The overconfident trader does not always overreact to his information

•We develop a model where the outsider is overconfident on the shared information.•A more confident outsider trades less aggressively on his information.•The overconfidence of the outsider leads to a larger insider's expected profits.•The overconfidence of the outsider leads to a less efficient and less stable market.

This article develops a strategic trading model in which the outsider is overconfident on the shared information. Our result shows that a more confident outsider underreacts to his information in the sense that he trades less aggressively on his information, leading to a less profit in the trading. However, the insider trades more aggressively on the shared information and less aggressively on the private information when he faces a more overconfident outsider. Also, the overconfidence of the outsider leads to a larger insider's expected profits, an increased expected loss of noise trader, and a less efficient and less stable market.