The curse of rationality in sequential scheduling games

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".