We model the stock market as a timing game, in which arbitrageurs who are not expected to be certainly rational compete over profit by bursting the bubble caused by investors' euphoria. The manager raises money by issuing shares and the arbitrageurs use leverage. If leverage is weakly regulated, it is the unique Nash equilibrium that the bubble persists for a long time. This holds even if the euphoria is negligible and all arbitrageurs are expected to be almost certainly rational. This bubble causes serious harm to the society, because the manager uses the money raised for his personal benefit.