ISSN (Print) 0473-453X

Discussion Paper No. 1151

ISSN (Online) 2435-0982

TRADING INFORMATION GOODS
ON A NETWORK:AN EXPERIMENT

Nobuyuki Hanaki
Yutaka Kayaba
Jun Maekawa
Hitoshi Matsushima

December 2021

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Trading information goods on a network:
An experiment∗
Nobuyuki Hanaki† Yutaka Kayaba‡
Jun Maekawa§ Hitoshi Matsushima¶
December 1, 2021

Abstract
We experimentally examine the impact of a cycle path on the trading of a copyable information good in networks. A cycle path in a network permits a buyer to become a reseller that can compete against
existing sellers by replicating the good. Theory predicts that the priceof the information good, even with the first transaction where there
is not yet a reseller competing with the original seller, will be lower in
networks with a cycle path than otherwise. However, our experiment
reveals that the observed price for the first transaction is significantly
higher in networks with a cycle path.

Keywords: Information good, Network
JEL codes: D42, L14∗

The experiments reported in this paper were approved by the Institutional Review
Board of the Institute of Social and Economic Research, Osaka University. We gratefully
acknowledge the financial support of grants-in-aid for scientific research (KAKENHI Grant
Nos. 18K12742, 18K19954, 20H00070, and 20H05631) from the Japan Society for the
Promotion of Science and the Japanese Ministry of Education, Culture, Sports, Scienceand Technology along with the Joint Usage/Research Center at the Institute of Social andEconomic Research, Osaka University, and the Center of Advanced Research in Finance(CARF) at the University of Tokyo. Ivan Conjeaud, Akishige Ikoma, and Takio Uesugi
provided valuable support in preparing the software for the experiment.
†
Institute of Social and Economic Research, Osaka University.
E-mail:nobuyuki.hanaki@iser.osaka-u.ac.jp‡
Graduate School of Economics, University of Tokyo. E-mail: ykayaba@e.u-tokyo.ac.jp§
Ritsumeikan Global Innovation Research Institution, Ritsumeikan University. E-mail:jmaekawa@fc.ritsumei.ac.jp¶
Graduate School of Economics, University of Tokyo. E-mail: hitoshi@e.u-tokyo.ac.jp1

1

Introduction

When information (such as images, videos, texts, computer programs, andtechnological innovation) is consumed and benefits consumers, it is defined
as an information good. Information goods, unlike ordinary goods, do notdisappear when consumed and can be easily copied. Given this property of
being copyable, every successful transaction of the information good createsa new seller and thus may negatively affect any benefit to its originator. Indeed, noting that information goods are typically exchanged bilaterally ina network,1 Polanski (2007) and Manea (2021) show that when information
goods are traded in such a way, the distribution of benefit among the parties involved may greatly differ depending on the network structure, namely,
whether the network has a cycle path.
A cycle path is a set of network links in which the starting and ending
points are on the same node. On the one hand, if there is no cycle path,the seller can enjoy a greater benefit because the resale of information by
the buyer would not introduce competition between the buyer and the seller.
On the other hand, if a cycle path exists, the act of the buyer reselling
the good results in competition between the seller and the buyer. As aresult, the seller’s benefit will be much less (and that for the buyer muchmore) than without a cycle path. Moreover, the benefit on the buyer side
extends upstream, even to the first transaction where no resale competitor
to the originator yet exists, because the market participants foresee pricecompetition in the future.
1
For example, when founded in 1999, Napster allowed users to transfer their digitalaudio files bilaterally through its peer-to-peer system.

2

In this paper, we experimentally verify these theoretical implications.
Namely, we pose the following research questions:
1. Are prices lower in a network with a cycle path compared with one
without?
2. Does the effect of competition with the latter transaction extend upstream to the first transaction?
To address these, we set up an experiment in which players trade information
goods in networks. We consider two simple networks, one with a cycle pathand the other without, of three players, originally consisting of one seller(i.e., the originator) and two buyers, and compare the behavior of the players
across the two networks.
Our main finding is that the prices observed in the network with a cycle
path are inconsistent with theory compared with those observed in the network without a cycle path. Specifically, although competition between theoriginator and the reseller lowers the observed prices in the final transactionin the network with a cycle path, its magnitude is much smaller than thatpredicted by theory. In addition, contrary to theory, the prices for the firsttransaction tend to be higher in the network with a cycle path.
Moreover, we reveal that learning does not resolve the gap between theory
and the experimental results in the network with a cycle path. Instead, it
could widen the discrepancy in the prices of the first transaction. This isbecause as participants gain experience by repeatedly playing the game, theprices of the first transaction in the network with a cycle path could risefurther given the increasing willingness of buyers to buy the good, which is3

inconsistent with theory.
Our study contributes to the literature on information goods and the network economy, for which there are many early studies concerning the buying
and selling of information goods. For example, Admati and Pfleiderer (1986,
1990) analyzed the trading of information in financial markets, while Raith(1996) presented a model in which information sharing in an oligopolistic
market arises in equilibrium. Elsewhere, Talor (2004) analyzed the customer information market for Amazon and other Internet companies, andBergemann et al. (2018) addressed information trading from the viewpointof mechanism design.
Many studies that focused on the characteristic that information goods
can be copied were related to copyright. For instance, Liebowitz (1985) andBasen and Kirby (2005) analyzed how the presence or absence of copyrightaffects social benefits and those of the original information supplier, andVarian (2005) and others conducted copyright research focusing on the digitization of information. However, Muto (1986), Takeyama (1994), and others
conducted research focusing on the externality of information, that is, thecollapse of monopoly as information spreads.
To this body of work, Polanski (2007) introduced graph theory and created a model in which information is traded through negotiations between
players linked in a network, revealing that the information externalities depend on the structure of the network. Later, Manea (2021) extended thetheory by Polanski (2007) by defining the equilibrium that holds in moregeneral situations. As noted above, their key finding is that the distributionof gains is affected by whether the network containing the seller and the4buyer has a cycle path.
Unlike existing experimental studies, our experiment deals with information good in the network economy. For instance, Gale and Kariv (2009)
investigated the case in which assets were traded through a network andfound that the transaction prices converged to competitive prices. Choi et al.
(2017) investigated path competition in their network experiment and foundthat the position of a node greatly affects the gain. However, unlike thesestudies, our experiment focuses on the price competition in the trading of an
information good in a network with a cycle path. In this setting, a seller inevitably creates a resale competitor when selling the good given its replicableproperty.
The remainder of the paper is organized as follows. Section 2 summarizes
the main theoretical results of the model to be tested in the experiment.
Section 3 discusses the experimental design and procedure. We summarize
the data in Section 4, followed by the results of the main analyses in Section 5.
Section 6 concludes.

2

TheoryIn this section, we explain the theoretical results of the model to be verified
in the experiment according to Polanski (2007) and Manea (2021).

5

2.1

Network Theory Preliminary: Tree Network and
Cycle

The network consists of nodes and links. Let N = {1, 2, .., n} be the set ofnodes in the network. The existence of a connection, or the link, between
nodes i and j (i, j ∈ N ) is represented by hij . If the link exists, hij = 1, andotherwise, hij = 0. We assume the network is undirected, that is, hij = hji
for all i, j. Let H be an n × n matrix whose (i, j) element is hij . A network
G is defined as the set of nodes N and the link matrix H, G = (N, H).
We use the notation ij for the link between i and j. A path connecting
nodes i and j in a network is a sequence of nodes {i0 , i1 , .., ik̄ }, where i0 = i,ik̄ = j, hik ik+1 = 1 for all k ∈ {0, 1, .., k̄ − 1}. A cycle is a path in which thefirst and last nodes are the same i0 = ik̄ , and from i0 to ik̄−1 are all different
nodes.
A connected component of G is a subnetwork of G induced by any maximal set of nodes that are mutually connected by paths in G. A network
is connected if it has a single connected component. A connected networkthat does not contain any cycle is called a tree. In this paper, the network
without cycle paths is a Tree, and the network with cycle paths is a Cycle.

2.2

Model

Figure 1 depicts the simplest three-node networks we use to assess the difference between a Tree (left) and a Cycle (right). Player 1 is connected toPlayers 2 and 3 in both the Tree and Cycle. While Players 2 and 3 are notconnected with each other in the Tree, they are connected in the Cycle.
6Figure 1: Tree and Cycle
As mentioned earlier, Player 1 is the originator of the information good,hence the sole seller at the start of the game. Player 1 gains payoff only by
selling the good to buyer players. Buyer players (i.e., Players 2 and 3) gain
a payoff of 100 from obtaining and consuming the good. Moreover, in the
Cycle, they can copy the information good and sell it to the buyer player that
does not yet possess the good. If the resale transaction is successful, theyearn additional resale benefit. Therefore, in the Cycle, competition between
the originator and a reseller could take place.
We assume, as in Polanski (2007), that at most one transaction occurs perperiod between a connected seller and buyer. If there are multiple trading
possibilities, one link is randomly selected with equal probability. Players at
each end of the selected link then negotiate over the transaction price. We
assume that a Nash bargaining solution determines the transaction price inwhich the market power of the seller is α and that of the buyer is 1 − α.
7α ∈ (0, 1) is an exogenous variable.
In our experiment, the game is terminated with a probability of 1 − δwhen negotiation fails. This ensures that the experiment concludes withina reasonable time. As a result, the equilibrium payoffs are subject to thecontinuation probability δ.

2.3

Equilibrium Payoff

The equilibrium payoffs are defined by the state of the network at the timeof the transaction. In our three-person network model, these are describedby two states, “Stage 1” and “Stage 2.”
Stage 1 is a state in which Player 1 is the only player owning the information, as shown in the top panel of Figure 2. The game starts in this state.
Stage 2 is a state in which one transaction is completed from Stage 1. As aresult, either Player 2 or 3 possesses the information in addition to Player
1. The bottom panel of Figure 2 displays the case in which Players 1 and 2
possess the good, and which is known to Player 3. If a further transaction iscompleted in this state, all players in the network will own the information,and the game ends. Therefore, the network is always in a state of either
Stage 1 or 2 in the middle of the game.
We denote the ex post (i.e., after the link for the current negotiation is
selected) expected payoff of the game by xnst,r , where n = C, T (Cycle, Tree),st = 1, 2 (Stage 1, Stage 2), r = s, b(seller, buyer). As the Stage 1 payoffs
are derived via backward induction from Stage 2 as shown below, the Stage 1
payoffs include the Stage 2 expected payoffs.

8

Stage 1 - Only Player 1 owns the good.

Stage 2 - Two players own the good.

Figure 2: Two States in the Game

9

The equilibrium payoffs are derived following the formulation of Polanski(2007). The expected payoff is defined by the state of the network. The
equilibrium expected payoff is the value obtained by allocating the surplus
generated from the transaction to the threat point payoff according to available market power. We also assume that the player is rational. That is,when a transaction produces a positive (negative) total surplus, the probability of the success of the transaction is 1 (0). To avoid multiple equilibria,
we assume that the transaction surplus is positive in each negotiation.

2.3.1

Stage 2 Payoff in Cycle

In Stage 2 of the Cycle, the threat points in the negotiation are δxC
2b for thebuyer and 21 δxC
2s for the seller. This is because if negotiation fails, while thebuyer player becomes a buyer again in the next negotiation for certain, theseller player is selected as the next seller only with the probability 12 . We
assume that the seller earns no gain if not selected as the seller in the next
negotiation and the buyer purchases the good from the other seller player.2
If the transaction is completed, a total gain of 100 is divided between thetwo players. Therefore, the following equations hold.
1 C
1 C
C
xC
2s = δx2s + α(100 − δx2s − δx2b )
2
2
1 C
C
C
xC
2b =δx2b + (1 − α)(100 − δx2s − δx2b )
2

(1)
(2)

Eqs. (1) and (2) represent the equilibrium conditions for the seller and2

Given the total surplus is positive, the next negotiation succeeds with probability 1.
The same argument applies below.

10

C
the buyer, respectively. Using the total gain equation (xC
2s + x2b = 100) andEq. (1) or (2), the Stage 2 payoffs are derived as follows.

2.3.2

xC
2s =

100(1 − δ)α1 − 12 δ − 12 αδ

(3)

xC
2b =

100(1 − α)(1 − 21 δ)
1 − 12 δ − 21 αδ(4)Stage 1 Payoff in the Cycle

If a negotiation fails in Stage 1, the buyer player will be the buyer again in
the next negotiation with the probability 12 . Otherwise, the player will be
the buyer in Stage 2, premising that the other buyer purchases the good in
the next negotiation and the game proceeds to Stage 2. The seller becomes
the seller in the next negotiation again for certain.
If a negotiation is successful, in addition to the 100 generated by the
resulting transaction, either the seller or the buyer of this negotiation will
become the seller player in the next negotiation in Stage 2 and will earn xC
2s ,which occurs with probability 12 for each. Therefore, the following equations
hold.
1 C
1 C
1 C
1 C
C
C
xC
(5)
1s =δx1s + α(100 + x2s + x2s − δx1s − δx1b − δx2b )2
2
2
2
1 C 1 C
1 C
1 C
1 C
1 C
C
xC
1b = δx1b + δx2b + (1 − α)(100 + x2s + x2s − δx1s − δx1b − δx2b )
2
2
2
2
2
2
(6)
Eqs. (5) and (6) represent the equilibrium condition for the seller and theCCbuyer, respectively. Using the total gain equation (xC
1s + x1b = 100 + x2s ) and11

Eq. (5) or (6), Stage 1 payoffs are derived as follows.
1
1
1
−1
C
C
xC
1s ={1 − δ + αδ} [α(1 − δ)(100 + x2s ) − δαx2b ]
2
2
2
1
1
−1
C
C
xC
1b ={1 − δ + αδ} [(1 − α)(1 − δ)(100 + x1s ) + δαx2b ]
2
2
2.3.3

(7)
(8)

Stage 2 Payoff in a TreeFor the case of Stage 2 in the Tree network, even if the transaction fails, thesame transaction is repeated. Thus, the following equations hold.

xT2s =δxT2s + α(100 − δxT2s − δxT2b )(9)xT2b =δxT2b + (1 − α)(100 − δxT2s − δxT2b )(10)

Eqs. (9) and (10) represent the equilibrium conditions for the seller andthe buyer, respectively. Using the total gain equation (xT2s + xT2b = 100) andEq. (9) or (10), Stage 2 payoffs are derived.

2.3.4

xT2s =100α(11)xT2b =100(1 − α)(12)Stage 1 Payoff in a Tree

If a negotiation fails in Stage 1, the buyer player of the current negotiation
will become the buyer again in the next negotiation with probability 12 . Otherwise, the player will be the buyer in Stage 2, premising that the other buyerpurchases the good in the next negotiation and the game proceed to Stage 2.
The seller player of the failed negotiation becomes the seller again for certain
12

in the next negotiation.
If a negotiation is successful, in addition to the 100 generated by thistransaction, the seller of the negotiation will be the seller in Stage 2 forcertain and will earn xT2s . Therefore, the following equations hold.
1
1
xT1s =δxT1s + α(100 + xT2s − δxT1s − δxT1b − δxT2b )
2
2
1
1
1
1
xT1b = δxT1b + δxT2b + (1 − α)(100 + xT2s − δxT1s − δxT1b − δxT2b )
2
2
2
2

(13)
(14)

Eqs. (13) and (14) represent the equilibrium conditions for the seller andthe buyer, respectively. Using the total gain equation (xT1s + xT1b = 100 + xT2s )and Eq. (13) or (14), the Stage 1 payoffs are as follows.
111xT1s ={1 − δ + αδ}−1 [α(1 − δ)(100 + xT2s ) − δαxT2b ]
2
2
2
1
1
xT1b ={1 − δ + αδ}−1 [(1 − α)(1 − δ)(100 + xT1s ) + δαxT2b ]
2
2

2.4

(15)
(16)

Equilibrium Price

The equilibrium price in each stage is computed from the abovementioned
expected payoff. Let pnst be the transaction price of Stage st (st = 1, 2) and13

network type n (n = C, T ). The analytical solutions are as follows.
1
1
1
1
−1
C
C
pC
1 ={1 − δ + αδ} [100α(1 − δ) − ( − α)(1 − δ)x2s − δαx2b ]
2
2
2
2
1
1
1
pT1 ={1 − δ + αδ}−1 [100α(1 − δ) − (1 − α)(1 − δ)xT2s − δαxT2b ]
2
2
2
100(1
−
δ)α
pC
2 =
1 − 12 δ − 21 αδ
pT2 =100α

(17)
(18)
(19)
(20)

Suppose that δ = 0.9 (as in our experiment) and α = 0.5. α = 0.5
is a reasonable benchmark case where the power of negotiation is equal between the seller and the buyer, both anonymously matched in the experiment.
T
Then, the equilibrium prices are pC
1 ≈ 26.04 and p1 ≈ 42.31 for Stage 1, andTpC
2 ≈ 15.38 and p2 = 50 for Stage 2. The Stage 2 equilibrium price in a

Cycle is drastically lower than in a Tree because of competition between theoriginator and the reseller.3 Moreover, the effect of competition on the pricein a Cycle also appears upstream in Stage 1, in which a reseller has not yet
appeared in the market. Our primary aim of the experiment is to verify these
theoretical predictions for prices.

3

Experimental Design and Procedure

We conducted six sessions of computer-based online experiments in October 2020.4 We recruited 141 subjects from a subject pool at the Institute3

Polanski (2007) and Manea (2021) analyze the Cycle and Tree equilibria in the caseCT
Tof δ = 1. When δ = 1, pC
1 = p2 = 0 and p1 = p2 = 100α.
4
The experiment was programmed and conducted with o-Tree (Chen et al., 2016),
and we used Zoom (https://zoom.us/) to welcome and communicate with participants.
After verifying their names in the waiting room, participants were given an anonymous

14

of Social and Economic Research, Osaka University, managed by ORSEE(Greiner, 2015). The subject pool consists of students, both undergraduate
and graduate, in various fields in the university. Our subjects are paid according to their performance in the experiment. Each subject experiences 16
trials in a session, and one trial is selected randomly at the end of the experiment. The points the subject earned in the selected trial is then converted
into Japanese yen (JPY) as a performance-based payment (at the rate of 40
JPY per point). In addition to the performance-based payment, our subjects
were paid a participation fee of 500 JPY. Payments were in the form of anemailed Amazon gift card.
A session consists of two treatments, each consisting of eight consecutive trials, regarding the network structure, and we denote the treatment
with a Tree structure as “Tree” and that with a Cycle structure as “Cycle.”
The experimental design is a within-subject design, whereby each subject
receives both treatments successively. However, the treatment order is counterbalanced among the subjects to offset the possible order effects, with 66
subjects receiving Tree first and Cycle later. The remaining 75 subjects received these treatments in reverse order.5 The number of subjects and thetreatment order in each of the six sessions are presented in Table I.1 in OSM I.
Each treatment consists of eight consecutive trials, and a trial includes
several rounds of negotiations. After the subjects read the experimental
participation ID (sub01, sub02, ..) when entering the meeting room. Their mobile cameras
as well as microphones were off during the experiment.
5
As the treatment order is counterbalanced among our subjects, the order effect should
not be a major concern. Nonetheless, we assess the magnitude of the order effects in theOnline Supplementary Material (OSM) II. The results indicate that the potential bias in
our analysis arising from the order effect is zero, or at most marginal.

15

instructions and completed a few quizzes that assessed their comprehensionof the rules of the game, the experiments were carried out in the following
procedure.6
At the beginning of the first trial, the position of each subject in the network is randomly determined after considering that there is an equal numberof participants in each of the three positions. This position is held constantacross all 16 trials.7
At the start of a trial, a group of three players occupying each of thethree positions is randomly formed. Player 1 is the originator of the good
and the only seller at the start of every trial. For each round, one negotiablelink, i.e., a link between a seller and a buyer, is selected, and a negotiation
for the transaction of the good starts between the linked seller and buyer.
In the negotiation, the buyer and the seller each simultaneously propose a
bid and an ask once for the transaction, respectively. Then, the bid and theask are displayed to both players. If the bid is equal to or higher than theask, the transaction is established in the round. Otherwise, the negotiationin the round fails. If the transaction is established, the price P is determinedas the middle value between the ask and the bid, and the price is announced
to both players in the transaction. The seller of the transaction earns a gainof P , and the buyer earns a gain of 100 − P . However, both players earnnothing if the negotiation fails.
6

The experimental instructions and screenshots of the actual experiments (translated
from Japanese to English) are provided in OSM VII.
7
The position of each subject in the network is kept unchanged through the entire
session, even across the two treatments, to ease the comprehension of the subjects in thegame. In addition, identical positions for the players in each session enable us to control for
individual heterogeneity in the statistical analysis in accordance with the within-subject
experimental design.

16

If the transaction is established, the link between the buyer and the seller
is no longer negotiable as the buyer of the transaction becomes an additional
seller. If that player is linked to a remaining buyer, the link becomes negotiable, and that player could sell the information to the remaining buyer if
the link is selected for negotiation hereafter in the trial. Sellers that sold thegood to a buyer remain as sellers.
The round ends once the negotiation is finished regardless of its successor failure. The experiment proceeds to the next round if the negotiation
is successful. In the case of failure, however, the trial is terminated witha 10% chance as discussed in Section 2.2. In the next round, a negotiablelink is newly selected to start a negotiation. The same negotiable link as
the previous round can be selected again. A trial also ends if all the players
possess the good, and no further negotiation is needed. The final point for a
subject in the trial is equal to the total points the subject has earned in thetrial.
Once a trial ends, the experiment proceeds to the next trial unless theterminated trial is the final one. The members of the three-person game arerematched when a new trial begins.

4

Summary of the Data

We briefly summarize the data by overviewing the sample size, share of successful trials, the frequency of negotiations, and the payoffs. Major behavioral data for our subjects are analyzed in Section 5.
The data contains 752 trials of three-person games, which consist of 2,077
17

Table 1: Share of Successful Trials

Treatment

Share of Successful Trials(whole transactions)Share of Partially Successful Trials(Stage 1 transaction)

Tree
Cycle

0.822
0.835

0.931
0.918

rounds of negotiations in total. Of the 752 trials, 623 trials (82.8%) weresuccessful in that both buyers obtained the good. Among the remaining 129
trials, no buyer obtained the good in 57 trials, and only one buyer obtained
the good in 72 trials. We refer to a trial as partially successful if at least one
transaction is established. Thus, the number of partially successful trials is
695 (92.4%).
The likelihood that a trial is finished successfully is almost identical acrossthe two treatments. As displayed in Table 1, the percentage of trials in which
two whole transactions are successfully established for all three players is
82.2% in Tree and 83.5% in Cycle. The two values do not differ statistically significantly (p − value = 0.629). Similarly, the percentage of trials
in which at least one transaction is done is 93.1% in Tree, which does notdiffer significantly from that in Cycle, which is 91.8% (p − value = 0.492 in
OSM III). These results suggest that we do not need to be concerned withthe unevenness of the sample failure across the two treatments due to sudden
failure amid ongoing negotiations. The detailed discussion and the statisticalanalysis are presented in OSM III.
Table 2 presents summary statistics of the number of negotiations per
18

Table 2: Number of Negotiations per Trial

Treatment

Mean

St. Dev.

Pctl(25)

MedianPctl(75)

Pctl(95)

Max

Tree
Cycle

3.579
3.092

2.062
1.581

2
2

3
3

4
4

7
6

14
14

Note: Limited to trials in which whole transactions are established among the three players.

trial for each treatment. The average number of negotiations in Tree is3.579, while that in Cycle is 3.092, which is statistically significantly different(p − value < 0.01, see OSM IV).
For the percentiles displayed in Table 2, there is little difference up to
the 75 percentile. Half of the trials are concluded within three negotiations,and 75% finish within four negotiations. A slightly larger number of trials
appear after the 75 percentile in Tree.
One might believe that the speed of learning about the optimal plays ofthe game could differ between the two treatments. Because Cycle has more
complicated game rules, subjects require more time to learn the optimal
plays. As a result, the dynamics of the number of negotiations could differ
across the treatments. Our analyses, reported in OSM IV, do not confirm
that the number of negotiations changes as our subjects gain experiencesin Cycle. Moreover, our subjects also tend to negotiate more in the later
trials in Tree. However, we do not find sufficient evidence that the speed oflearning differs across the two treatments. In OSM IV, we also compare thenumbers of negotiations across Stages 1 and 2, but we again do not find asignificant difference.

19

Table 3: Mean Payoff of Players
Treatment
Tree
Cycle

Originator
101.560(15.633)
78.588(26.400)

PooledBuyerFirst Buyer

Last Buyer

49.220(9.588)60.706(20.761)47.702(9.239)68.753(25.650)50.738(9.704)52.659(8.694)

Note: Standard deviations in parentheses.

Table 3 presents the players’ payoff according to the roles they are assigned in the game, that is, as originators or buyers. Buyers are further
classified into two distinct types. One is a class of buyers that reached abuying agreement in Stage 1. We denote this type of buyer as “first buyer.”
The other is the class of buyers that finally bought the good in Stage 2. Werefer to this other type of buyer as “last buyer.”
As displayed in Table 3, the mean payoff of an originator in Tree is 101.56,
which is far larger than that of buyers in the treatment, which is 49.22.
Roughly speaking, an originator is expected to earn twice as much as abuyer. Among the buyers, a first buyer earns nearly the same as a last buyer
in Tree. The mean payoff of the former is 47.70, and that of the latter is
50.74. While the difference is small, it is statistically significant (Wilcoxon
pairwise test, p − value < 0.01). The almost identical share of the twobuyers is a straightforward result of the theory in Tree, in which any buyer
is equivalently required to buy the good from the originator.
In Cycle, in which transactions between the first and last buyers cantake place, originators earn less than in Tree. The mean payoff of an orig20

inator is 78.59, which is statistically significantly smaller than that in Tree
(Wilcoxon pairwise test, p − value < 0.01). Naturally, buyers earn more in
the treatment as they obtain the remainder, such that a buyer earns 60.71
on average. Among buyers, a first buyer earns 68.75 on average, which is statistically significantly larger than in Tree (p − value < 0.01, after controllingfor individual-level fixed effects with cluster-robust standard errors). A lastbuyer earns 52.66 on average, which is slightly, but statistically significantly,
larger than in Tree (p − value = 0.029, again after controlling for individuallevel fixed effects with cluster-robust standard errors). The payoff of a firstbuyer is significantly larger than that of a last buyer in Cycle on average by
16.09 (Wilcoxon pairwise test, p − value < 0.01). We further discuss thepayoff difference between buyers in Section 5.5.
Although the payoffs differ across the two treatments, it does not necessarily imply that the players also behave differently across the two treatments.
Given a transaction between the first buyer and the last buyer is allowed in
Cycle, the payoff of the originator becomes smaller in Cycle than in Tree,even if the pricing behavior of the originator (i.e., the values of the proposedasks) remains unchanged, simply because the originator now has less chanceof selling as the first buyer has a chance to sell too.8 In the following section,
we focus our analysis on transaction prices, bids, and asks to address any
behavioral differences among our subjects across the two treatments.9
8In addition, the standard deviation of the originator’s payoff becomes larger in Cycle
than in Tree simply because they have only a stochastic chance to sell the good in thetreatment. Note that the standard deviations of the prices do not differ so much as shownin Figures 3 and 4 below.
9
The only exception is the payoff of last buyers. The difference in last buyers’ payoff
across the two treatments necessarily implies that the behavior associated with the final
transactions differs.

21

Note: Red: data. Green: theory. Error bars show plus-minus one-standard error range.

Figure 3: The Average Price in Stage 2

5

Prices, Bids, and Asks

5.1

Prices in Stage 2

As discussed in Section 2.3, the model is solved by backward induction. With
that in mind, we first discuss the results of Stage 2, then proceed to those ofStage 1.
Figure 3 plots the mean price in Stage 2 for Tree (49.26) as well as Cycle (47.34), together with their theoretical prediction (50 and 15.38, respectively). While the mean price in Tree is not statistically significantly different from the theoretical prediction (p − value = 0.156), that in Cycle is
far greater (p − value < 0.01). Instead, the mean price in Cycle is only
slightly less than that in Tree, although the difference is statistically significant (p − value < 0.01, Model 1 in the third column in Table 4). This result
suggests that the downward pressure in prices induced by competition, which

22manifests itself as statistical significance, is weak.
Result 1: While the Stage 2 prices in Tree are consistent with theory, thosein Cycle are not, as the Stage 2 prices in Cycle are only slightly smaller
than those in Tree.
Does this discrepancy between the data and theory in Cycle resolve itself as our subjects accumulate experience? This is because our subjects
might not have learned the power of competition yet in the early trials of
the treatment, which they might learn in the latter trials. To address this,we estimate the following linear regression, which includes variables capturing learning effects, by regressing the prices on four explanatory variables,
Cycle, Latter, Cycle × Latter, and a constant. Cycle is a dummy variable
that takes a value of one if the trial belongs to Cycle, otherwise zero. Latter
is a dummy variable that takes a value of one if the trial lies in the latter
half of each treatment (i.e., the 5th to 8th trials), otherwise zero, and thiscaptures the overall learning effects across the two treatments.
Cycle×Latter is the cross term of Cycle and Latter, which captures additional impacts on the learning effect specifically appearing in Cycle. The statistical significance of the variable suggests that learning effects differ acrossthe two treatments (i.e., the existence of a treatment-specific learning effect).
The learning effect in Tree is captured by the coefficient of the term Latter,and that in Cycle by the sum of the coefficients of the terms Latter andCycle × Latter. We also report the results of a regression in which only
two regressors are included, Cycle and a constant, to overview the treatment
effect over all trials.
23

Table 4: Regression Results for Price
Dependent Variable
Price
Stage 1
Cycle

Model 1Model 2Model 1Model 21.512∗∗(0.687)-−1.921∗∗∗(0.738)-49.262∗∗∗(0.524)−2.221∗∗(1.039)0.656(1.470)−2.257∗∗(1.044)50.373∗∗∗(0.732)623
0.0108623
0.0220Latter-Const.

52.343∗∗∗(0.484)0.698(0.973)1.627(1.374)−0.971(0.969)52.829∗∗∗(0.685)Observations
R2695
0.0069695
0.0101

Cycle × Latter∗

Stage 2-

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.

The results of these regressions appear under Model 2 in the fourth column of Table 4. The coefficient for the term Latter is −2.257, which issignificant (p − value = 0.03), implying that the overall learning effect tends
to lower prices. However, our primary focus here is the value of the coefficient for the cross term Cycle×Latter, which captures the treatment-specificlearning effect in Cycle. Its value of 0.656 is not significantly different fromzero. This indicates that contrary to our earlier speculation, price competition between the two sellers in Cycle does not lower prices more in later trials
by which time our subjects should have accumulated experience. Instead, thepositive value of the point estimate, while not significant, implies that thetreatment-specific effect in Cycle could have resisted the overall tendency to24lower the prices observed with the coefficient for the term Latter. Indeed,
the sum of the coefficients of the terms Latter and Cycle × Latter, that is,
the magnitude of the learning in Cycle, is −1.601, which is not statisticallysignificant (F-test, p − value = 0.122).10
Result 2: The price competition in Stage 2 in Cycle does not facilitate
subject learning in converging to the equilibrium implied by the theory.
Competition is a strong power to guide economies to equilibria. For
example, Roth et al. (1991) report that prices converge to a competitive
equilibrium in their multiplayer market experiments. However, our resultsfor Stage 2 suggest that the effect of competition is quite limited. Althoughcompetition between the two sellers lowers the prices in Cycle, the extent of
this is far below the level implied by theory. This limited effect of competition is similar to that reported in experiments with Bertrand price competition (Dufwenberg and Gneezy, 2000; Baye and Morgan, 2004) and travelers’
dilemma (Capra et al., 1999) games.

5.2

Prices in Stage 1

As our empirical findings for the prices in Stage 2 deviate from the theoretical
implications for Cycle, those in Stage 1 could deviate too.
Figure 4 illustrates the mean Stage 1 prices for Tree (52.35) and Cycle(53.86), together with the theoretical predictions (42.31 and 26.04, respectively).
10

The insignificance of the learning effect in Cycle is also confirmed, even if we employ
Cycle data only (p − value = 0.103).

25

Note: Red: data. Green: theory. Error bars show plus-minus one-standard error range.

Figure 4: The Average Price in Stage 1
In Tree, the mean Stage 1 price is larger than that of Stage 2. Although
the difference (3.08) is small, it is statistically significant (Wilcoxon pairwise
test, p − value < 0.01). The mean price is statistically significantly higher
than the theoretically predicted level (p − value < 0.01).
In Cycle, the mean price in Stage 1 is 53.86, which is larger than that inStage 2 by 6.514 (Wilcoxon pairwise test, p − value < 0.01) and is also farlarger than the level implied by theory (p − value < 0.01). This variationfrom the theoretical prediction is larger than that in Tree by 17.78. Thus,
similar to the Stage 2 prices, we observe that the Stage 1 prices in Cycle
deviate from theory, and the deviation is far larger than that in Tree.
In addition, the mean Stage 1 price in Cycle is larger than that in Treeby 1.51 (p − value = 0.028, Model 1 in the first column in Table 4), which is
opposite to the theoretical prediction that prices should be far lower in Cycle
than in Tree.

26

Result 3: The Stage 1 prices in Cycle deviate from theory considerably
more than in Tree. In addition, again in contrast to theory, the Stage 1
prices in Cycle are even larger than the prices in Tree.
We now address whether the discrepancy between our experimental data
and the theory in Cycle could be resolved by learning. Similar to the abovementioned analysis of Stage 2, we undertake identical linear regression analysis to address the existence of a learning effect in Stage 1. The result ispresented in Model 2 in the second column of Table 4. The coefficient ofLatter is not significantly different from zero (p − value = 0.316), indicatingthat no learning appears in Tree. Moreover, the coefficient of Cycle × Latteris also not significant (p − value = 0.237), suggesting that there exists notreatment-specific learning effect in Cycle. Indeed, the sum of the coefficientsof the terms Latter and Cycle × Latter, which is only 0.656, is not significantly different from zero (F-test, p − value = 0.502). These results jointly
indicate that there is little evidence for the existence of learning, not only in
Cycle but also in Tree. Thus, as in Stage 2, there is little possibility that thediscrepancy between the theory and the data in Cycle is resolved by learningin Stage 1.
Result 4: We do not observe any learning effect in the prices in Stage 1.

5.3

First Bids and Asks in Stage 1

We have obtained little evidence of subjects learning to play according to thetheoretical prediction based on our analysis of prices. However, as prices are27

determined jointly by bids and asks, this may mask the effect of learning.
We thus turn our attention to bids and asks separately.
We particularly focus on the bids and asks proposed in the first negotiations of each trial because they carry uncontaminated information. The
first bids and asks are proposed before the player observes any behavior of
the other players in the trial11 ; thus, they are considered to directly reflect
the player’s initial prospects for the prices in the trial.12 Here we focus ouranalysis on the first bids and asks in Stage 1.
Figure 5 plots the dynamics of the first bids and asks in each of thetreatments. Although the first asks present similar dynamics in the twotreatments, the first bids exhibit distinct patterns across these same twotreatments. As the trial proceeds, the bids tend to become lower in Tree,
whereas they tend to become higher in Cycle.
We perform the following linear regression analysis to test this observation. We regress the first bids and asks on the same four explanatory variables
as our earlier regression for prices (i.e., Cycle, Latter, Cycle × Latter, anda constant). Now the regression model is a fixed-effect model in which thesubject-level individual heterogeneity is controlled for by individual fixed effects. In addition, we employ cluster-robust (subject-level) standard errors
for the hypothesis tests. As before, we also report the result of a regression
including only two regressors, Cycle and a constant.
Table 5 presents the regression results for the first bids and asks in Stage 1.
11

Recall that players are randomly rematched into groups of three at the beginning ofeach trial, but while maintaining their roles.
12
One concern is that first bids and asks also reflect the individual heterogeneity ofplayer, such as negotiation style. For this reason, we control for individual differences in
the following regression analysis.

28

Red: Cycle, Blue: Tree.
Solid: bids, Long-dash: asks

Figure 5: Dynamics of the First Bids and Asks
The first column in Table 5 indicates that the first bids in Tree is larger thanin Cycle by 2.302 (p − value = 0.024). The second column displays theregression result to address the presence of learning effects. The value ofthe coefficient of Latter is −3.289, which is significantly different from zero(p − value < 0.01), indicating that the first bids in Tree have a strong downward trend as observed in Figure 5. For Cycle, the value of the coefficient of
the cross term Cycle × Latter is 4.227, which is significantly different fromzero (p − value < 0.01). This indicates the presence of a treatment-specificlearning effect. The sum of the coefficients of Cycle × Latter and Latter,
which captures the magnitude of the learning effect in Cycle, is 0.938, suggesting the possibility of an upward trend in first bids in Cycle. Although29

Table 5: First Bids and Asks in Stage 1
Dependent Variable
First Bids
Cycle

Model 1Model 2Model 1Model 22.302∗∗(1.006)-0.436(0.916)-52.859∗∗∗(0.458)−0.027(1.541)0.926(1.878)−1.080(1.499)53.399∗∗∗(0.951)752
0.0003752
0.0011

Latter-Const.

50.297∗∗∗(0.503)0.188(1.545)4.227∗∗∗(1.525)−3.289∗∗∗(1.083)51.942∗∗∗(0.826)

Observations
R2752
0.0121752
0.0209Cycle × Latter∗

First Asks-p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Cluster-robust standard errors in parentheses.

this value is not statistically significant using pooled data of the two treatments (F-test, p − value = 0.3319), using the data only in Cycle, we confirm
a statistically significant positive upward trend in Cycle, as shown in Figure 5 (p − value = 0.038, Table V.1 in OSM V). The first bids exhibit
treatment-specific learning in opposite directions across the two treatments.
Unlike the first bids, we do not observe any treatment-specific learningin the first asks. The third column in Table 5 indicates that the overalllevel of the first asks does not differ significantly across the two treatments(p − value = 0.636). Moreover, in the fourth column, neither the coefficientof the cross term Cycle×Latter nor the term Cycle is significant (p−value =0.624 and 0.986, respectively). These results jointly imply that the behaviorof sellers does not differ across the two treatments.
30

Red: Cycle. Blue: Tree

Figure 6: Share of Successful Negotiations in the First Trials
Result 5: In Stage 1, buyers become more willing to buy as trials proceedin Cycle. By contrast, buyers become less willing in Tree. Sellers do
not exhibit any treatment-specific learning.
As we observe distinct treatment-specific learning effects in the first bids
but not the first asks, we expect that the likelihood of success in the first trials
evolves differently across the two treatments as the trials progress. That is,
the first negotiations should more likely succeed in Cycle than in Tree inlater trials. To see this, we plot the dynamics of the likelihood of the successof negotiations in the first trials in Figure 6. As expected, this likelihood
displays an upward (downward) trend in Cycle (Tree).
To examine the difference, we perform the following linear regression analysis. We regress a dummy variable reflecting the success of the first trials
31

Table 6: Likelihood of Success in the First Negotiations
Dependent Variable
Success
Model 1Model 20.064∗(0.036)-

Latter-Const.

0.527∗∗∗(0.026)−0.032(0.051)0.191∗∗∗(0.072)−0.096(0.051)0.574∗∗∗(0.036)

Observations
R2752
0.0041752
0.0134Cycle
Cycle × Latter∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.

on the same four explanatory variables to the earlier regression analysis ofprices (i.e., Cycle, Latter, Cycle × Latter, and a constant). Table 6 presents
the regression results. As shown in the first column, we do not identify any
clear difference in the likelihood of success in the first negotiations across thetreatments. However, in the second column, we observe a strong treatmentspecific learning effect as the coefficient of the cross term Cycle × Latter is0.191 and is significant (p − value < 0.01). According to these results, thefirst negotiations in Cycle are more likely to be successful in later trials byapproximately 19% than in Tree.
The abovementioned findings consistently suggest that buyers become
more willing to buy in the latter trials in Stage 1 in Cycle. It then becomesdifficult that prices in Stage 1 in Cycle will be lower as learning progresses.
32Thus, and once again, we conclude that learning does not help to achieve
equilibrium in Stage 1 in Cycle, at least in the eight trials in our experiments.
Instead, it tends to widen the gap from the equilibria.
One straightforward explanation for the results in Cycle is that, first,
buyers could earn large profits in Stage 2 because, unlike the theoretical prediction, the prices are high in Stage 2. Expecting positive profits in Stage 2,
buyers then compete to purchase the good in Stage 1. As the expected
returns in Stage 2 are gradually learned, a learning effect then appears inStage 1.
A puzzle is why the sellers in Cycle do not exploit their advantage incompetition and become more eager to earn profits in Stage 1. As discussed,
the first asks do not differ across the two treatments, nor do they seemto respond to the upward trend in first bids. It might be the case in our
experiments that those who are competing only become urged, though thereason behind it is unclear.

5.4

First Bids and Asks in Stage 2

We find that the buyers in Stage 1 in Cycle become more willing to buy the
good. Naturally, a next question would be whether the sellers competing inStage 2 learn to be more aggressive. More specifically, we hypothesize thatthe first asks proposed by the sellers in Stage 2 in Cycle are lower than thosein Tree. Here, the “first ask” in Stage 2 is defined as the ask proposed in theround immediately following establishment of the Stage 1 transaction.
To test our hypothesis, we perform linear regression analysis of the first33

Table 7: First Bids and Asks in Stage 2
Dependent Variable
First Bids
Model 1Model 2Model 1Model 20.018
(1.060)-−3.969∗∗∗(1.211)-50.144∗∗∗(0.601)−4.422∗∗∗(1.635)0.915(1.836)−0.441(1.505)50.362∗∗∗(1.023)695
0.0193695
0.0190Latter-Const.

48.066∗∗∗(0.526)−1.166(1.200)2.391(1.462)−1.858∗(0.954)48.989∗∗∗(0.794)

Observations
R2

695
0.0000695
0.0043

Cycle
Cycle × Latter∗

First Asks-p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Cluster-robust standard errors in parentheses.

asks and the first bids in Stage 2. The regression models are identical to thoseused for Stage 1 (i.e., identical variable definition, fixed-effect models forcontrolling subject-level heterogeneity, and cluster-robust standard errors).
The results are presented in Table 7. Consistent with the abovementioned
hypothesis, the first asks in Cycle are significantly lower than those in Tree.
The results in the third column show that the value of the coefficient of
Cycle is −3.969, which is significant (p − value < 0.01).13 This result echoes
our earlier findings for Stage 2 prices that prices tend to be lower in Cycle,
although the magnitude of this is not sufficient to satisfy the theoreticalprediction.
13

The difference in the first asks in Stage 2 could also result from differences in asking
behavior between originators and resellers. However, OSM VI shows that this is not the
case.

34

However, different from the case of the first bids in Stage 1, we do notreveal learning effects for the first asks in Stage 2. The fourth column ofTable 7 shows that the coefficient of the term Latter is not significantly
different from zero (p − value = 0.770). The coefficient of the cross term
Cycle×Latter is also not significant (p−value = 0.619), nor is the sum of thecoefficients of Cycle × Latter and Latter (F-test, p − value = 0.630). These
results jointly suggest that there is no learning effect in either treatment in
the first asks in Stage 2. One reason for the difference in this to the first bids
in Stage 1 is that optimal trading in Stage 1 might require more cognitive
ability. To make an appropriate offer in Stage 1, players need to foresee
the expected profit they could obtain in Stage 2, unlike the transactionsin Stage 2. It is then possible that the buyers in Cycle learn the prices
determined in Stage 2 as the trials progress and gradually adapt their bids
in Stage 1.
In addition, similar to the first asks in Stage 1, we do not observe any
significant difference in the first bids across the two treatments in Stage 2. As
shown in the first column of Table 7, the coefficient for Cycle is not significant(p − value = 0.987). Moreover, in the second column, the coefficient for the
cross term Cycle × Latter as well as the coefficient for the term Cycle arealso not significant (p − value = 0.105 and 0.333, respectively). These results
jointly suggest that the behavior of buyers in Stage 2 is similar across thetwo treatments. This aligns with our earlier speculation that those who arecompeting only feel urged, though the reason behind it is still puzzling.
Result 6: In Stage 2, sellers are more willing to sell in Cycle than in Tree,

35

though the magnitude of this is not sufficient to satisfy the theoretical prediction. Moreover, there is no evidence of learning or buyers
behaving differently across the two treatments.

5.5

Forward-looking Behavior Given the Observed Stage 2
PricesWe have documented a gap between the theoretical prediction and the experiment results in Cycle. Recall that, in theory, the Stage 1 price is low in
Cycle because buyers expect the competition between sellers to push down
the Stage 2 price, and thus the expected profit from reselling the good should
also fall. Therefore, if the price is high in Stage 1, the buyer prefers to let
the current negotiation pass, wishing to be the buyer in Stage 2.
However, the high Stage 1 price observed in the experiment could bereasonable if subjects expect a high price in Stage 2. The larger the expected
reselling profit in Stage 2, the more willing buyers in Stage 1 are to buy thegood, which in turns raises the Stage 1 price. Here, we address the possibility
that the observed prices in Stage 1 are explained by reasonable profit-seeking
behavior of subjects foreseeing the prevailing high prices in Stage 2.
To assess the reasonable level of the Stage 1 price given the prevailingStage 2 price, as denoted by the “pseudo equilibrium Stage 1 price,” weplug the mean observed Stage 2 prices into Eq. (6). The derived pseudo
equilibrium Stage 1 price is 48.16. The mean Stage 1 price (53.86) is thenhigher than its pseudo equilibrium level by 5.73, which is within the extent
that can be explained by the risk-averse behavior of our subjects, as discussed

36

in Appendix A. Thus, the observed prices in Stage 1 do not contradict
our subjects pursuing a larger benefit by foreseeing future reselling prices inStage 2.

6

Conclusion

This study experimentally examines the trading of information goods in networks. Information goods are copyable; hence, a buyer can become a resalecompetitor to existing sellers once the good is purchased and if resales channels are available in the network. We examine whether competition throughreselling lowers the prices of the good in line with theory.
Our experimental treatment is the network structure that permits competition through reselling. In one treatment, Cycle, the network includes acycle path, which secures a sales channel for the reseller. Thus, price competition could lower prices between the originator and the reseller in the
network. According to theory, the lowering effect in prices even moves upstream to the first transaction where no resale competitor yet exists, because
the market participants foresee competition through reselling in their futuretransactions. In the other treatment, Tree, there is no cycle path in the network, and thus resale of the good is not possible. The originator can thenenjoy monopoly power and post higher prices.
We find that the prices observed in Cycle are inconsistent with theory
compared with those observed in Tree. Specifically, although competition
between the originator and the reseller lowers the observed prices in the final
transaction more in Cycle than in Tree, the extent of this is very small com37

pared with the theoretical prediction. In addition, contrary to the theoreticalprediction, the prices in the first transaction tend to be higher in Cycle thanin Tree.
Furthermore, learning does not resolve the discrepancy between the theory and the data in Cycle as the Stage 1 prices carry signs of further priceincreases according to the bidding behavior of the buyers. On the contrary,in Tree, the bidding behavior suggests signs of further decreases in prices
toward the level implied by the theory.
As we discussed in Section 5.5, the observed prices in Stage 1 of Cycle,
although inconsistent with their theoretical prediction, are consistent withparticipants rationally responding to the prevailing high prices in Stage 2.
Thus, there is the possibility that Stage 1 prices could adjust toward their
theoretical level once the Stage 2 prices fall due to competition.
It is possible that the bargaining protocol we employed in our experiment,
namely, the Nash demand game, serves to soften the competitive pressure inStage 2 in Cycle. Thus, an obvious direction for future research would be
to consider an alternative trading mechanism, such as a continuous double
auction. Another possibility is that the two players in our experiment are
not sufficient for competition to be effective. For example, in Dufwenberg
and Gneezy (2000), when the number of players was three or more, participants quickly learned to compete more aggressively in a Bertrand competition experiment. Thus, other obvious and fruitful future research would be
to consider networks involving a larger number of players.

38

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41

A

Case for Risk-averse Players

As in Section 5.5, the observed Stage 1 price is higher than the pseudo
equilibrium Stage 1 price by 5.73. Here we show that this difference can be
explained by the risk aversion of players.
To address this, we modify Eq. (6) to consider risk-averse players maximizing their expected utilities over final payoffs.
1
1
CCu(100 − pC
1 ) + u(100 − p1 + p2 ) =
2
2
1 1
1
1
C
C
C
δ{ u(100 − pC
1 ) + u(100 − p1 + p2 )} + δu(100 − p2 )+
2 2
2
2
1
1
1
1
C
C
C
C
C
(1 − α)[ u(pC
1 ) + u(p1 + p2 ) + u(100 − p1 ) + u(100 − p1 + p2 )−
2
2
2
2
1
1
1
1
1
1
C
C
C
C
C
C
δ{ u(pC
1 )+ u(p1 +p2 )}− δ{ u(100−p1 )+ u(100−p1 +p2 )}− δu(100−p2 )]
2
2
2 2
2
2
(A.1)
where u(·) is the utility function of the players.
Let us specify the utility function with a standard, constant relative risk
aversion utility function with the coefficient of relative risk aversion γ (i.e.,1u(x) = 1−γ
x1−γ ). Substituting the values for the observed prices into pC
1 and

pC
2 , we obtain γ = 5.11. This value of γ is within the scope of reasonable
degrees of risk aversion in existing studies (for example, Abdulkadri andLangemeier, 2000).

42

Online Supplementary Materials
I

Sessions and Treatment Order
Table I.1: Sessions
Subject
October 1, 2020 (morning)
21
October 1, 2020 (afternoon)
24
October 2, 2020 (morning)
24
October 2, 2020 (afternoon)
18
October 14, 2020 (morning)
24
October 15, 2020 (morning)
30

IIFirst Treatment
Cycle
Tree
Cycle
Tree
Tree
Cycle

Order Effect

As the treatments are reverse ordered among our subjects by roughly dividing them in half, the order effects should offset each other at the aggregate
level. However, fully documenting the order effects in our data would bemeaningful. In addition, there may be some concern that the remaining unevenness of the numbers of subjects between the reverse-ordered sessions (66subjects starting from Tree, and 75 from Cycle) could be a source of potential
bias, even though the difference in the number of subjects is small.
To address this, we regress the prices on four explanatory variables,
T reeF irst, Cycle, Cycle×T reeF irst, and a constant. T reeF irst is a dummy
variable that takes a value of one if the subject is assigned to the session thatstarts with Tree, otherwise zero. This variable captures the existence of an
overall order effect. Cycle is a dummy variable that takes a value of one if
1

Table II.1: Order Effect in Prices
Dependent Variable
Price
Stage 1Model 1Model 2Model 1Model 2

−3.136∗∗∗(0.681)-−2.736∗∗∗(0.737)-49.532∗∗∗(0.496)−2.569∗∗(1.043)−0.311(1.469)−1.766∗(0.988)50.418∗∗∗(0.700)623
0.0217623
0.0324Cycle-

Const.

54.551∗∗∗(0.464)−2.339∗∗∗(0.957)−1.617(1.357)2.276∗∗(0.925)53.426∗∗∗(0.651)

Observations
R2695
0.0297695
0.0387

T reeF irst
T reeF irst × Cycle∗

Stage 2-

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.

the trial belongs to Cycle, otherwise zero. T reeF irst × Cycle is the crossterm of T reeF irst and Cycle, whose significance would indicate the presenceof distinct order effects across the two treatments. We also report the resultsof a regression including only two regressors, T reeF irst and a constant.
The results of the regressions are presented in Table II.1, with the resultsfor Stage 1 prices in the first and second columns and those for Stage 2
in the third and fourth columns. These results suggest some order effects
in the price determinations as the coefficients for T reatF irst are uniformly
significantly different from zero to the negative side in both Stages 1 and 2
for both Models 1 and 2 (p − value < 0.05 for all). These results imply thatthe prices tend to be lower if the subjects receive Tree first.
2However, we do not confirm a treatment-specific order effect as neitherof the coefficients for the cross term T reeF irst × Cycle in Stage 1 (second
column) or in Stage 2 (the fourth column) statistically significantly differ
from zero (p − value = 0.234 and 0.833 respectively).
Accordingly, the order effect observed in the data only changes the overall
price levels across the treatments, but not the level in a specific treatment.
Thus, the bias should not appear when we compare behavior between the
two treatments, even if there is some discrepancy in the number of subjects
between the reverse-ordered sessions.

III

Likelihood of Successful Trials

This section of OSM documents the statistical comparison of the likelihoodof successful trials across the two treatments. Here we examine the treatment
effects and the associated learning effects.
To do this, we perform the following linear regression analysis. We regress
the dummy variable for the success of the trial on the four explanatory variables, Cycle, Latter, Cycle × Latter, and a constant. Cycle is a dummy
variable that takes a value of one if the trial belongs to Cycle, otherwise
zero. Latter is a dummy variable that takes a value of one if the trial lies in
the latter half of each treatment (i.e., 5th to 8th trials), otherwise zero. This
captures the overall learning effects across the treatments (unless a negatively
significant treatment-specific learning effect exists in Cycle). Cycle × Latteris the cross term of Cycle and Latter, and this captures any additional impact on the learning effect specifically appearing in Cycle. The statistical3

Table III.1: Likelihood of Successful Trials
Dependent Variable
Success
Whole transactions
Stage 1 transaction
Model 1Model 2Model 1Model 20.013
(0.028)-−0.013(0.019)-0.931∗∗∗(0.014)−0.016(0.027)0.005(0.039)0.000(0.027)0.931∗∗∗(0.019)752
0.0006752
0.0007

Latter-Const.

0.822∗∗∗(0.019)−0.011(0.039)0.048(0.055)−0.027(0.039)0.835∗∗∗(0.028)Observations
R2

752
0.0003752
0.0013

Cycle
Cycle × Latter∗-

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.

significance of the variable indicates that the learning effects differ acrossthe treatments (i.e., the existence of treatment-specific learning effects). The
learning effect in Tree is captured by the coefficient of the term Latter,and that in Cycle by the sum of the coefficients of the terms Latter andCycle × Latter. We also report the result of a regression in which only two
regressors are included, Cycle and a constant, to gauge the treatment effectover all trials.
The regression results are presented in Table III.1. The results for thewhole transaction are presented in the first and second columns. The coefficient of Cycle in Model 1 in the first column does not statistically significantly
differ from zero (p − value = 0.629), indicating that the likelihood of success4

does not differ across the two treatments on average over all trials. Moreover,the coefficient of Cycle×Latter in Model 2 in the second column does not differ statistically significantly from zero (p − value = 0.385), indicating that atreatment-specific learning effect does not exist. Indeed, the results of the insignificant coefficient of Latter (p − value = 0.495) and the insignificant sumof the coefficients of Latter and Cycle × Latter (F-test, p − value = 0.585)
imply that there exists no learning effect in both treatments.
The results for the first transaction basis are also similar as presented in
the third and fourth columns. The coefficient of Cycle in Model 1 in the thirdcolumn does not statistically significantly differ from zero (p−value = 0.492).
The coefficient of Cycle × Latter in Model 2 in the fourth column does notdiffer statistically significantly from zero (p − value = 0.891). The coefficientfor Latter is also not significant (p − value = 1.000), nor is the sum of thecoefficients Latter and Cycle × Latter (F-test, p − value = 0.846).
These results suggest that the likelihood of a successful trial does not differ
across the two treatments. In addition, we do not identify any treatmentspecific learning effect, or any learning effects themselves in both treatments.
Thus, we do not need to be unduly concerned about uneven sample dropouts
across the two treatments resulting from sudden ceases in ongoing negotiations.

5

IV

Number of Negotiations

As discussed above, we do not find any significant difference in the likelihood of successful trials across the two treatments, which eliminates any
concern about uneven sample dropouts across the two treatments. However,it might be useful to also analyze the numbers of negotiations. Like the caseof the likelihood of successful trials, we examine the treatment effects andthe associated learning effects.
We perform a linear regression analysis similar to the analysis for the
likelihood of successful trials in OSM III, where we regress the number ofnegotiations in the trial on the four explanatory variables, Cycle, Latter,
Cycle × Latter, and a constant. We also report the results of a regression
including only two regressors, Cycle and a constant.
Table IV.1 displays the regression results. As shown in the first and thirdcolumns, the coefficients for Cycle differ statistically significantly from zeroon the negative side, indicating that the overall number of negotiations issmaller in Cycle (p − value < 0.01 for both), as first suggested in Table 2 inSection 4.
For the learning effects, the results for the whole transaction basis displayed in the second column suggest a learning effect in Tree as the coefficientfor Latter is significantly different from zero (0.414, p − value = 0.048 <0.05). However, the existence of a learning effect in Cycle is less clear as thesum of the coefficients for Latter and Cycle × Latter is near zero (F-test,p − value = 0.773), which implies less possibility that a learning effect exists
in Cycle. Nonetheless, the coefficient for Cycle × Latter is not significant

6

Table IV.1: Number of Negotiations
Dependent Variable
Number of Negotiations
Whole transactionsFirst transaction
Model 1Model 2Model 1Model 2−0.487∗∗∗(0.147)-−0.255∗∗∗(0.084)-

1.783∗∗∗(0.060)−0.094(0.118)−0.321∗(0.168)0.155(0.119)1.707∗∗∗(0.083)623
0.0146623
0.0204Latter-Const.

3.579∗∗∗(0.104)−0.253(0.207)−0.473(0.294)0.414∗∗(0.208)3.376∗∗∗(0.146)

Observations
R2

623
0.0173623
0.0256

Cycle
Cycle × Latter-∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Limited to trials with whole transactions among the three players.

(p − value = 0.108), although the value of the point estimate is negativeand large (−0.473), suggesting that while a treatment-specific learning effect could exist, the evidence for this is not sufficiently strong. For the firsttransaction basis, not only do we not identify a significant treatment-specificlearning effect, but we also do not find any significant learning effect in thetreatments. This is because while in the fourth column the coefficient for
Cycle × Latter has a large negative value (−0.321), it is only marginally significant (p − value = 0.056). Thus, while a treatment-specific learning effectcould exist, there is insufficient evidence to support it. Indeed, the coefficientfor Latter is not significant (p − value = 0.194), along with the sum of thecoefficients for Latter and Cycle × Latter (p − value = 0.159), suggesting7

that the presence of learning effects themselves is unclear.
Overall, some differences in learning effects across the two treatments
might exist as the large values in the coefficients of the term Cycle × Lattersuggest. However, the evidence for this is not statistically meaningful.
Moreover, we also examine the number of negotiations across the twostages (first vs. second), which could be different in Cycle in which the negotiation structure changes drastically across the two stages. We regress thenumber of negotiations in each stage of each trial on the four explanatory
variables, SecondST , Latter, SecondST ×Latter, and a constant. SecondST
is a dummy variable that takes a value of one if the corresponding negotiations are attempted in Stage 2. Thus, the cross term of SecondST and
Latter captures a stage-specific learning effect. We also report the result ofa regression including only two regressors, SecondST and a constant.
The regression results are presented in Table IV.2. It is a straightforward
result that none of the regressors associated with the term SecondST aresignificantly different in Tree (the first and second columns). However, thisalso holds even in Cycle, in that the coefficient of SecondST in the thirdcolumn is not significant (p − value = 0.681), or are the coefficients for the
cross term SecondST × Latter (p − value = 0.109) and SecondST (p −value = 0.394). These results suggest that the numbers of negotiations do
not change significantly across the stages, despite the considerable differencein negotiation structure in Cycle.

8

Table IV.2: Comparison of the Number of Negotiations across Stages
Dependent Variable
Number of Negotiations
Tree
Cycle
Model 1Model 2Model 1Model 20.129
(0.104)-0.035(1.529)-1.529∗∗∗(0.060)−0.103(0.121)
0.273(0.170)−0.166(0.120)1.613∗∗∗(0.086)628
0.0003628
0.0046

Latter-Const.

1.783∗∗∗(0.073)−0.038(0.145)0.104(0.207)0.155(0.147)1.707∗∗∗(0.103)Observations
R2

618
0.0000618
0.0069SecondST
SecondST × Latter∗-

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Limited to trials with whole transactions among the three players.

9V

Supplemental Regression Results for theFirst Bids in Stage 1

Table V.1: Supplemental Regression Results for the First Bids in Stage 1
Dependent Variable
First Bid
LatterConst.
Observations
R2

Tree

Cycle

−3.639∗∗∗(1.074)51.851∗∗∗(0.537)1.636∗∗(0.775)52.047∗∗∗(0.388)376
0.0124376
0.0084∗p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Fixed-effect models for controlling subjectlevel individual heterogeneity.
Cluster-robust standard errors in parentheses.

10Red: Originator, Green: Reseller (First Buyer)

Figure VI.1: First Asks in the Second Stages

VI

First Asks in Stage 2

In Section 5.4, we observe that the first asks in Stage 2 differ significantly
across the two experimental treatments. We could then consider the possibility that this difference arises because of the distinct roles of the sellers
initially assigned in the experiment, either as an originator or as a buyer.
This is because in Tree, the originator is the only seller even in Stage 2,
while the first buyer could become a reseller in Stage 2 in Cycle.
To assess any behavioral differences between the two types of sellers in
the first asks in Stage 2, we plot the dynamics of the mean value of thesedifferences across trials in Figure VI.1. As displayed, the asks of originators
are smaller than those of resellers in the early trials; they then converge to11

an almost identical level.
However, we do not statistically confirm a significant difference between
them even in the early trials. Table VI.1 presents regression results to address
the difference of the Stage 2 first asks between the two sellers. In Model 1,
shown in the first column, the coefficient for Originator is not significantly
different from zero (p − value = 0.343), indicating that the overall mean
does not differ between the two types of sellers. Even for the early trials, thecoefficient for Originator in Model 2 in the second column, which captures
the difference in the early trials in the regression model specification, is only
marginally significant (p − value = 0.062).
Accordingly, while the first asks could differ in the early trials, any difference is not sufficient to be statistically significant. Moreover, this difference,
if any, soon disappears as the trials proceed.

12Table VI.1: First Asks in Stage 2
Dependent Variable
First Ask
Model 1Model 2

−1.858(0.195)-Latter-Const.

47.494∗∗∗(1.039)−4.184∗(2.218)4.626∗∗(1.916)−2.723∗(1.570)48.886∗∗∗(1.307)

Observations
R2

345
0.0071345
0.0186

Originator
Originator × Latter∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors in parentheses.

13

VII

English translation of the instructions andthe quiz
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