一个具有有限反馈的防止持续策略竞争的3人协议
A 3-player protocol preventing persistence in strategic contention with limited feedback
摘要：
本文从博弈论的角度研究了竞争解决协议。在最近的一项工作中，我们考虑了基于传输的协议，其中用户仅在尝试传输时才从信道获得反馈。在这种情况下，她将了解她的传输是否成功。ESA 2016的主要结果之一是，没有任何基于平衡的协议可以处于平衡状态。事实上，似乎许多自然的基于持久性的协议无法阻止用户单方面切换到总是以概率1传输的持久性协议。因此，人们自然会问，一个协议必须有多强大，才能击败顽固的偏离者。在本文中，我们考虑基于年龄的协议，它可以描述在每个时间步的传输概率序列。这些概率是预先给定的，不会根据传输历史而改变。我们提出了一个基于年龄的3人协议，可以防止用户单方面偏离到一个持久的协议，以减少他们的预期传输时间。值得注意的是，这个问题的答案并不来自ESA 2016的结果和证明思想。我们的协议是不平凡的，在这个意义上说，当所有的球员使用它，有限的预期传输时间得到保证。事实上，我们表明，该协议是最好的任何截止日期协议，在一些固定的时间后，尝试在随后的每一步传输概率为1。我们的协议的一个优点是，它是非常简单的描述，用户只需要一个计数器来跟踪时间。是否存在$n$播放器基于年龄的协议，不使用计数器，可以防止持久性是一个开放的问题，为未来的研究。
英文摘要：
In this paper, we study contention resolution protocols from a game-theoretic perspective. In a recent work, we considered acknowledgment-based protocols, where a user gets feedback from the channel only when she attempts transmission. In this case she will learn whether her transmission was successful or not. One of the main results of ESA2016 was that no acknowledgment-based protocol can be in equilibrium. In fact, it seems that many natural acknowledgment-based protocols fail to prevent users from unilaterally switching to persistent protocols that always transmit with probability 1. It is therefore natural to ask how powerful a protocol must be so that it can beat persistent deviators. In this paper we consider age-based protocols, which can be described by a sequence of probabilities of transmitting in each time step. Those probabilities are given beforehand and do not change based on the transmission history. We present a 3-player age-based protocol that can prevent users from unilaterally deviating to a persistent protocol in order to decrease their expected transmission time. It is worth noting that the answer to this question does not follow from the results and proof ideas of ESA2016. Our protocol is non-trivial, in the sense that, when all players use it, finite expected transmission time is guaranteed. In fact, we show that this protocol is preferable to any deadline protocol in which, after some fixed time, attempt transmission with probability 1 in every subsequent step. An advantage of our protocol is that it is very simple to describe, and users only need a counter to keep track of time. Whether there exist $n$-player age-based protocols that do not use counters and can prevent persistence is left as an open problem for future research.
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