多信道竞争解决策略
Strategic Contention Resolution in Multiple Channels
摘要：
我们考虑的问题，解决竞争的通信网络与自私的用户。在一个\textit{contention game}中，每个$n \geq 2$相同的播放器具有一个她想使用$k \geq 1$多址信道之一来发送的信息分组。要做到这一点，玩家选择一个时隙协议，规定在给定的时间步长，她将尝试在每个通道传输的概率。如果多个玩家试图在同一个信道上传输（冲突），则该信道上不会发生传输。每个参与者试图通过选择她的协议来最小化她自己的预期\textit{latency}，即她的预期时间，直到成功传输。在这样的设置中出现的自然问题是，给定$n$和$k$，为参与者提供一个公共的匿名协议（如果存在的话），这样就没有人会单方面偏离它（均衡协议）。所有以前的理论研究结果的战略竞争解决的情况下，只有一个单一的通道，并表明，平衡协议依赖于反馈的通信系统给球员。在这里，我们提出了两个主要的反馈类，即\textit{acknowledgement-based}和\textit{ternary}的多通道均衡协议。特别是，我们提供了一个以上的渠道的均衡特征，并给出具体的匿名，均衡协议与有限和无限的预期延迟。在具有无限期望延迟的均衡协议中，所有参与者都在最优时间（即$Θ(n/k)$）成功发送，概率趋于1，即$n/k \to \infty$。
英文摘要：
We consider the problem of resolving contention in communication networks with selfish users. In a \textit{contention game} each of $n \geq 2$ identical players has a single information packet that she wants to transmit using one of $k \geq 1$ multiple-access channels. To do that, a player chooses a slotted-time protocol that prescribes the probabilities with which at a given time-step she will attempt transmission at each channel. If more than one players try to transmit over the same channel (collision) then no transmission happens on that channel. Each player tries to minimize her own expected \textit{latency}, i.e. her expected time until successful transmission, by choosing her protocol. The natural problem that arises in such a setting is, given $n$ and $k$, to provide the players with a common, anonymous protocol (if it exists) such that no one would unilaterally deviate from it (equilibrium protocol). All previous theoretical results on strategic contention resolution examine only the case of a single channel and show that the equilibrium protocols depend on the feedback that the communication system gives to the players. Here we present multi-channel equilibrium protocols in two main feedback classes, namely \textit{acknowledgement-based} and \textit{ternary}. In particular, we provide equilibrium characterizations for more than one channels, and give specific anonymous, equilibrium protocols with finite and infinite expected latency. In the equilibrium protocols with infinite expected latency, all players transmit successfully in optimal time, i.e. $Θ(n/k)$, with probability tending to 1 as $n/k \to \infty$.
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