Numbers 1, 2, . . . , M are assigned to bidding prices from the minimum to maximum values V1 to VN. For a bidding value Vvi each user 11-i generates two sequences of information si={si,1, si,2, . . . , si,M} and ti={ti,1, ti,2, . . . , ti,M} such that si,1=ti,1, . . . , si,vi−1=ti,vi−1, si,vi≠ti,vi, . . . , si,M≠ti,M, then secretly sends the two sequences of information si and ti to quantitative competition apparatuses 15A and 15B, respectively, and sends hash values H1i=h(si) and H2i=h(ti) of the two sequences of information si and ti and a hash value h(Vvi∥ri) containing an intended value Vvi to a bulletin board apparatus 21. The quantitative competition apparatuses 15A and 15B extract w-th elements si,w from respective sequences s1 to sN and w-th elements ti,w from respective sequences t1 to tN, then create a concatenation Seqs,w of N elements si,w and a concatenation Seqt,w of N elements ti,w, then compare them using a one-way function without revealing their values, and, if they differ, deciding that the intended value Vvi equal to or smaller than a value Vw is present, and determines the minimum value by changing w.