\emph{Contention Resolution} is a fundamental symmetry-breaking problem in which $n$ devices must acquire temporary and exclusive access to some \emph{shared resource}, without the assistance of a mediating authority. For example, the $n$ devices may be sensors that each need to transmit a single packet of data over a broadcast channel. In each time step, devices can (probabilistically) choose to acquire the resource or remain idle; if exactly one device attempts to acquire it, it succeeds, and if two or more devices make an attempt, none succeeds. The complexity of the problem depends heavily on what types of \emph{collision detection} are available. In this paper we consider \emph{acknowledgement-based protocols}, in which devices \underline{only} learn whether their own attempt succeeded or failed; they receive no other feedback from the environment whatsoever, i.e., whether other devices attempted to acquire the resource, succeeded, or failed. Nearly all work on the Contention Resolution problem evaluated the performance of algorithms \emph{asymptotically}, as $n\rightarrow \infty$. In this work we focus on the simplest case of $n=2$ devices, but look for \underline{\emph{precisely}} optimal algorithms. We design provably optimal algorithms under three natural cost metrics: minimizing the expected average of the waiting times ({\sc avg}), the expected waiting time until the first device acquires the resource ({\sc min}), and the expected time until the last device acquires the resource ({\sc max}).

翻译：\emph{竞争解析}是一个基本的对称性破缺问题，其中$n$个设备必须在没有中介权威协助的情况下，临时且排他地访问某个\emph{共享资源}。例如，这$n$个设备可能是传感器，每个都需要通过广播信道传输一个数据包。在每个时间步，设备可以（概率性地）选择获取资源或保持空闲；如果恰好有一个设备尝试获取，则它成功，如果两个或更多设备尝试，则没有一个成功。该问题的复杂性在很大程度上取决于可用的\emph{冲突检测}类型。在本文中，我们考虑\emph{基于确认的协议}，其中设备\underline{仅}能获知其自身的尝试是成功还是失败；它们从环境中得不到任何其他反馈，即无法得知其他设备是否尝试获取资源、成功或失败。几乎所有关于竞争解析问题的工作都\emph{渐近地}评估算法性能，即当$n\rightarrow \infty$时。在本工作中，我们关注最简单的$n=2$设备情况，但寻求\underline{\emph{精确}}最优算法。我们设计了在三种自然成本度量下可证明最优的算法：最小化等待时间期望平均值（{\sc avg}）、首个设备获取资源的期望等待时间（{\sc min}）以及最后一个设备获取资源的期望时间（{\sc max}）。