Abstract
The selfish bin packing problem (SBP) considers the classical bin packing problem in a game-theoretic setting where each item is controlled by a selfish agent. It is well-known that the classical bin packing problem admits an asymptotic fully polynomial-time approximation scheme (AFPTAS). However, all previously-studied cost-sharing mechanisms for the selfish bin packing problem (SBP) have PoA greater than 1.6. Obviously, there is quite a big gap between the results of the two highly-related problems. In this paper, we revisit the SBP and find more efficient mechanisms for SBP to narrow the gap. We first present a simple mechanism with \(PoA=1.5\), which significantly improves previous bounds. We observe that for a large class of mechanisms for the SBP, 1.5 is actually a lower bound of PoA. Finally, we propose new rules for the SBP which lead a better mechanism with \(PoA \le 1.467\).
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