We experimentally investigate an information leakage problem in supply chain where two competing retailers procure from the same supplier. The incumbent retailer who first places an order has known the real state of market while the entrant retailer and the supplier only know the distribution. A revenue-sharing (S) contract is considered to incentivize the supplier to not leak the incumbent retailer's order information in the rational model. We design an experiment to test the performance of the S contract, while the wholesale price (W) contact is also tested as a benchmark. We find the S contract does not yield supply chain surplus as high as the rational model predicts. Instead, the supply chain surplus under two contracts is not significantly different. Especially, under the S contract, the suppliers leak high state market information with a relatively large percentage compared to no information sharing suggested by the rational theory. To decompose the deviation observed in the revenue-sharing treatment, we also design four new treatments with controlling the irrational retailers. We find that the entrant retailer's ambiguity aversion towards demand distribution uncertainty is the key driver to cause the S contract's inefficiency in preventing information leakage.