JP4098672B2 - Electronic bidding method for multiple goods, apparatus thereof, apparatus processing method thereof and program thereof - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an electronic bidding method in which a plurality of seller (seller) devices and a plurality of purchaser (buyer) devices distributed on a communication network bid by electronic means, a device for the organizer, The present invention relates to the processing method and the program.
[0002]
[Prior art]
In an electronic bidding method in which there are a plurality of one commodity such as stock trading and a plurality of sellers and buyers, there is a fictitious name bidding problem as a problem specific to the network environment. Threshold Price Double Auction Protocol (TPD), which is robust to fictitious nominated bids, under the constraint that the marginal utility (differential value of the evaluation value relative to the number of goods) does not increase to solve this problem Has been proposed (for example, Patent Document 1). Here, the fictitious name bidding means that one buyer (buyer) or seller (seller) pretends to be a plurality of buyers and / or sellers.
[0003]
Hereinafter, the TPD protocol will be described.
First, the organizer of an auction (competitive bidding) sets a threshold price r. Next, the purchaser and the seller declare the evaluation value only once. The purchaser's evaluation value is the highest price that the purchaser may purchase, and the seller's evaluation value is the lowest price that the seller may sell. Assume that the stated evaluation values are as follows.
[0004]
The buyer's stated evaluation value b_(i)Are arranged in ascending order as follows. b_(i)Is the i-th largest value among the evaluation values expressed by the purchaser.
b₍₁₎≧ b₍₂₎≧… ≧ b_(i)≧ r> b_{(i + 1)}, ...
The seller's stated evaluation value s_(j)Are arranged in ascending order as follows.
s_(j)Is the jth smallest value among the evaluation values expressed by the seller.
s₍₁₎≦ s₍₂₎≦… ≦ s_(j)≦ r <s_{(j + 1)}, ...
[0005]
The processing procedure of this TPD protocol is described as follows.
1. When i = j: (1) to (i) purchasers and sellers make a transaction at price r.
2. When i> j: (1) th to (j) th purchasers and sellers conduct transactions. Buyer is b_{(j + 1)}And the seller gets r. The organizer of the auction is j · (b_{(j + 1)}-R).
3. When i <j: (1) to (i) purchasers and sellers conduct transactions. The buyer pays r and the seller pays s_{(i + 1)}Get. The organizer of the auction is i · (rs_{(i + 1)})
[0006]
[Patent Document 1]
JP 2002-203144 A
[0007]
[Problems to be solved by the invention]
In the TPD protocol, it is necessary to arrange the evaluated evaluation values in descending order for the buyer and in ascending order for the seller regardless of the bidder. Therefore, other than this, dealing with unnecessary (all-or-nothing) bids (for example, a bid that requires a plane ticket for four family members for a family trip and is not required other than that number) I can't. In other words, the TPD protocol can be used only when the marginal utility (increment of utility relative to the addition of one unit) is reduced or constant. SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to propose an electronic bidding method, an apparatus and a program for declaring an arbitrary evaluation value when marginal utility increases.
[0008]
[Means for Solving the Problems]
  According to one aspect of the one-way bidding method of the present invention, the organizer notifies the purchaser as the number K of sales units, which is obtained by subtracting one less than the maximum demand unit number t from the number of units K ′ that can be sold. Equipment foreachStores the evaluation value column for each unit of single goods received from the buyer, and for each price for each purchaser based on the evaluation value column, Out of the number of units that can be purchased below the rating valueFind the number of units that maximize utility as demand,eachFor each buyer, For each priceDeduct the total demand of other buyers from the number of units soldThepriceUnits available for purchase inAskingRemember,eachFor each buyer, Available for purchase at each priceThe number of unitsRead out the price when purchasing the kth product and the minimum number of units that can be purchased ≧ kTo do.
[0010]
In the interactive bidding method of the present invention, the organizer sets in advance the number of goods to be bought and sold, and further sets a threshold price (for buyers / sellers, the price at which the transaction is below or above that price). By controlling the number of transactions and the price of the transaction, even if the supply and demand are not balanced, it is ensured that the organizer is within the number determined in advance. Further, two parameters a and b are set to eliminate the problem of fictitious name bidding, and based on these a and b, the supply sum s at the threshold price r, and the demand sum d, , One-way bidding method of the present invention, and other one-side or other-side transaction.
[0011]
DETAILED DESCRIPTION OF THE INVENTION
Embodiment 1
Embodiment 1 of the present invention is a one-way electronic bidding method that can be applied when marginal utility increases.
A system configuration example to which the method of the present invention is applied is shown in FIG. A plurality of seller (seller) devices 200, a plurality of buyer (buyer) devices 300, and an auction organizer device 400 are connected via the communication network 100. The first embodiment is intended for a case where the organizer can sell and purchase goods. Accordingly, the purchaser device 300 and the organizer device 400 are used, and the seller device 200 is not used. Here, we explain the case where the organizer sells goods, but the seller (seller) and the purchaser (buyer) are basically symmetrical, so the organizer bids in the same way when buying goods. Can explain the method.
[0012]
It is assumed that the organizer knows the upper limit unit (unit) number t of each buyer's demand based on past auction experience. That is, each buyer does not need more than t + 1 units.
In the present invention, if the organizer owns the K ′ unit, that is, if the K ′ unit can be sold, the K ′ unit is not expressed to the buyer as the number of units sold, but the K unit satisfying K <K ′ is not expressed. As the default sales unit number, the default sales unit number K is expressed to the purchaser as the sales unit number. While this may seem uneconomical at first glance, the organizer leaves K'-K units to ensure that the number of units sold does not exceed K units.
[0013]
Price determination is based on each buyer's residual supply function. Here, the residual supply function is as follows. For any unit price (price per unit) p, the utility of buyer i (v_i(j) -unit demand d that maximizes p × j)_i(p) and each demand d in the set of buyers_iThe sum of (p) is d (p), and the evaluation value (the highest value that can be purchased) of buyer i for j units is v_i(j). If the same maximum utility is obtained for multiple units, the minimum number of units is the demand d_i(p), that is, the lower limit of the number j of units that maximizes utility is d_i(p). These are formulated as follows.
d_i(p) = inf {j | arg max_j(v_i(j) −p × j)} (3)
d (p) = Σ_id_i(p) (4)
[0014]
At this time, the remaining supply function s ~ of the buyer i at the price pⁱ(p) is the larger value of the difference between the total supply of goods (the number of default sales units) K and the number of units that other buyers want to purchase and 0, and can be expressed by the following equation.
s ~ⁱ(p) = max {K−Σd_q(p), 0} (5)
Σ is d other than q = i_qRepresents the sum of (p).
Figure 2 shows buyer i's residual supply function s ~ⁱAn example of (p) is shown. In this figure, the horizontal axis represents the number of units, and the vertical axis represents the price per unit. When the unit price p increases, the demands of other buyers are the same or decrease, so the residual supply function value (hereinafter referred to as residual supply) increases.
[0015]
The procedure of this embodiment will be described below.
FIG. 3 shows a functional configuration example of the organizer apparatus 400, and FIG. 4 shows an example of the processing procedure.
The organizer can sell a maximum of K 'units. At this time, when t is the maximum demand unit number of each buyer, the default sales unit number K = K ′ − (t−1)>assert t. This condition K>t is for ensuring robustness to fictitious name bidding, and if this condition is not satisfied, there is a possibility that the buyer may have the effect of fictitious name bidding for a number of units of K or more.
[0016]
In FIG. 3, the organizer's device 400 sends the sales unit number K to all participating buyer devices 300 for notification, or posts it on the bulletin board device 500 connected to the communication network 100 for notification. At this time, the deadline date is also notified. Moreover, it memorize | stores in the memory | storage part 420 (step S1).
The buyer i inputs an evaluation value for each number of units by operating the input unit to the buyer's device 300, and the buyer's device 300 transmits the evaluation value to the organizer's device 400. To express.
(V_i(1), v_i(2), ..., v_i(t)) (6)
[0017]
In the organizer apparatus 400, when the evaluation value sequence is received from the buyer apparatus 300 by the receiving unit 410 (step S2), it is stored in the storage unit 420 (step S3). When the bid closing date / time is reached (step S4), the evaluation value string is read from the storage unit 420, and the price of the buyer i for the j unit is determined as follows. Therefore, first, for each evaluation value column, the demand d for the number of units purchased for each good_i(p) is detected and stored by the maximum utility unit number detection unit 440 according to equation (3) (step S5). Then, buyer i's residual supply function s ~ⁱDemand d storing (p)_i(p) is read out and created by the residual supply function creation unit 430 (step S6). Residual supply function s ~ⁱ(p) is created by first setting unit price p = 0, and demand d of each buyer other than buyer i_q(0) is obtained by the maximum utility detection unit 440 according to the equation (3), and these demands d_q(0) is used to generate the residual supply function s ~ⁱ(0), and in the same manner, for each of the unit prices p = 1, 2,..._q(1), d_q(2), ..., d_q(K) is calculated and the remaining supply s ~¹(1), s ~¹(2), ..., s ~¹Find (K).
[0018]
At this time, when the purchase price of the buyer i purchases j units, the sum of the unit prices from the first unit to the jth unit, that is, the area of the hatched portion in FIG. It becomes. Price p of buyer i's kth unit_i(k) is determined by the unit price determination unit 450 using an equation (step S7).
p_i(k) = inf {p | s ~ⁱ(p)>k} (7)
In other words, to purchase k units, the remaining supply s ~ⁱ(p) must be greater than or equal to k, and the residual supply s ~ greater than kⁱUnit price p with the lower limit in price p giving (p) is the kth unit price p_i(k). In general, the lower the price p, the better for the buyer. Therefore, the residual supply function s ~ⁱ(p) is a function that increases the demand for other buyers as p becomes larger, and is an increasing function for p._iThe determination of (k) is s ~ⁱ(p)>The minimum price is within the range satisfying k.
[0019]
Next, the auctioneer organizer determines the number of units to be allocated so as to maximize the utility of each purchaser (step S8). If there are multiple units that can achieve the same utility, choose the organizer guess. That is, for each buyer i, k = 1 unit price p of the first unit_i(1) is determined by the unit price determination unit 450 according to the equation (7), and k = 2,..., The purchase unit price p of the Kth unit._i(2), ..., p_iDetermine (K). Then, for each buyer i, the determined purchase unit price p_iThe number of units k that maximizes the utility of buyer i using (k)_MiIs determined by Equation (3) using the maximum utility detector 440.
[0020]
For each buyer i, the payment calculator 470_i(1) + ... p_i(k_Mi) To calculate the payment amount P_iIs determined (step S9). In this case, unit price p for each k-th unit of buyer i previously obtained_i(k) may be used. Number of units k applied to buyer i on buyer's device 300_MiAnd payment amount P_iFrom the transmission unit 480 or through the bulletin board device 500 (step S10).
The organizer's device 400 is provided with an input unit 490, and the input unit 490 performs the input unit number K and other input settings. In addition, the control unit 495 can perform reading / writing with respect to the storage unit 420 and operations of other units.
[0021]
Example 1
If the maximum purchase unit number t of each buyer is 3, and the total supply unit number of the organizer is 9, the organizer sets the default sale unit number K = 9− (3-1) = 7 as the total supply unit number. Express. Assume that four buyers participate in the auction, and the evaluation value of each buyer is all-or-nothing. That is, the buyer needs any number of units of 3 units or less, and the evaluation value is zero if the number of units is not met. The evaluation value for Buyer i's 1 unit, 2 units, 3 units is (v_i(1), v_i(2), v_i(3)) and shown below.
Buyer 1: (0, 18, 18)
Buyer 2: (0,0,24)
Buyer 3: (0, 0, 21)
Buyer 4: (0,12,12)
[0022]
At this time, buyer 1 needs at least two units, and the price of buyer 1 is calculated as follows. At p = 0, buyer 2 demand d₂(0) = 3, Buyer 3 demand d_Three(0) = 3, demand 4 of buyer 4_Four(0) = 2 and the total demand of buyers other than buyer 1 is 3 + 3 + 2 = 8, and K = 7−8 = −1.¹(0) = 0. Similarly, buyer 1's remaining supply s ~¹(1) ~ s ~¹(5) is 0, demand d of buyers other than buyer 1 at p = 6₂(6) = 3, d_Three(6) = 3, but Buyer 4 has 2 × 6 = 12 for 2 units and its evaluation value is 12, so its utility is 0, and its evaluation value is 12 for 3 units. Therefore, the utility is zero, and the total demand d (6) of buyers other than buyer 1 is 3 + 3 = 6, and the remaining supply s of buyer 1 starts at p = 6^-1(6) is not 0, but 7−6 = 1. Therefore, the price p of the first unit of buyer 1₁(1) is the definition formula (7), and s of k = 1 or more^-1Lower limit s of (p)^-1In (6), p = 6.
[0023]
Next, the price p of Buyer 1 in the second unit₁(2) is the equation (7) where k = 2 and s ~¹The lower limit value 7 of p for which (p) is 2 or more. Since the evaluation values for 1 unit, 2 units and 3 units of Buyer 1 are 0, 18, and 18, the utility is maximized for Buyer 1 when 2 units are purchased. The sum is p₁(1) + p₁(2) = 6 + 7 = 13, and the price 13 is paid to purchase 2 units. Similarly, Buyer 2 pays 6 + 6 + 7 = 19 and purchases 3 units, Buyer 3 pays 6 + 6 + 8 = 20 and purchases 3 units. As a result, the total number of demands is 2 + 3 + 3 = 8 <K + (t−1) = 7 + 2 = 9.
[0024]
Features of the one-way bidding method of the present invention
The characteristics of the one-way bidding method (hereinafter referred to as a one-way auction protocol) of the present invention described in the first embodiment will be described. First of all, it is obvious that this one-way auction protocol satisfies incentive compatibility (utilization is maximized by declaring a true evaluation value) without a fictitious name bid. This is because the price is determined by a residual supply function based on other buyers' valuation values, and the allocation is determined so that the utility of each buyer is maximized. Therefore, the remaining problem is that the organizer can choose a feasible allocation, ie an allocation that does not exceed K ′ = K + (t−1) units. Further, the lower limit value of the assignment is K− (t−1) units, that is, the following theorem 1 holds.
[0025]
Theorem 1
The one-way bidding method of the present invention ensures that the number sold is K− (t−1) or more and K + (t−1) or less.
Theorem 1 is proved using FIG. The horizontal axis in FIG. 5 represents the total demand d (p), and the vertical axis represents the price per unit (unit price).
First, it shows that the lower limit of the number of sales units is K- (t-1). p₁Is the lowest price where d (p) does not exceed K units, and p₂Is the highest price where d (p) exceeds K units. Price p₁In each buyer's residual supply s ~ⁱ(p₁) Is demand d_i(p₁At this time, buyer i has demand d_i(p₁) You can be assured that you are going to buy more. This proof is as follows. Here, m <d_i(p₁) Is better when you get m units_i(p₁) Contradiction is assumed by assuming that the utility is greater than the utility used to obtain the unit. Figure 6 shows m units and d_i(p_i) Comparison of utility in units. In FIG. 6, p ′ = v_i(d_i(p₁)) / d_i(p₁), P = v_i(m) / m. In FIG. 6, the sum of the areas of A, C and D, that is, the payment amount P for m units from p × m_miThe remainder after subtracting the value indicates the utility when m units are obtained, and is the sum of the areas of B, C, D and E, that is, p ′ × d_i(p₁To d_i(p ) Payment amount P_{di (p1) i}The remainder after subtracting d_i(p₁) Utility when a unit is obtained. The utility when you get m units is d_i(p₁) At least A> B must be satisfied because it is greater than the utility at which the unit is obtained. On the other hand, price p₁The optimal demand for buyer i is_i(p₁) Because it is a unit
v_i(d_i(p₁))-P₁Xd_i(p₁)>v_i(m) -p₁× m (8)
And B + C>A + C is obtained. However, this inequality contradicts the previous inequality A> B. Therefore, buyer i has price p₁At d_i(p₁) Hope to buy more than a unit.
[0026]
So d against buyer set_i(p D (p) which is the sum of₁) For d (p₁)>If it is K- (t-1), the proof ends.
On the other hand, d (p₁) <K- (t-1), the price is p₂To p₁The maximum demand of each buyer is at most t and d (p₂)> K reduces demand for at least two buyers. Here, it is assumed that the buyer i is a buyer who minimizes the decrease in demand, and r_iIs a decrease in demand. Buyer i is r_iWhen you get additional units, p₁, But its utility is unchanged. By repeating this process, the number of units to be allocated can be increased to K− (t−1).
[0027]
Next, it is shown that the number of assigned units is at most K + (t−1). As shown in FIG. 5, the minimum price satisfying d (p) <K + t is defined as p._ThreeAnd d (p)>P is the highest price that satisfies K + t_FourAnd
At this time, the price of the first unit for all buyers is p_ThreeThat's it. This is price p_FourThis is because there is no residual supply because the demand of each buyer is at most t units. Further, as shown in FIG. 2, the price for additional units does not decrease, so the number of units that Buyer i gets is the price p_ThreeIt can be said that the demand in Japan is not exceeded. d (p_Three) Is the price p_ThreeThe total number of units that buyers get is d (p_Three) Is not exceeded. Therefore, the total number of units is less than K + t.
[0028]
Next, we will prove the robustness to fictitious name bidding.
Theorem 2
The one-way bidding method of the present invention is robust against fictitious name bidding.
First, the following lemma is shown.
Lemma 1
If Buyer i bids using two fictitious names i ′ and i ″ and obtains j ′ and j ″ units respectively, Buyer i is the same or with the same or less payment by using a single name j = j ′ + j ″ can be obtained.
From the equation (7), the following equation holds for an arbitrary k ′, k ″.
max {p_{i '}(K ′), p_{i ''}(K ″)}>p_i(k ′ + k ″) (9)
Two more inequalities are derived.
p_{i '}(K ′)>p_i(k ') (10)
p_{i ''}(K ″)>p_i(k ″) (11)
Σ_{k '= 1} ^{j '}p_{i '}(k ′) + Σ_{k '' = 1} ^{j ''}p_{i ''}(k ″) and Σ_{k = 1} ^jp_iWhen comparing (k), max {p_{i '}(J '), p_{i ''}(J ″)}>p_i(j ′ + j ″). As a result, the payment amount of i is smaller than the sum of i ′ and i ″ from the equations (10) and (11).
[0029]
A similar argument can also be made when a buyer bids using more than two names. This lemma and the method of the first invention can show Theorem 2 because it is incentive compatible if there is no fictitious name bidding.
In the above description, the one-way bidding method of the present invention is applied to the purchase of goods, but can also be applied to the sale of goods. In this case, as described above, since purchase and sale are basically symmetrical, the case of applying to sale of goods in parentheses in FIGS. 3 and 4 will be briefly described.
[0030]
In step S1 of FIG. 4, K = K ′ − (t−1) ≧ t (t is the supply upper limit value of each seller) for the maximum number of units K ′ that can be purchased by the organizer (the default purchase). An example of an evaluation value (v) that is the lowest price that can be sold for each number of units, which is input by the seller i._i(1), v_i(2), ..., v_i(t)) is transmitted to the organizer apparatus 400.
[0031]
The organizer apparatus 400 supplies the supply s that maximizes the utility of the seller i for an arbitrary price p in step S5._i(p) is calculated by the maximum utility unit number detector 440 according to the following equation (12).
s_i(p) = inf {j | arg max_j(p × j−v_i(j))} (12)
In step S6, the residual demand function d ~ⁱ(p) is calculated by the residual demand function creation unit 430 by the following equation (14).
d ~ⁱ(p) = max {K−Σs_q(p), 0} (14)
Σ is q_iS for q other than_qRepresents the sum of (p).
d ~ⁱ(p) is the remaining supply s of seller q other than seller i_qIt is the larger value of 0 and the value obtained by subtracting the sum of (p) from the total demand K.
[0032]
In step S7, unit price p of seller i's k-th unit_i(k) is determined by the unit price determination unit 450 using equation (7) ′.
p_i(k) = sup {p | d ~ⁱ(p)<k} (7) ′
In other words, the larger the price p, the smaller the number of goods that other sellers want to supply.ⁱ(p) is a decreasing function with respect to p, and the remaining demand d ~ⁱSince (p) is k or more and it is better to sell high, the price per unit supplying k goods is d ~ⁱThis is the upper limit value of p in (p).
Number of units k that maximizes utility of seller i in step S8_MiIn step S9, the acquisition amount calculation unit 470 similarly calculates the acquisition amount of the seller i. Notify each seller i of the allocated unit and the amount of acquisition.
[0033]
Embodiment 2
It can be applied even when an arbitrary evaluation value, that is, a marginal utility is gradually increased, and is robust against a fictitious name bidding. ). This GTPD protocol uses the one-way auction protocol of the first embodiment.
[0034]
In the GTPD protocol, the auctioneer presets two parameters for setting a threshold price and a neutral zone. This neutral zone is intended to eliminate the fictitious name bidding problem.
In the embodiment, s ~ⁱIn this GTPD protocol, the residual supply function s ~ⁱ(p) and residual demand function d ~ⁱTwo of (p) are used. Residual supply for all sellers_iLet s (p) be the sum of (p) and all remaining demands d_iLet d (p) be the sum of (p).
s (p) = Σ_is_i(p) (13)
d (p) = Σ_id_i(p) (13) '
[0035]
The GTPD protocol is as follows. Assume that the auctioneer knows the upper limit t of each bidder's demand / supply at a given threshold price. Here, for simplification, the supply s for the threshold price r_iThe sum s (r) of (r) is simply expressed as s, and the demand d for the threshold price r_iThe sum d (r) of (r) is simply expressed as d.
The auctioneer sets two parameters a and b so as to satisfy the following inequality in order to set the neutral zone.
a + b>t-1 (15)
Here, as long as Expression (15) is satisfied, a and b may be any non-negative numbers. For example, a = b = t / 2 may be used. Also, a threshold price r is set. The threshold price r is a lower limit price that is not sold to the buyer below the price, and is an upper limit price that is not purchased to the seller at a price higher than the price, and may be an arbitrary value. Predict the value that maximizes. For example, in the case of stocks, exchange rates, etc., a prediction calculation is performed based on the price transition before the threshold is set. Or simply, it may be determined from the sales performance of the organizer in the previous competitive bidding.
[0036]
Furthermore, the number K of goods that can be bought and sold is determined and set in advance. The parameters a and b, the threshold price r, and the number of goods K that can be bought and sold are set and input by the input unit 605 in the organizer apparatus shown in FIG. 7 and stored in the parameter storage unit 610. FIG. 7 shows a functional configuration example of the organizer apparatus, and FIG. 8 shows an example of the processing procedure. This auction is performed using, for example, the system shown in FIG.
[0037]
The organizer sets the total demand amount to K that is less than K ′, for example, K = K ′ − (t−1) ≧ t (t is the bidder's purchase / supply upper limit value) with respect to the maximum number of units that can be sold / purchased K ′. Set as K.
The organizer device 400 stores the input total demand K, threshold price r, and parameters a and b in the parameter storage unit 610 (step S1). The organizer's device 400 sends K to the participating bidder devices, ie, the seller's device 200 and the purchaser's device 300, or posts it on the bulletin board device 500 and notifies it as the number of tradeable items (step S2).
[0038]
The apparatus 200 for sellers is an array of evaluation values (sales evaluation value string) input by the seller is.
(V_is(1), v_is(2), ..., v_is(t))
Is transmitted to the organizer's device 400, and the purchaser's device 300 receives the evaluation value array (purchase evaluation value string) input by the purchaser ib
(V_ib(1), v_ib(2), ..., v_ib(t))
Is transmitted to the organizer apparatus 400.
[0039]
When the organizer device 400 receives the sales evaluation value sequence and the purchase evaluation value sequence at the receiving unit 615 (step S3), if the sales evaluation value sequence is received, the sales evaluation value storage unit 620 stores the sales evaluation value sequence. The purchase evaluation value storage unit 625 stores the purchase evaluation value (step S4). When the bid closing date / time is reached (step S5), the maximum utility unit detector 630 determines the remaining supply s at the threshold price r for each sales evaluation value string._i(r) is calculated and stored according to equation (12), and the residual demand d at the threshold price r for each purchase evaluation value sequence_i(r) is calculated and stored by equation (3) (step S6).
[0040]
Residual supply of all sellers at threshold price r_iThe total sum s of (r) is calculated and stored by the supply sum calculation unit 635 according to the equation (13), and the residual demand d of all buyers_iThe total sum d of (r) is calculated and stored by the total demand calculation unit 640 using the equation (13) ′ (step S7).
The determination unit 645 determines whether s + a <d using the parameters a and b, the supply sum s, and the demand sum d (step S8). If s + a <d is not satisfied, s<d<s + a or d<s<It is determined whether d + b (step S9). Based on these determination results, the process is divided into the following three cases.
[0041]
• The auctioneer determines the number of units to be traded and the price.
Case 1: s + a <d (when step S8 is positive)
A seller whose evaluation value is equal to or less than the threshold price r is assigned the number of units that maximizes utility at the threshold price r as a supply unit (step S10). Supply s determined in step S6_i(r) is the number of allocated supply units for seller i.
The larger max (t, s + a) of the sum of the supply sum s and the parameter a and the upper limit t is set as the default sales unit number K (step S11), and the one-way auction protocol for the buyer according to the first embodiment is the buyer one-way auction. This is executed by the execution unit 650, and the number of purchased units for the buyer i is assigned (step S12).
[0042]
Case 2: s<d<s + a or d<s<d + b (when step S9 is affirmative) In this case, the transaction is in the neutral zone, and the number of units that the seller and the buyer desire at the threshold price r, that is, the number of units that maximize the utility at the threshold price r, respectively. The number of supply units and the number of purchased units are allocated (step S13). The number of these units is obtained from step S6._i(r), d_i(r) can be used.
[0043]
Case 3: d + b <s (when step S9 is negative)
The number of units whose utility is maximized at the threshold price is assigned to the buyer having the threshold price or more as the number of purchased units (step S14). Also in this case, d obtained in step S6._iAssign (r) to buyer i. The larger max (t, d + b) of the sum of the total demand d and the parameter b and the upper limit t is set as the default sales unit number K (step S15), and the one-way auction protocol for sales in the first embodiment is the sales one-way protocol. This is executed by the execution unit 655, and the number of supply units for the seller i is assigned (step S16).
[0044]
The payment / acquisition amount calculation unit 660 calculates the payment amount and the acquisition amount for the number of units allocated to the seller and the buyer determined as described above (step S17). When the number of assigned units is determined at the threshold price r, the threshold price r and demand d_i(r) and supply s_iEach product with (r) is an acquisition amount and a payment amount. In other cases, the product is obtained as described for step S9 in FIG.
[0045]
The transmission unit 665 sends a notification of the determined number of supply units and the acquired amount to the corresponding seller device 200, and notifies the determined purchase unit and the payment amount to the corresponding purchaser device 300, or posts them on the bulletin board device 500. (Step S18).
In order to execute the buyer one-way auction protocol and the seller one-way auction protocol, the organizer device 400 is also provided with a residual supply function creation unit 670, a residual demand function creation unit 675, and the like, and performs reading and writing to each storage unit. A control unit 680 for operating each unit is provided.
[0046]
In the GTPD protocol, the number of units sold / purchased by the auctioneer can be suppressed to 2t-1. The worst case when the organizer sells is when there is no supply while there is a large amount of demand, and since Case 1 and a <t, the organizer of the auction has a larger value t between t and s + a. Is set to the default number of sales units, the actual number of transactions is at most t + (t−1). Similarly, the worst case when the organizer purchases is Case 3, and t is the larger of t and d + b, so the number of transactions is at most 2t-1 in order to set the number of default purchase units to t. is there.
[0047]
Example 2
As in Example 1, the evaluation value for all participants is all-or-nothing. Further, t = 3 and r = 5 with respect to the threshold price. For simplification, a = b = 3. The evaluation values of the two sellers 1 and 2 and the evaluation values of the four buyers 1, 2, 3, and 4 are as follows.
Seller 1: (6, 6, 0)
Seller 2: (8, 8, 0)
Buyer 1: (0, 18, 18)
Buyer 2: (0,0,24)
Buyer 3: (0, 0, 21)
Buyer 4: (0,12,12)
[0048]
The supply that seller 1 has the maximum utility when the threshold price r = 5 or less is p = 5, because the utility is negative for 1 unit and the utility is 4 for 2 units.₁(5) = 2 units. Similarly, if the seller 2 has the threshold price r = 5 or less and the maximum utility is p = 5, the utility is negative for 1 unit and the utility is 2 units. 2 because s₂(5) = 2 units. Therefore, the total supply s below the threshold price is 2 + 2 = 4 units.
[0049]
Further, the demand that the buyer 1 has the maximum utility at the threshold price r = 5 or more is the demand d for p = 5 from the equation (3).₁(5) = 2, and buyers 2 and 3 do not wish to purchase anything other than 3 units, so the demand that maximizes utility at price r = 5 or higher is d₂(5) = 3, d_Three(5) = 3, and the demand that maximizes the utility when buyer 2 has a threshold price r = 5 or more is d_Four(5) = 2. Therefore, the total demand d is 2 + 3 + 3 + 2 = 10 units.
[0050]
Since s + a = 4 + 3 = 7 <10 = d, the condition of case 1 is satisfied, and all sellers can sell goods at a threshold price. Therefore, the supply is 4 units, and the sum of the received amounts is 5 × 2 + 5 × 2 = 20. On the other hand, for the buyer, the default number of sales units is set to max (3,7) = 7. In this state, it is equivalent to the case of Example 1, the buyer's demand is 8, and the sum of the payment amount is 52. As a result, the organizer sells 4 units.
[0051]
Features of the bidding method of the present invention
Theorem 3
The GTPD protocol is robust to fictitious name bidding.
The proof for Theorem 2 clarified that the one-way auction protocol described in the first embodiment is robust to fictitious name bidding. Therefore, it is only necessary to show that the utility does not increase even if the seller / buyer impersonates another buyer / seller and makes a fictitious name bid. Furthermore, since the buyer and the seller are basically symmetrical, the case where the seller pretends to be a buyer and makes a fictitious name bid is considered here.
Seller i is s_iWhen selling a unit, seller i_i+ D_iSell unit and d by fictitious name_iSuppose you get a unit. Where s ~ⁱIs the total supply other than seller i.
[0052]
First, seller i is in the real name_iSuppose you sell units. If the total supply s is less than the total demand d by the setting parameter a, s ~ⁱ+ S_i+ A<If d holds, it becomes GTPD protocol case 1 or case 2, and seller i has a threshold price, which is the highest selling price for the seller, s_iSell units. Therefore, in this case, fictitious name bidding is not effective.
[0053]
On the other hand, when the total supply s satisfies the case 3, which is greater than the total demand d by the setting parameter b, that is,
d + b <s ~ⁱ+ S_i                                (16)
The seller i's receipt will be lower than the threshold price, and seller i will calculate the fictitious name bid, i.e., the number of units sold._i+ D_iAnd d_iYou may try to increase utility by purchasing units. Therefore, Case 3 indicates that the utility does not increase even if seller i changes to another situation by fictitious name bidding.
The supply of seller i is s'_i+ D_i(S '_i >s_i), And d '_i(d '_i >d_i).
[0054]
Case 3: s ~ⁱ+ S '_i+ D_i> D + b + d ′_iSince all buyers can get the desired number of units at the threshold price, d '_iD_iCan be set. In this case, the default number of sales units is K ′ = d + d_i+ B and seller i's residual demand function is d_{K '}~ⁱIt is. On the other hand, if seller i does not make a fictitious name bid, the default number of sales units is K = d + b, and the residual demand function of seller i is d_K~ⁱIt becomes. d_{K '}~ⁱIn the first unit to d-th_iThe price per unit up to the unit is the total demand d_iIt depends on the residual demand brought about by the unit increase. And d_i+1 from the first unit_{K '}~ⁱThe price determined by_K~ⁱIt is equivalent to the price from the first unit. Therefore, seller i_iThe price of the unit cannot be lowered, and d at the threshold price_iBuy a unit and d_iUnits will be sold below the threshold. That is, seller i cannot increase utility using fictitious name bidding.
[0055]
Case 2: d + d ′_i <s ~ⁱ+ S '_i+ D_i <d + d '_i+ B or s ~ⁱ+ S '_i+ D_i <d + d '_i <s ~ⁱ+ S '_i+ D_iWhen + a, all sellers / buyers are trading at a threshold price. In this case, s'_i= S_iAnd d '_i= D_iAnd d<s ~ⁱ+ S_i <d + b or s ~ⁱ+ S '_i <d<s ~ⁱ+ S '_i+ A. In either case, the seller i cannot change from the case 3 to the case 2 using the fictitious name bidding because it contradicts the equation (16).
[0056]
Case 1: d + d ′_i+ A> s ~ⁱ+ S '_iThen all sellers can sell goods at a threshold price. Therefore, s'_iS_iAnd The default number of units sold is K = s ~ⁱ+ S_i+ D_i+ A. In the one-way auction, as shown in Theorem 1, to guarantee that at least K- (t-1) units are sold, the minimum number of units to be traded is s ~ⁱ+ S_i+ D_i+ A− (t−1), d + d_i >s ~ⁱ+ S_i+ D_i+ A- (t-1). For both sides of this inequality, d_iSubtraction and b_iD + b>s ~ⁱ+ S_i+ A + b- (t-1). Since a + b− (t−1) is 0 or a positive value from the equation (15), this inequality is contrary to the equation (16). Therefore, the seller i cannot change from the case 3 to the case 1 by the fictitious name bidding.
[0057]
The organizer apparatus shown in FIGS. 3 and 7 can be made to function by a computer. In this case, a program for causing the computer to execute each step of the processing method shown in FIG. 4 or FIG. 8 is downloaded to the computer via a recording medium such as a CD-ROM, a magnetic disk, a magneto-optical disk, or a communication line. The computer may be executed by the program.
[0058]
【The invention's effect】
As described above, according to the present invention, any evaluation value can be bid in either one-way bidding or two-way bidding for multiple units of single goods, that is, even when marginal utility increases. Apply and be robust against fictitious name bidding, that is, each bidder will ensure that their profits are maximized by bidding for the correct evaluation value.
[Brief description of the drawings]
FIG. 1 is a diagram showing an example of an electronic bidding system to which the present invention is applied.
FIG. 2 is a diagram showing an example of a remaining supply curve of a buyer i.
FIG. 3 is a diagram showing a functional configuration example of the organizer apparatus according to the first embodiment of the present invention.
4 is a diagram showing an example of a processing procedure of the organizer apparatus shown in FIG. 3;
FIG. 5 is a diagram showing an example of the relationship between demand and unit price.
FIG. 6: m unit and d_i(p₁) The figure for demonstrating the comparison of utility with a unit.
FIG. 7 is a diagram illustrating a functional configuration example of the organizer device according to the second embodiment.
8 is a diagram showing an example of a processing procedure of the organizer apparatus shown in FIG.

Claims (6)

In the processing method of the competitive bidding organizer apparatus for determining the number of units of purchased goods of each purchaser based on the evaluation value column for each number of units of single goods received from a plurality of purchasers,
Supply total number of goods in the storage unit of the organizer's system is Yes stored,
Store the received evaluation value sequence of each purchaser in the storage unit,
Read out the evaluation value sequence of the purchaser, and for each purchaser, for each price, find the number of units that maximize the utility among the number of units that can be purchased with less than the evaluation value, and store it in the storage unit And
Reads the demand for each buyer, a total demand of other buyers for each price, Pull insert Ri by said feed total number, in the storage unit determined as the number of units available for purchase at the price Remember,
Each upper Symbol each purchaser, from the storage unit reads the number of units available for purchase at the price, that shall be the minimum price the unit number ≧ k purchasable price when buying the k th An apparatus processing method for a multi-goods electronic bidding organizer, which is characterized. A host device of electronic bids to determine the cart unit for single goods multiple units,
A storage unit which supplied the total number are stored in the goods,
An evaluation value storage unit for storing an evaluation value string for each number of goods received from each purchaser;
An evaluation value column for each purchaser is input, and for a given unit price , a maximum utility unit number detection unit that obtains the maximum number of units that can be purchased with less than the evaluation value ,
The inputted maximum utility unit number for each unit price of each purchaser, for each buyer, remaining subjected to the sum of the maximum utility unit number of the same unit price other buyers by subtracting et whether the supply total number calculates the refueling number knit, a function that associates a purchaser and a unit price and residuum supply unit number, and a residual supply function creating unit that creates a balance supply function,
The unit price determination unit that outputs the number of units that can be purchased at each price for each purchaser by the above-described residual supply function, and sets the price when purchasing the kth product as the minimum price that satisfies the number of residual supply units ≧ k and,
Comprising the organizer for the equipment. In an electronic bidding method for a plurality of units of a single good using a plurality of seller devices, a plurality of purchaser devices, and a competitive bidding organizer device connected thereto via a communication network ,
The parameters a and b satisfying a + b > t−1, the total demand K, and the threshold price r are stored in the organizer device for the seller's goods supply upper limit and the buyer's goods demand upper limit t. Every
The seller device sends a sales evaluation value sequence that is an array of evaluation values for each number of units of the seller to the organizer device,
The purchaser device sends a purchase evaluation value sequence that is an array of evaluation values for each number of units of the purchaser to the organizer device,
The organizer device stores the received sales evaluation value sequence and purchase evaluation value sequence in the storage unit,
The total sum s of each seller's supply for the threshold price r is obtained based on the sales evaluation value column
A total sum d of demands of each purchaser with respect to the threshold price r is obtained based on the purchase evaluation value column,
A first determination is made as to whether the sum of the supply sum s and the parameter a is less than the demand sum d;
If the first determination is small, for each sales evaluation value column, the number of units that maximize the utility at the threshold price is determined as the number of supply units of the corresponding seller,
The electronic bidding method according to claim 1 is executed by determining the larger of the total supply s and the sum of parameters a and the upper limit t as the supply goods total number K, and determining the number of purchased units of each purchaser,
If the first determination is not small, the demand sum d is not less than the sum of supply s and not more than the sum of the sum of supply s and parameter a, or the sum of supply s is not less than the sum of demand d and not more than the sum of demand sum d and parameter b. A second determination of whether or not
If the second determination is affirmative, the number of units maximizing the utility at the threshold price r for each sales evaluation value column and each purchase evaluation value column is set to the number of supply units of the corresponding seller, and the purchase unit of the purchaser. Decide on a number,
If the second determination is negative, the number of units that maximizes the utility at the threshold price r for each purchase evaluation value column is determined as the number of purchased units for the corresponding purchaser,
The electronic bidding method according to claim 4 is executed with the larger of the total demand d and the sum of the parameters b and the upper limit t as the total demand K, and the number of supply units of the seller is determined.
An electronic bidding method for a plurality of goods, wherein the determined supply unit number of each seller and the purchase unit number of each purchaser are transmitted to the corresponding seller device and purchaser device, respectively. Electronic bidding for multiple units of a single good using a plurality of seller devices and a plurality of purchaser devices and a competitive bidding organizer device connected thereto via a communication network A processing method for an organizer device,
Parameters a and b satisfying a + b > t−1, total demand amount K, and threshold price r are stored in the storage unit with respect to the seller's goods supply upper limit and the buyer's goods demand upper limit t.
Store in the storage unit a sales evaluation value sequence that is an array of evaluation values for each number of units of the seller received from the device for the seller,
A purchase evaluation value sequence that is an array of evaluation values for each number of units of the purchaser received from the purchaser device is stored in the storage unit,
The sales evaluation value string is read out, and the sum s of supply of each seller for the threshold price r is obtained and stored in the storage unit.
The purchase evaluation value string is read, and the total sum d of each buyer's demand for the threshold price r is obtained and stored in the storage unit,
A first determination is made as to whether the sum of the supply sum s and the parameter a is less than the demand sum d;
If the first determination is small, the sales evaluation value sequence is read, and the number of units that maximize the utility at the threshold price for each sales evaluation value sequence is determined as the number of supply units of the corresponding seller.
The electronic bidding method according to claim 1 is executed by determining the larger of the total supply s and the sum of parameters a and the upper limit t as the supply goods total number K, and determining the number of purchased units of each purchaser,
If the first determination is not small, the demand sum d is not less than the sum of supply s and not more than the sum of the sum of supply s and parameter a, or the sum of supply s is not less than the sum of demand d and not more than the sum of demand sum d and parameter b. A second determination of whether or not
If the second determination is affirmative, the sales evaluation value column and the purchase evaluation value column are read out, and the number of units whose utility is maximized with the threshold price r for each sales evaluation value column and for each purchase evaluation value column, respectively. Decide on the number of supply units of the corresponding seller, the number of purchased units of the buyer,
If the second determination is negative, the purchase evaluation value sequence is read, and for each purchase evaluation value sequence, the number of units that maximizes the utility at the threshold price r is determined as the number of purchase units of the corresponding purchaser,
The electronic bidding method according to claim 4 is executed with the larger of the total demand d and the sum of the parameters b and the upper limit t as the total demand K, and the number of supply units of the seller is determined.
A method for processing a multi-goods electronic bidding organizer characterized by transmitting the number of supply units of each seller determined above and the number of purchase units of each purchaser to the corresponding seller device and purchaser device, respectively. . Electronic bidding for multiple units of a single good using a plurality of seller devices and a plurality of purchaser devices and a competitive bidding organizer device connected thereto via a communication network An organizer device,
A parameter storage unit in which parameters a and b satisfying a + b > t−1, total demand amount K, and threshold price r are stored with respect to the goods supply upper limit of the seller and the goods demand upper limit t of the purchaser;
A sales evaluation value storage unit that stores a sales evaluation value sequence that is an array of evaluation values for each number of units of the seller received from the device for the seller;
A purchase evaluation value storage unit that stores a purchase evaluation value sequence that is an array of evaluation values for each number of units of the purchaser received from the purchaser device;
A supply sum total calculation unit for obtaining a sum s of supply of each seller for the threshold price r based on a sales evaluation value sequence;
A demand sum total calculation unit for obtaining a sum d of demands of each purchaser with respect to a threshold price r based on a purchase evaluation value sequence;
First determination as to whether or not the sum of supply sum s and parameter a is smaller than demand sum d, and demand sum d is greater than or equal to supply sum s and less than or equal to sum of supply sum s and parameter a or supply sum s is demand A determination unit that performs a second determination as to whether or not the sum is greater than or equal to the sum d and less than or equal to the sum of the demand sum d and the parameter b;
The buyer piece that determines the number of purchased units of each purchaser by executing the electronic bidding method according to claim 1, wherein the larger of the sum of the supply sum s and the parameter a and the upper limit value t is the supply goods total number K. A direction auction department,
The first judgment is small, and for each sales evaluation value column, the number of units that maximize the utility at the threshold price is determined as the number of supply units of the corresponding seller,
If the second determination is affirmative, the number of units maximizing the utility at the threshold price r for each sales evaluation value column and each purchase evaluation value column is set to the number of supply units of the corresponding seller, and the number of purchased units of the purchaser. If the second determination is negative, an allocation unit determination unit that determines the number of units that maximizes utility at the threshold price r for each purchase evaluation value column as the number of purchased units for the corresponding purchaser;
The seller one-way auction execution unit which determines the number of supply units of the seller by executing the electronic bidding method according to claim 4, wherein the larger of the total demand d and the upper limit t of the sum of the parameters b is the total demand amount K. When,
An organizer device comprising: the determined supply unit number of each seller, the purchaser device number corresponding to each purchaser, and a transmission unit that transmits the purchaser device to the purchaser device. Claim 1, 3, 4 programs for executing each process of the plurality goods electronic bidding organizer's device processing methods described computer to either.

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