  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".
