The curse of rationality in sequential scheduling games

TL;DR

This paper investigates how limited computational rationality of players affects the efficiency of outcomes in sequential scheduling games, revealing that less rational players can sometimes lead to better equilibria.

Contribution

It characterizes the sequential price of anarchy under bounded rationality models, showing how different levels of lookahead and simplicity influence inefficiency.

Findings

SPoA increases with lookahead level k, as O(k^2) for two machines.

Simple-minded players achieve SPoA exactly m, matching online greedy performance.

Bounded rationality can improve equilibrium quality compared to perfect rationality.

Abstract

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".