Despite the emphases on computability issues in research of algorithmic game theory, the limited computational capacity of players have received far less attention. This work examines how different levels of players' computational ability (or "rationality") impact the outcomes of sequential scheduling games. Surprisingly, our results show that a lower level of rationality of players may lead to better equilibria. More specifically, we characterize the sequential price of anarchy (SPoA) under two different models of bounded rationality, namely, players with $k$-lookahead and simple-minded players. The model in which players have $k$-lookahead interpolates between the "perfect rationality" ($k=n-1$) and "online greedy" ($k=0$). Our results show that the inefficiency of equilibria (SPoA) increases in $k$ the degree of lookahead: $\mathrm{SPoA} = O (k^2)$ for two machines and $\mathrm{SPoA} = O\left(2^k \min \{mk,n\}\right)$ for $m$ machines, where $n$ is the number of players. Moreover, when players are simple-minded, the SPoA is exactly $m$, which coincides with the performance of "online greedy".

中文翻译：

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顺序调度博弈中的理性诅咒

尽管算法博弈论的研究强调可计算性问题，但玩家有限的计算能力却很少受到关注。这项工作研究了不同级别的玩家计算能力（或“理性”）如何影响顺序调度游戏的结果。令人惊讶的是，我们的结果表明，较低水平的玩家理性可能会导致更好的均衡。更具体地说，我们在两种不同的有限理性模型下描述了无政府状态（SPoA）的连续价格，即具有 $k$-lookahead 的玩家和头脑简单的玩家。玩家具有 $k$-lookahead 的模型在“完美理性”（$k=n-1$）和“在线贪婪”（$k=0$）之间进行插值。我们的结果表明，均衡的低效率 (SPoA) 增加了 $k$ 的前瞻程度：$\mathrm{SPoA} = O (k^2)$ 对于两台机器和 $\mathrm{SPoA} = O\left( 2^k \min \{mk,n\}\right)$ 对于 $m$ 机器，其中 $n$ 是玩家数量。而且，当玩家头脑简单时，SPoA正好是$m$，这与“在线贪婪”的表现不谋而合。