RB_CH01_Q050. Maximize firm value uniform

You are bidding for a firm whose unknown true value is uniformly distributed between 0 and 1. Although you do not know the true value of the firm, you can expect that any limited offer you make for it that is less than the value of the firm, however, you do, however, will be accepted only if it is at least as large as the original value of the firm. How do you bid so as to maximize your expected payoff?