Numbers 1, 2, . . . , M are assigned to bidding prices from the minimum to maximum values V₁ to V_N. For a bidding value V_vi each user 11-i generates two sequences of information s_i={s_i,1, s_i,2, . . . , s_i,M} and t_i={t_i,1, t_i,2, . . . , t_i,M} such that s_i,1=t_i,1, . . . , s_i,vi-1=t_i,vi-1, s_i,vit_i,vi, . . . , s_i,Mt_i,M, then secretly sends the two sequences of information s_i and t_i to quantitative competition apparatuses 15A and 15B, respectively, and sends hash values H1_i=h(s_i) and H2_i=h(t_i) of the two sequences of information s_i and t_i and a hash value h(V_vir_i) containing an intended value V_vi to a bulletin board apparatus 21. The quantitative competition apparatuses 15A and 15B extract w-th elements s_i,w from respective sequences s₁ to s_N and w-th elements t_i,w from respective sequences t₁ to t_N, then create a concatenation Seq_s,w of N elements s_i,w and a concatenation Seq_t,w of N elements t_i,w, then compare them using a one-way function without revealing their values, and, if they differ, deciding that the intended value V_vi equal to or smaller than a value V_w is present, and determines the minimum value by changing w.