Announcement games, where information is disseminated by announcers and challenged by validators, are prevalent in real-world scenarios. Validators take effort to verify the validity of the announcements, gaining rewards for successfully challenging invalid ones, while receiving nothing for valid ones. Optimistic Rollup, a Layer 2 blockchain scaling solution, exemplifies such games, offering significant improvements in transaction throughput and cost efficiency. We present a game-theoretic model of announcement games to analyze the potential behaviors of announcers and validators. We identify all Nash equilibria and study the corresponding system losses for different Nash equilibria. Additionally, we analyze the impact of various system parameters on system loss under the Nash equilibrium. Finally, we provide suggestions for mechanism optimization to reduce system losses.

翻译：宣告博弈在现实场景中普遍存在，其中信息由宣告者发布并由验证者挑战。验证者付出努力来核实宣告的有效性，成功挑战无效宣告可获得奖励，而对有效宣告则无所得。乐观汇总（Optimistic Rollup）作为第二层区块链扩容方案，正是此类博弈的典型实例，它在交易吞吐量和成本效益方面实现了显著提升。本文提出了宣告博弈的博弈论模型，用以分析宣告者和验证者的潜在行为。我们识别了所有纳什均衡，并研究了不同纳什均衡对应的系统损失。此外，我们分析了在纳什均衡下各类系统参数对系统损失的影响。最后，我们提出了降低系统损失的机制优化建议。