协议（通过智能合约）。我们的解决方案创建了一个激励结构来对抗此类攻击。我们证明，遵循该协议会产生一个稳定状态，称为联盟证明纳什均衡，任何由一部分玩家组成的联盟都不能同意偏离。在这种稳定状态下，鲁棒性和保密性都得到满足。最后，我们在以太坊上实现了我们的 EVR 源。任何由一部分玩家组成的联盟都不能同意偏离。在这种稳定状态下，鲁棒性和保密性都得到满足。最后，我们在以太坊上实现了我们的 EVR 源。任何由一部分玩家组成的联盟都不能同意偏离。在这种稳定状态下，鲁棒性和保密性都得到满足。最后，我们在以太坊上实现了我们的 EVR 源。