A Model of Pricing Data and Their Constituent
Variables Traded in Two-Sided Markets with Resale:
A Subject ExperimentToshihiko Nanbaa , Kazuhito Ogawab , Naoki Watanabec ,Teruaki Hayashid , Hiroki Sakajida KUAS (econ), b Kansai Univ. (socio), c Keio Univ. (business), d U. of Tokyo (eng)August 13, 2023
Economic Theory Workshop in Morioka

1/1Part of this work was published in Proceedings of 2022 IEEE Int’lConference on Big Data from IEEE Xplore in January 2023.

These slides are available at my website.
First, search for my website using naoki watanabe and keio as
keywords. Then, find the url of (presentation slide) at [2] in<Publications Written in English>.
http://labs.kbs.keio.ac.jp/naoki50lab/index.html
Alternatively,
http://labs.kbs.keio.ac.jp/naoki50lab/DataExPresentation3.pdf

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Imagine the following data service,as a simple familiar example.

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Creating a new market for used digital communication devices
various factors (variables) that determine the price of a used device
in-store or online retail prices and specifications of new products
transaction information in online auctions of second-hand products,
including damage, network restrictions, and so onothersa set of “processed and summarized” variables (data) of a used device
specified for each user

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1. Introduction: Research Question

Each instance of data consists of several variables.
variable: address, gender, # of households, ... (for real-estate markets)
data: a set these variables constitute that makes sense when used for agiven purpose

Data and variables are easily replicable. ⇒ not scarce ⇒ difficult toput a price on variables and data
How can we price the data and its constituent variables?

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1. Introduction: Major Features
a new model from the perspective of cooperative games
1

Muto and Nakayama (1992): resale of information (withoutproduction)

2

Watanabe and Muto (2008): disadvantage arising due to not owning
information (under patent protection)

The prices of variables are exogenously set at the initial round, and they
are updated for the next round based on the outcomes of trades made in
the current round.
Conjecture: backward induction ⇒ prices never move in any rounds
that proceed after the initial round.
There is no budget constraint on subjects’ decision-making. (Weconducted additional sessions under budget constraints recently.)
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1. Introduction: Main Results

The prices of data and the constituent variables fluctuated overrounds (probably due to no budget constraint), but
the average prices of those variables were not far from the initialvalues we set theoretically.
No significant difference in amounts of producer surplus, regardless ofwhether subjects were informed of values of gross profits trades
generated (whether the information was complete or incomplete).
Real trades are conducted with incomplete information.
Theoretical inference of this work was derived with completeinformation.

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2. Model

2 instances of data, each consisting of 3 items of variables, traded in
12 rounds (r = 0, 1, 2, . . . , 12) by 4 traders.
At each round, the prices of the variables are given to traders andupdated for the next round immediately at the end of the round,based on the outcomes of trades.
pi (r ): price of variable i in round r
replicability ⇒ Traders purchase one unit of the variable.
The production cost of data is the sum of the expenditure
for the constituent variables.
tj (r ): price of data j in round r
replicability ⇒ Users of data j purchase one unit of the data.
no budget constraints

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the gross profits for an individual user and those for a non-user of thedata satisfy the following relationship:
Wj (1) ≥ Wj (2) ≥ · · · ≥ Wj (n) > Lj (0)≥ Lj (1) ≥ Lj (2) ≥ · · · ≥ Lj (n − 1).

(1)

When there are s owners of data j, a user obtains Wj (s) while anon-user obtains Lj (s). (disadvantages for non-users)The data can be replicated and resold freely.
each owner of the data proposes the price and the number of instancesof the data, andtraders who do not own the data may purchase the data at theproposed price.

ti (r ) is the price at which the initial owner sells. The resale process
stops for all data ⇒ transactions proceed to the next round.
Any data expire for the use within each round in order to avoid
dynamic competition among instances of data at the markets.
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# of users of data j (j = 1, 2) ⇒ demand for variable iqi (r ): threshold for variable i in round r . This threshold value is used
for updating its price pi (r ) that is set at the market in the next round.
The initial values of qi (0) and pi (0) are exogenously given.
Demand for variable i in round t exceeds qi (t) ⇒ the price in roundt + 1 is updated to pi (t + 1) = pi (t) + ai . The threshold in roundt + 1 is also updated to qi (t + 1) = qi (t) + bi .
Demand falls below qi (t). ⇒ pi (t + 1) = max(0, pi (t) − ai ) andqi (t + 1) = max(0, qi (t) − bi ).
· · · ai and bi are positive constants exogenously given.

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3. Experimental Design: Gross Profits
Data 1 and Data 2 are traded.
The gross profits are specified as follows.
Data 1: W1 (1) = 200, W1 (2) = 150, W1 (3) = 70, W1 (4) = 50,
L1 (0) = 40, L1 (1) = 30, L1 (2) = 20, L1 (3) = 10.
Data 2: W2 (1) = 200, W2 (2) = 120, W2 (3) = 70, W2 (4) = 50,
L2 (0) = 40, L2 (1) = 30, L2 (2) = 20, L2 (3) = 10.
complete information environment: the values of gross profits areshown to the subjects.
incomplete information environment: subjects are informed of theorders of those gross profits. In practice, traders have to estimate
those values.

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3. Experimental Design: Demands for Variables# of users of data j (j = 1, 2) ⇒ demand for variable iFirst, find the largest integer e such that 2 ≤ e ≤ 3 andWj (e) ≥ Wj (4) + (4 − e)(Wj (4) − Lj (e)).

When e = 3, Wj (3) = 70 and Wj (4) + (4 − 3)(Wj (4) − Lj (3)) = 90.
Namely, when there are 3 data holders, each one obtains 70 but hecan obtain 90 by reselling the data, but the amount is at most 90.
When e = 2, W1 (2) = 150 and W2 (2) = 120, but
Wj (4) + (4 − 2)(Wj (4) − Lj (2)) = 110 for j = 1, 2.
Namely, when there are 2 data holders, each data holder does nothave an incentive to resell the data.
The solution of the above problem is thus e = 2.
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Second, consider a situation in which there are 2 data holders.
If one of the data holders resells to a trader, then he can receive
Wj (3) − Lj (2) = 50 for Data j = 1, 2 from the trader.
In the case of e = 3, however, another resale is expected to occur,as shown previously. Thus, the data holders can eventually obtainat most Wj (3) − Lj (2) + Wj (4) + (Wj (4) − Lj (3)) = 140 for Dataj = 1, 2.
In the case of Data 1, any resale should not occur when e = 2,because W1 (2) = 150.
Even in the case of Data 2, any resale should not occur when e = 2;
Truly, W2 (2) = 120, but when e = 3, resale should be competitive
among 3 resellers and thus the resale price would decrease to thesmallest possible monetary unit; W2 (3) − L2 (2) + W (4) = 100.
Resale does not occur when there are 2 data holders.

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Finally, compare the case of e = 2 and e = 1.
If the initial holder of Data 1 does not sell the data, then he obtains
W1 (1) = 200, but he can obtain
W1 (2) + (2 − 1)(W1 (2) − L1 (1)) = 270through monetary transfer by selling the data to a trader.
Similarly, consider the case of Data 2. W2 (1) = 200, but he canobtain W2 (2) + (2 − 1)(W2 (2) − L2 (1)) = 210
through monetary transfer by selling the data to a trader.
According to the backward induction, 2 data holders should not resell thedata to any traders.

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3. Experimental Design: Note

Muto and Nakayama (1992) showed that these outcomes are in a variantof Bargaining Set recurrently defined in a dynamic context, whenWj (1) ≥ Wj (2) ≥ · · · ≥ Wj (n) > Lj (0)=Lj (1)=Lj (2)= · · · =Lj (n − 1)= 0,(2)and one instance of data is traded.

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3. Experimental Design: Social Welfare

Compute the maximal amounts of producer surplus. (The payments arecancelled between payers and recipients, when summing up their profits.)
Data 1: the total sum of profits (producer surplus) is maximized ate = 2; 2W1 (2) + 2L1 (2) = 2 ∗ 150 + 2 ∗ 20 = 340.
Data 2: it is maximized at e = 1;
W2 (1) + 3L2 (3) = 200 + 3 ∗ 30 = 290.
(2W2 (2) + 2L2 (2) = 2 ∗ 120 + 2 ∗ 20 = 280)
Therefore, in terms of “social welfare” of traders, the initial holder ofData 2 should not sell Data 2 to any users.

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3. Experimental Design: Theoretical Predictions

payoff maximization: The initial holders of Data 1 and Data 2 should
sell their data to a trader, respectively. Resale should not occur.
social welfare: It is maximized when there are 2 data holders in thecase of Data 1, while it is maximized when the initial holder of Data 2
does not sell the data to any traders.

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3. Experimental Design: Session Details
We conducted 4 experimental sessions, each consisting of 12 rounds.

The initial prices of variables x, y and z : p1 (0) = 10, p2 (0) = 20,p3 (0) = 30.
q1 (0) = q2 (0) = q3 (0) = 2 for Data 1, and q1 (0) = q2 (0) = 2 or
q1 (0) = q3 (0) = 2 for Data 2 (by the previous backward induction)
The constants for updating those prices and thresholds are
a1 = a2 = 10 and b1 = b2 = 10, respectively.

18 / 1In every session, 16 subjects divided into 4 groups of 4 subjects at thebeginning of the session.

The initial holder of each data is determined randomly and does notchange in all rounds.

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Data 1 ⇒ Data 2: The transactions of Data 2 proceed in a manner
similar to those for Data 1.
After the transactions for Data 1 and Data 2, the price of thevariables are updated.
Then, the transactions for the next round start in a similar manner.

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Resale can be made at most twice.
The payoff for the initial holder of Data j = (gross profit obtained fromData j − prices of Data j’s constituent variables + selling price of Data j+ total resale price of Data j) + (gross profit obtained from Data i purchase price of Data i + total resale price of Data i),where i = 1, 2 and i 6= j.
The payoff for a trader who is not the initial holder = gross profit obtained
from Data 1 − buying price of Data 1 + total resale price of Data 1 +gross profit obtained from Data 2 − buying price of Data 2 + total resale
price of Data 2.

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4. Result: Prices of Variables
Result 1
Without budget constraints, the prices of variables fluctuated, but for any
i = x, y , z, the averages are not far from its initial price pi (0).

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sessioncomp xy
comp xz
incomp xy
incomp xz

variable x
12.917 (10.097)
12.292 (11.530)
10.417 ( 8.742)
10.208 ( 7.852)

variable y
20.625 (12.949)
17.292 ( 8.688)
16.875 (10.750)
22.917 ( 8.495)

variable z
34.375 ( 7.118)
25.833 (13.657)
25.000 (11.109)
29.167 ( 9.187)

Table: Average prices of variables. No budget constraints. Values in parentheses
represent standard deviations
Note: The initial prices of variables are set as p1 (0) = 10, p2 (0) = 20, and p3 (0) = 30.

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sessioncomp xy
comp xz
incomp xy
incomp xz

variable x
8.889 ( 9.428)
9.500 ( 8.719)
13.646 (10.966)
12.708 ( 9.394)

variable y
13.472 ( 9.952)
22.167 ( 7.831)
21.458 (12.813)
22.292 ( 6.270)

variable z
23.472 (11.279)
25.000 (12.003)
29.271 (11.262)
29.583 (12.831)

Table: Average prices of variables. Under budget constraints. Values inparentheses represent standard deviations.
Note: The initial prices of variables are set as p1 (0) = 10, p2 (0) = 20, and p3 (0) = 30.

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4. Result: Prices of Data
Result 2
Without budget constraints, for both Data 1 and Data 2, there are somerounds in which soaring prices of data were observed in a session.

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sessioncomp xy
comp xz
incomp xy
incomp xz

Data 190.644 (39.448)
144.293 (69.744)
91.176 (32.908)
100.404 (57.896)

Data 291.097 (44.582)
150.119 (66.961)
62.581 (20.036)
110.220 (56.987)

p-value
0.632
0.7762<0.001
0.214

Table: Average prices of data offered by the initial data holders. No budget
constraints
Note: Transactions were not made at extraordinarily high prices. Those prices areexcluded in computing the average listed above. The p-values for the Brunner-Munzel
test are also listed, where the null hypothesis is that the prices are on average the same
between Data 1 and Data 2.

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sessioncomp xy
comp xz
incomp xy
incomp xz

Data 195.758 (38.793)
92.889 (39.910)
101.961 (37.197)
78.450 (26.330)

Data 293.111 (51.899)
83.618 (21.500)
92.978 (40.622)
79.568 (34.506)

p-value
0.395
0.694
0.089
0.574

Table: Average prices of data offered by the initial data holders. Under budget
constraints
Note: The p-values for the Brunner-Munzel test are also listed.

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4. Result: Social Welfare 1
Result 3
Without budget constraints, the efficiency rates observed in theincomplete information environment were not significantly different fromthose observed in the complete information environment.

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comp xy
comp xz
incomp xy
incomp xz

Data 10.813 (0.174)
0.849 (0.145)
0.820 (0.131)
0.797 (0.159)

Data 20.915 (0.122)
0.940 (0.105)
0.911 (0.118)
0.937 (0.109)

n48
48
48
48

Table: Average efficiency rates without budget constraints

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comp xy
comp xz
incomp xy
incomp xz

Data 10.827 (0.120)
0.829 (0.172)
0.824 (0.152)
0.860 (0.160)

Data 20.924 (0.114)
0.940 (0.107)
0.886 (0.122)
0.881 (0.128)

n72609648

Table: Average efficiency rates under budget constraints

There would be a significant difference in efficiency rates for Data 2.

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4. Result: Social Welfare 2
Result 4
There was no significant difference in efficiency rates between Data 1 andData 2, except in a session. (No budget constraints)
Table III shows the results of a two-way ANOVA.

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negative test results: Normality of samples in some sessions andhomoscedasticity of samples in Data 2. ⇒ Brunner-Munzel test

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4. Result: What Factors Made Efficiency Rates Lower?
Result 5
Social welfare declines as the frequency of resale increases. (No budgetconstraints)

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5. Final Remarks: For Future Research

Conducting additional treatment.
Result 4 may imply that the order of trading Data 1 and Data 2
affected the difference in efficiency rates.
more realistic budget constraints

Extension to a more general model.
We need to introduce asymmetric gross profits in to our model.

Are the outcomes derived by the backward Induction in the Bargaining Set
defined in the spirit of Muto and Nakayama (1992)?

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