We propose a decentralized task allocation strategy by estimating the states of task loads in market-like negotiations based on an announcement-bid-award mechanism, such as contract net protocol (CNP), for an environment of large-scale multi-agent systems (LSMAS). CNP and their extensions are widely used in actual systems, but their characteristics in busy LSMAS are not well understood and thus we cannot use them lightly in larger application systems. We propose an award strategy in this paper that allows multiple bids by contractors but reduces the chances of simultaneous multiple awards to low-performance agents because this significantly degrades performance. We experimentally found that it could considerably improve overall efficiency.