ISSN (Print) 0473-453X

Discussion Paper No. 1151

ISSN (Online) 2435-0982

TWO EXPERIMENTS ON
TRADING INFORMATION GOODS
IN A NETWORK

Nobuyuki Hanaki
Yutaka Kayaba
Jun Maekawa
Hitoshi Matsushima

Revised October 2023
December 2021

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

Two experiments on trading information
goods in a network∗
Nobuyuki Hanaki† Yutaka Kayaba‡
Jun Maekawa§ Hitoshi Matsushima¶
October 3, 2023
Abstract
We examine the impact of a cycle path on the trading of a copyable information good in a network experimentally. A cycle pathin a network allows a buyer to become a reseller who can compete
against existing sellers by replicating the good. A theoretical prediction considers that the price of the information good, even with thefirst transaction where there is not yet a reseller competing with theoriginal seller, will be lower in networks with a cycle path than otherwise. However, our experiment reveals that the observed price forthe first transaction is significantly higher in networks with a cycle
path. An additional experiment that enhances competition also does
not support the theoretical prediction.

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, 20H05631, and 23H00055) from the Japan
Society for the Promotion of Science and the Japanese Ministry of Education, Culture,
Sports, Science and Technology along with the Joint Usage/Research Center at the Institute of Social and Economic Research, Osaka University, and the Center of Advanced
Research in Finance at the University of Tokyo. Ivan Conjeaud, Akishige Ikoma, Takio
Uesugi, and Yuta Shimodaira provided valuable support in preparing the software for theexperiment. We very much appreciate the comments and suggestions of seminar participants at Waseda and National Taiwan University.
†
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. Unlike ordinary goods, information goods do not disappear when consumed and can be copied easily. Given this copyable property,
every successful transaction of the information good creates a new seller andthus may negatively affect any benefit to its originator. Indeed, noting that
information goods are typically exchanged bilaterally in networks,1 Polanski(2007) and Manea (2021) show that when information goods are traded insuch a way, the distribution of benefit among the parties involved may greatly
differ depending on the network structure, namely, whether the network hasa cycle path.
A cycle path is a set of network links in which the start and end points areon the same node. On the one hand, if there is no cycle path, the seller canenjoy a greater benefit because the resale of information by the buyer does
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 incompetition between the seller and the buyer. As a result, the seller’s benefit
will be much less (and that for the buyer much more) 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 price competition in the future.
In this paper, we verify these theoretical implications experimentally
through posing the following research questions:
1. Are prices lower in a network with a cycle path compared to one with1
For example, when founded in 1999, Napster allowed users to transfer their digitalaudio files bilaterally through its peer-to-peer system.

2

out?
2. Does the effect of competition with the latter transaction extend upstream to the first transaction?
To address these implications, we set up an experiment based on the theoretical analyses of Polanski (2007) in which players trade information goodsin networks using a series of simultaneous move demand games as the trading protocol. We consider two simple networks, one with a cycle path andthe other without, comprising three players, and originally consisting of one
seller (i.e., the originator) and two buyers, and compare the behavior of theplayers across the two networks.
Our main finding is that the prices observed in the network with a cycle
path are inconsistent with the theoretical prediction compared with thoseobserved in the network without a cycle path. Specifically, although competition between the originator and the reseller lowers the observed prices
in the final transaction in the network with a cycle path, its magnitude ismuch smaller than that predicted by the theoretical prediction. In addition,and contrary to the theoretical prediction, the prices for the first transaction
tend to be higher in the network with a cycle path.
Moreover, we reveal that learning does not resolve the gap between thetheoretical prediction and the experimental results in the network with acycle path. Instead, it could widen the discrepancy in the prices of the firsttransaction. This is because as participants gain experience by repeatedly
playing the game, the prices of the first transaction in the network with acycle path could rise further given the increasing willingness of buyers topurchase the good, which is inconsistent with the theoretical prediction.
Potential reasons for the prices in the final transactions in the networkwith a cycle path being much higher than the level predicted by the theory3

include: (1) a lack of competition between the originator and the reseller, and(2) the other-regarding preferences of the participants. Indeed, we provide
evidence that the last buyers are willing to pay higher prices to the originator
than to the reseller in the final transaction.
To test the effect of a lack of competition between the originator and thereseller in the network with a cycle path, we conducted an additional experiment employing a continuous double auction as the trading protocol insteadof a simultaneous move game. While the enhanced competition between theoriginator and the reseller indeed substantially lowers the observed prices in
the final transaction in the network with a cycle path, they are still higher
than their theoretical prediction. Furthermore, because of the enhanced competition between the two buyers in the first transaction, the observed prices
are similar between the networks with or without a cycle path, which is inconsistent with the theoretical prediction. Individual characteristics, such as
cognitive ability, willingness to take risks, and patience, do not consistently
explain these results. However, the last buyer’s degree of altruism seems toprevent prices in the final transaction from falling further.

1.1

Related literature

Many economic theories and experiments use graph theory to analyze various economic phenomena. Kranton and Minehart (2001), Corominas-Bosch(2004) and Judd and Kearns (2008) identified linked buyer–seller trading
equilibria and their theoretical results showed that the outcome of transactions is highly dependent on the shape of the network. Charness et al. (2007)
experimentally tested the theory of Corominas-Bosch (2004) and found thatthe results were close to the theoretical predictions, and further concluded
that social learning is taking place.
4Allen and Gale (2000) and Acemoglu et al. (2015) present a model offinancial contagion caused by liquidity shocks using the network structure
existing among banks. Choi et al. (2017b) reproduced financial linkages on
this network in an experiment used to investigate which networks are prone
to contagion.
There is also a series of theoretical and experimental analyses of phenomena occurring in large networks. Choi et al. (2022) experimentally tested
whether large networks form a correct consensus of guesses and opinions
based on the theoretical predictions of Degroot (1974). Their study showedthat the ease of consensus formation and the correctness of consensus differ
depending on the shape of the network. Choi et al. (2023) experimentallyinvestigate the relationship between the profits of intermediary and the geometry of large networks.
Our study contributes to the literature on information goods and the
network economy, for which there are many early theoretical 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 Internetcompanies, and Bergemann et al. (2018) addressed information trading fromthe viewpoint of mechanism design.
Many studies focused on the characteristic that information goods canbe copied have been related to copyright. For instance, Liebowitz (1985)
and Basen and Kirby (2005) analyzed how the presence or absence of copyright affects social benefits and those of the original information supplier, andVarian (2005) and others conducted copyright research focusing on the digiti-

5zation of information. Muto (1986), Takeyama (1994), and others conducted
research focusing on the externality of information, that is, the collapse ofmonopoly as information spreads.
Polanski (2007) introduced graph theory to this body of work and createda model in which information is traded through negotiations between players
linked in a network, revealing that information externalities depend on the
network structure. Later, Manea (2021) extended the theory by Polanski(2007) by defining the equilibrium that holds in more general situations. As
noted earlier, their key finding is that the distribution of gains is affected bywhether the buyer–seller network includes a cycle path. To the best of ourknowledge, this insight has not been tested experimentally.
Unlike existing experimental studies, our experiment deals with an 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. In their
network experiment, Choi et al. (2017a) investigated path competition andconcluded that the position of a node greatly affects the gain. See the survey
by Choi et al. (2016) for other experimental studies. Unlike these studies,
however, 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. The results ofthe main analyses are in Section 4. An additional experiment is described in
Section 5 followed by its results in Section 6. Section 7 concludes.

6

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).

2.1

Model

Figure 1 depicts the simplest three-node networks we use to assess the difference between a Tree (left) and a Cycle (right).2 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.
Player 1 is the originator of the information good and hence the sole seller
at the start of the game. Player 1 gains a payoff only by selling the good tobuyer players. Buyer players (i.e., Players 2 and 3) gain a payoff of 100 fromobtaining and consuming the good. Moreover, they can copy the information
good in the Cycle and sell it to the buyer player that does not yet possess
the good. If the resale transaction is successful, they earn additional resale
benefits. Therefore, competition between the originator and a reseller could
take place in the Cycle.
We assume, as in Polanski (2007), that at most one transaction occurs
per step 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.
Namely, the seller and the buyer simultaneously submit their prices, andthe transaction is successful only when the buyer’s price is greater than orequal to the seller’s price. The transaction price is the average of two prices
submitted. The game is terminated with a probability of 1 − δ when negotiation fails. This ensures that the experiment concludes within a reasonable
2

A “Tree” in our paper is a network conventionally called a “line.”

7

Stage 1 - Only Player 1 owns the good.

Stage 2 - Two players own the good.

Figure 1: Two States in the Game8

time. As a result, the equilibrium payoffs are subject to the continuation
probability δ.

2.2

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 (see the top panel of Figure 1).
The game begins in this state. Stage 2 is a state in which one transaction
is completed from Stage 1. As a result, either Player 2 or 3 possess theinformation in addition to Player 1. The bottom panel of Figure 1 displays
the case in which Players 1 and 2 possess the good, and which is known toPlayer 3. If a further transaction is completed in this state, all players in the
network own the information, and the game ends. Therefore, the network isalways in a state of either Stage 1 or 2 during a 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 , the strategy for the buyer
and the seller by pnst,r , and the transaction price pnst , 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, theStage 1 payoffs include the Stage 2 expected payoffs.
The equilibrium payoffs are derived following the formulation of Polanski(2007). That is, we assume that a Nash bargaining solution determines thetransaction price in which the market power of the seller is α and that of thebuyer is 1 − α where α ∈ (0, 1) is an exogenous variable. The expected payoff
is defined by the state of the network, and the equilibrium expected payoff isthe value obtained by allocating the surplus generated from the transaction
9

to the threat point payoff according to the available market power. We also
assume that when a transaction produces a positive (negative) total surplus,
the probability of the success of the transaction is 1 (0). Furthermore, toavoid multiple equilibria, we assume that the transaction surplus is positivein each negotiation. We first derive the equilibrium for Cycle, starting from
Stage 2, and then the equilibrium for Tree.

2.2.1

Stage 2 Payoff in Cycle

C
Strategies for the seller and the buyer are pC
2s ∈ [0, 100], p2b ∈ [0, 100]. Their

payoff functions are:

xC
2s =




p C
2

C
if pC
2b ≥ p2s 1 δxC
2s

otherwise2

where pC
2 =C
pC
2s +p2b
.
2

xC
2b =

,




100 − pC

C
if pC
2b ≥ p2s



δxC
2b

otherwise2

In Stage 2 of the Cycle, the threat points in the ne-Cgotiation are 12 δxC
2s for the seller and δx2b for the buyer. This is because if

negotiation fails, while the buyer player becomes a buyer again in the following negotiation for certain, the seller player is selected as the next seller onlywith probability 21 . We assume that the seller earns no gain if not selected
as the seller in the next negotiation and the buyer purchases the good fromthe other seller player.3 If the transaction is completed, a total gain of 100
is divided between the two players.
1
C
C
C
C
C
Every strategy profile (pC
2s , p2b ) satisfying p2 ≥ 2 δx2s , 100 − p2 ≥ δx2b ,CC4and pC
Therefore, for any α ∈ (0, 1), the2 = p2s = p2b is an equilibrium.
3

Given the total surplus is positive, the next negotiation succeeds with probability 1.
The same argument applies below.
4
Although we omit them, similar conditions are required in deriving equilibrium Stage 1
in Cycle as well as Stages 1 and 2 in Tree.

10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 and theCbuyer, respectively. Together with the total gain equation (xC
2s + x2b = 100),for any α ∈ (0, 1), the Stage 2 payoffs are derived as:

xC
2s =

2.2.2

100(1 − δ)α,1 − 12 δ − 12 αδ

xC
2b =

100(1 − α)(1 − 21 δ)
1 − 12 δ − 12 αδStage 1 Payoff in the Cycle

C
Strategies for the seller and the buyer are pC
1s ∈ [0, 100], p1b ∈ [0, 100]. Their

payoff functions are:

xC
1s =




p C + 1 x CC
if pC
1b ≥ p1s



δxC
1s

otherwise1

where pC
1 =

2 2s

C
pC
1s +p1b
.
2

,

xC
1b =




100 − pC + 1 xC

C
if pC
1b ≥ p1s
1C 1 δxC
1b + δx2b

otherwise

1

2

2 2s

2

If a negotiation fails in Stage 1, the buyer player willbe the buyer again in the next negotiation with probability 12 . Otherwise,
the player will be the buyer in Stage 2 under the premise that the otherbuyer purchases the good in the next negotiation and the game proceeds toStage 2. The seller certainly becomes the seller in the next negotiation. If
a negotiation is successful, in addition to the 100 generated by the resulting
transaction, either the seller or the buyer in this negotiation will become theseller player in the next negotiation in Stage 2 and will earn xC
2s , which occurs
with probability 12 for each party.

11

In an equilibrium, for any α ∈ (0, 1), the following equations that represent the equilibrium condition for the seller (Eq. (3)) and the buyer (Eq. (4))
hold.
1 C
1 C
1 C
1 C
C
C
xC
(3)
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
(4)
C
C
With the total gain equation (xC
1s + x1b = 100 + x2s ), for any α ∈ (0, 1),

Stage 1 payoffs become

xC
1s =

2.2.3

1
1
C
C
(1 − α)(1 − δ)(100 + xC
α(1 − 12 δ)(100 + xC
2s ) + 2 δαx2b2s ) − 2 δαx2b
C
,
x
=
1b
1 − δ + 12 αδ
1 − δ + 21 αδStage 2 Payoff in a Tree

Let us now derive the equilibrium payoffs in a Tree. We start from Stage 2.
The strategies for the seller and the buyer are pT2s ∈ [0, 100], pT2b ∈ [0, 100]and their payoff functions are:xT2s =

where pT2 =




pT
2

if pT2b ≥ pT2sδxT2sotherwise

xT2b =,


100 − pT

if pT2b ≥ pT2sδxT2botherwise

2TpT
2s +p2b. Note that, for the case of Stage 2 in the Tree, even if the2transaction fails, the same transaction will be repeated.
In an equilibrium, the following equations hold for any α ∈ (0, 1).

xT2s =δxT2s + α(100 − δxT2s − δxT2b )(5)

xT2b =δxT2b + (1 − α)(100 − δxT2s − δxT2b )

(6)

12

Eqs (5) and (6) represent the equilibrium conditions for the seller and thebuyer, respectively. With the total gain equation (xT2s + xT2b = 100), for any
α ∈ (0, 1), we obtain the following as the Stage 2 payoffs.

xT2s = 100α,2.2.4xT2b = 100(1 − α)Stage 1 Payoff in a Tree

The strategies for the seller and the buyer are pT1s ∈ [0, 100], pT1b ∈ [0, 100],and their payoff functions are:xT1s =p T + x T

if pT1b ≥ pT1sδxT1sotherwise2s1

where pT1 =T
pT
1s +p1b.
2,

xT1b =


100 − pT

if pT1b ≥ pT1s
 1 δxT2b + 1 δxT1botherwise1

2

2

Note that if a negotiation fails in Stage 1, the buyer

player in the current negotiation will become the buyer again in the next
negotiation with probability 12 . Otherwise, the player will be the buyer inStage 2, premising that the other buyer purchases the good in the next
negotiation and the game proceeds to Stage 2. The seller player of the failed
negotiation becomes the seller again for certain in the next negotiation. If anegotiation is successful, in addition to the 100 generated by this transaction,
the seller of the negotiation will be the seller in Stage 2 for certain and will
earn xT2s .
In an equilibrium, the following equations hold for any α ∈ (0, 1).
11
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

(7)
(8)

From the total gain equation (xT1s + xT1b = 100 + xT2s ) and Eqs (7) and (8), forany α ∈ (0, 1), the Stage 1 payoffs becomexT1s =α(1 − 12 δ)(100 + xT2s ) − 12 δαxT2b(1 − α)(1 − δ)(100 + xT2s ) + 12 δαxT2b
T
,
x
=
1b
1 − δ + 12 αδ
1 − δ + 21 αδ

2.3

Equilibrium Price

The equilibrium price in each stage is computed using the abovementioned
expected payoffs. The analytical solutions are as follows:

pC
1 =

1
C
100α(1 − 12 δ) + (α − 12 + 12 δ − 43 αδ)xC
2s − 2 δαx2b1 − δ + 21 αδ

100α(1 − 12 δ) − (1 − α)(1 − δ)xT2s − 12 δαxT2b1 − δ + 12 αδ100(1 − δ)αpC
2 =1 − 12 δ − 12 αδ
pT1 =pT2 =100α

(9)
(10)
(11)
(12)

Suppose that δ = 0.9 (as in our experiment) and α = 0.5, i.e., the power ofnegotiation is equal between the seller and the buyer.5 Then, the equilibrium
TC
prices are pC
1 ≈ 31.36 and p1 ≈ 42.31 for Stage 1, and p2 ≈ 15.38 and

pT2 = 50 for Stage 2. The Stage 2 equilibrium price in a Cycle is drasticallylower than in a Tree because of competition between the originator and thereseller.6 Moreover, the effect of competition on the price in a Cycle also
appears upstream in Stage 1, in which a reseller has not yet appeared in themarket. Our primary aim of the experiment is to verify these theoretical5

In the theoretical model, equilibrium occurs at any α between 0 and 1. Polanski(2007) uses an equilibrium where the gain is equally divided (α = 0.5) when buyers andsellers trade bilaterally as a benchmark, which is also followed in this paper. Given thetheoretical price of Stage 2 of the Tree is 100α, and as the experimental data (Figure 2)
shows that the average price of Stage 2 is 49.26, which is not significantly different from50, it is appropriate to set α=0.5.
6Polanski (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.

14predictions for prices.

3

Experimental Design and Procedure

We conducted six sessions of computer-based online experiments in October
2020.7 We recruited 141 subjects from a subject pool at the Institute of Socialand Economic Research, Osaka University, managed by ORSEE (Greiner,2015). The subject pool consists of undergraduate and graduate students
from various fields at the university. Our subjects were paid according totheir performance in the experiment. Each subject experienced 16 trials ina session and one trial was selected randomly at the end of the experiment.
The points the subject earned in the selected trial were 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. The payments were made in the form ofan emailed 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.8 The number of subjects and the7

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
participation ID (sub01, sub02,...) when entering the meeting room. Their cameras aswell as microphones were off on Zoom during the experiment.
8
As the treatment order is counterbalanced among our subjects, the order effect should

15

treatment order in each of the six sessions are presented in Table I.1 in Online
Appendix I.
Each treatment consists of eight consecutive trials, and a trial includes
several rounds of negotiations. After the subjects read the experimental
instructions and completed a few quizzes that assessed their comprehensionof the rules of the game, the experiments employed the following procedure.9
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.10 At the start of a trial, a group of three players occupying each of the three positions is randomly formed and play the game wehave described in the previous section.
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

Results

We primarily focus on payoffs and prices. Other analyses regarding the rateof successful transactions, the number of negotiations, and the bids and asks
are summarized in Online Appendix I and II
not be a major concern. Nonetheless, we assess the magnitude of the order effects in theOnline Appendix I.1. The results indicate that the potential bias in our analysis arisingfrom the order effect is at most marginal.
9
The experimental instructions and screenshots of the actual experiments (translated
from Japanese to English) can be downloaded from https://bit.ly/3sYOvjJ (the filename is instructionOriginal.pdf).
10
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

Table 1: 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.

4.1

Payoffs

Table 1 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 a buying agreementin Stage 1. We denote this type of buyer as “first buyer.” The other is theclass of buyers that finally bought the good in Stage 2. We refer to this othertype of buyer as “last buyer.”
As displayed in Table 1, 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 almost earns the same as a lastbuyer in Tree. The mean payoff of the former is 47.70, and that of the latter
is 50.74 (insignificant difference, p − value = 0.137).11 The almost identicalshare of the two buyers is a straightforward result of the theoretical predictionin Tree, in which any buyer is equivalently required to buy the good fromthe originator.
In Cycle, in which transactions between the first and last buyers can take11

Here and below, we report p-values after controlling for individual-level fixed effects
with cluster-robust standard errors in this subsection.

17

place, originators earn less than in Tree. The mean payoff of an originator is
78.59, which is statistically significantly smaller than that in Tree (p−value <0.01). Naturally, buyers earn more in the treatment as they obtain theremainder, such that a buyer earns 60.71 on average. Among buyers, a firstbuyer earns 68.75 on average, which is statistically significantly larger thanin Tree (p − value < 0.01). A last buyer earns 52.66 on average, which isslightly, but statistically significantly, larger than in Tree (p−value = 0.015).
The payoff of a first buyer is significantly larger than that of a last buyer in
Cycle on average by 16.09 (p − value < 0.01). We further discuss the payoff
difference between buyers in Section 4.4.
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 and last buyers 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 proposed asks)
remains unchanged, simply because the originator now has less chance ofselling as the first buyer has a chance to sell too.12 In the following subsection, we focus our analysis on transaction prices, bids, and asks to address
any behavioral differences among our subjects across the two treatments.13

4.2

Prices in Stage 2

As discussed in Section 2.2, the model is solved through backward induction.
With that in mind, we first discuss the results of Stage 2, then proceed to12

In 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 shown
below.
13
The only exception is the payoff of last buyers. The difference in last buyers’ payoff
across the two treatments necessarily implies that the behaviors associated with the final
transactions differ.

18

Note: Red: Theory (50 in Tree and 15.38 in Cycle)

Figure 2: The Distribution of Observed Prices in Stage 2
those of Stage 1.
Figure 2 plots the distribution of observed prices in Stage 2 for Cycle(top) and Tree (bottom). The average prices in Tree and Cycle are 49.26
and 47.34, respectively. While the mean price in Tree is not statisticallysignificantly different from the theoretical prediction (p − value = 0.549),
the mean price 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 differenceis statistically significant (p − value < 0.01.)14 This result suggests that the
downward pressure in prices induced by competition, which manifests itself
as statistical significance, is weak.
Result 1: While the Stage 2 prices in Tree are consistent with the theoreticalprediction, those in 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 theoretical prediction in Cycle resolve itself as our subjects accumulate experience? This is because our
14

After controlling for session-level fixed effects with cluster-robust standard errors, see
Model 1 in the third column of Table 2.

19subjects may have not yet learned the power of competition in the early trialsof the treatment, which they might learn in the later trials. To address this,we estimate the following linear regression, which includes variables capturing learning effects, by regressing the prices on four explanatory variables(i.e., Cycle, Latter, Cycle × Latter, and a constant). Cycle is a dummy
variable that takes a value of 1 if the trial belongs to Cycle, otherwise 0.
Latter is a dummy variable that takes a value of 1 if the trial lies in thelatter half of each treatment (i.e., the 5th to 8th trials), otherwise 0, 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 (i.e., Cycle and a constant) to overview the treatment
effect over all trials.
The results of these regressions appear under Model 2 in the fourth column of Table 2. Our primary focus here is the value of the coefficient forthe cross term Cycle × Latter, which captures the treatment-specific learning effect in Cycle. Its value of 0.656 is not significantly different from 0(p − value = 0.394). This indicates that contrary to our earlier speculation,
price competition between the two sellers in Cycle does not lower prices morein later trials by which time our subjects should have accumulated experience. Instead, the positive value of the point estimate, while not significant,implies that the treatment-specific effect in Cycle could have resisted the20Table 2: Regression Results for Price
Dependent Variable
Price
Stage 1
Cycle

Model 1Model 2Model 1Model 21.512∗∗(0.501)-−1.921∗∗(0.532)-49.262∗∗∗(1.150)−2.221∗∗(0.582)0.656(0.703)−2.257(1.136)50.373∗∗∗(1.097)623
0.0108623
0.0220Latter-Const.

52.343∗∗∗(1.321)

0.698(0.480)1.627∗∗∗(0.391)−0.971∗∗(0.246)52.829∗∗∗(1.357)

Observations
R2695
0.0069695
0.0101

Cycle × Latter

Stage 2-∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Cluster-robust standard errors (session level)in parentheses.

overall tendency to lower the prices observed with the negative coefficient for
the term Latter (insignificant, p − value = 0.104). Indeed, the sum of thecoefficients of the terms Latter and Cycle × Latter, that is, the magnitude ofthe learning in Cycle, is −1.601, which is statistically marginally significant(F-test, p − value = 0.065 < 0.1).15
Result 2: The price competition in Stage 2 in Cycle does not facilitate subject learning in converging to the equilibrium implied by the theoreticalprediction.
Competition is a strong power that guides economies to equilibria. For
example, Roth et al. (1991) report that prices converge to a competitive
equilibrium in their multiplayer market experiments. However, our results
15

The marginal significance of the learning effect in Cycle is also confirmed, even if we
employ Cycle data only (p − value = 0.064 < 0.1).

21Note: Red: theory. 42.31 in Tree and 31.36 in Cycle.

Figure 3: The Distribution of Observed Prices in Stage 1
for 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 the theoretical prediction. 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.

4.3

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 also deviate.
Figure 3 plots the distribution of the observed prices in Stage 1 prices
for Cycle (Top) and Tree (Bottom). The mean prices are 53.86 and 52.35 in
Cycle and Tree, respectively. In Tree, the mean Stage 1 price is larger thanthat of Stage 2. Although the difference (3.08) is small, it is statisticallysignificant (p − value = 0.02).16 . The mean price is statistically significantly
16

After controlling for session-level fixed effects with cluster-robust standard errors, see
Model 1 in the first column in Table 2.

22higher than the theoretically predicted level (p − value < 0.01).17
In Cycle, the mean price in Stage 1 is 53.86, which is larger than thatin Stage 2 by 6.514 (p − value < 0.01) and is also far larger than the level
implied by the theoretical prediction (p − value < 0.01). This variation fromthe theoretical prediction is larger than that in Tree by 17.78. Thus, likethe Stage 2 prices, we observe that the Stage 1 prices in Cycle deviate fromthe theoretical prediction, and the deviation is far larger than that in Tree(p − value < 0.01)18 .
Result 3: The Stage 1 prices in Cycle deviate from the theoretical prediction
considerably more than in Tree. In addition, again in contrast to thetheoretical prediction, the Stage 1 prices in Cycle are larger than theprices in Tree.
We now address whether the discrepancy between our experimental data
and the theoretical prediction in Cycle could be resolved by learning. As
for 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 is presented in Model 2 in the second column of Table 2. The coefficientof Latter is significantly negatively different from 0 (p − value = 0.011),
indicating that prices fall as trials proceed in Tree. Moreover, the coefficientof Cycle × Latter is also significant (p − value < 0.01), suggesting that there
exists a treatment-specific learning effect in Cycle. However, the sum of thecoefficients of the terms Latter and Cycle × Latter, which is only 0.656, is
not significantly different from 0 (F-test, p − value = 0.124). These results
jointly indicate that learning exists only in Tree and not in Cycle. Thus, as in
17

Here and below, we report p-values after controlling for session-level fixed effects withcluster-robust standard errors in this subsection.
18
We compared the deviation from the theory in Cycle and that in Tree based on the
regression coefficients in Model 1 in the first column in Table 2

23

Stage 2, there is little possibility that the discrepancy between the theoreticalprediction and the data in Cycle is resolved by learning in Stage 1.
Result 4: We do not observe any learning effect in the prices in Stage 1 inCycle.

4.4

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; hence, 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 is 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. (4). The derived pseudoequilibrium Stage 1 price is 64.55. The mean Stage 1 price (53.86) is lower
than its pseudo-equilibrium level by 10.69, which is within the extent thatcan be explained by the risk-averse behavior of our subjects, as discussed in
Online Appendix III. Thus, the observed prices in Stage 1 do not contradict

24

Table 3: First Bids in Stage 2
Dependent Variable
First Bid
4.201∗∗(2.026)45.935∗∗∗(1.859)Originator
Const.
Observations
R2

173
0.0288∗p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (subject
level) in parentheses.

our subjects pursuing a larger benefit by foreseeing future reselling prices inStage 2.

4.5

Fairness and Pricing

We observed that the Stage 2 price in Cycle is higher than the level predictedby the theoretical prediction. One possible hypothesis behind the observationis that final buyers might regard lower trading prices in Stage 2 as unfair,believing that originators should not admit a price discount resulting fromthe competition with a reseller.
To address whether this is the case, we examine whether the bids of lastbuyers differ depending on the type of seller, that is, either originators or
resellers. Last buyers might accept higher prices if they make transactions
with originators rather than resellers. We regress the last buyers’ bids onthe dummy variable Originator, which takes a value of 1 if the trading partner is the originator. Also, we employ the data in the latter trials where
we assume the subjects have learned the game better. The regression result25

is presented in Table 3. The coefficient for Originator is positively significantly different from 0 (4.201, p − value = 0.041), indicating that last buyers
are willing to accept higher prices if the trading partner is the originator.19
However, we also confirm that the difference is only marginally significant
when we compare the bids in subject-level means (p − value = 0.080, employing subject-level bootstrapped standard errors). Accordingly, last buyers
might have a tendency to accept higher prices when the trading partner isthe originator, however, the statistical evidence is not strong.20

5Additional Experiment

Observing that the experimental results are far from the theoretical prediction, we conduct an additional experiment aiming to address the factors that
may bring the gap between the data and theoretical prediction. In the additional experiment, we employ a continuous double auction as the trading
protocol to encourage competition. We assess whether price drops occur inboth stages by the encouraged competition to test whether the insufficientcompetition in Stage 2 in our earlier experiment could have been the causeof the deviation from the theoretical prediction. Below we refer to our firstexperiment as Experiment 1 and this additional experiment as Experiment 2.
Besides the competition in Stage 2, personal traits of subjects, such aslack of certain cognitive abilities or existence of other-regarding preferences,might induce deviations from the theoretical prediction. To address thispossibility, we also collected information on the personal traits of subjects
after participants finished playing the trading games.
19

If we look at all the trials, the result becomes weaker. The estimated coefficient of thedummy variable is 2.744 with p − value = 0.097.
20
Furthermore, this willingness to pay a higher price by last buyers does not result insignificantly higher prices when the last buyers trade with the originator than when they
trade with the resellers (p − values = 0.561).

26

5.1

Experimental Design and Procedure

The additional experiment employs an open-book continuous double auction for the negotiation protocol. During each round of negotiation, buyers(sellers) can submit bids (asks) at any time. While these bids and asks are
displayed and updated on the screen in real time, the identity of the playersthat submit each of them is not. A transaction is established if a newly submitted bid (ask) is higher (lower) than or equal to the smallest ask (largestbid) currently being posted in the market. The price of the transaction is determined to the value of the smallest ask (highest bid) that has existed. The
round is terminated if a transaction is established, or the time limit exceeded.
The time limit is set to 45 seconds if the number of market participants in
the round is three, and 20 seconds if the number of the participants is two.21
A next round of negotiation starts if there still exists at least one buyerthat has not yet obtained the good, and random termination has not occurred at the end of the previous round of negotiation (the trial is randomly
terminated with a 10% chance when each round of negotiation ends). Noteunlike Experiment 1 in which random termination could occur only when thetransaction fails, in Experiment 2 random termination could occur regardlessof the result of the transaction.22
In addition, after the main part of the experiment, we measure the following individual characteristics of participants: willingness to take risk, patience, altruism, positive and negative reciprocity, trust, math skills using the
Global Preference Survey (GPS) by Falk et al. (2018), and a few dimensionsof cognitive abilities. The measures based on GPS below are marked with
21

These time limits are set based on our pilot experiments to limit the duration of theexperiment. Most of the transactions finished within these time limits.
22
An English translation of the instruction can be obtained from https://bit.ly/
3sYOvjJ. The file name is DAInstruction(English ver)HO.pdf.

27

GP S at the beginning and are standardized within our participants. The
measures of cognitive ability include the score on the extended 6-question
version of the Cognitive Reflection Test (Frederick, 2005; Toplak et al., 2014,
called CRT ), the fluid intelligence measured using the four questions chosenfrom the matrix reasoning test included in the International Cognitive Ability Resource (Condon and Revelle, 2014, called matrix), and the ability tobackward induct measured using the Game of 21 (Dufwenberg et al., 2010).
While the measures from Falk et al. (2018), CRT, and matrix are based on
nonincentivized tasks, participants earned an additional 500 JPY if they won
the Game of 21. In this game, a participant, who acts as the first mover, anda computer take turns and choose an integer from {1, 2, 3} each time they are
given the chance. The chosen number is sequentially added to the numbers
already chosen, starting from 0. The player that reaches 21 in their turn isthe winner. The computer chooses randomly each time, and the participant
is informed of this random choice. There is a clear winning strategy for theparticipant, where they must choose an integer so that they reach 1, 5, 9, 13,
and 17 before reaching 21. Our measure of the ability to backward induct(BI) is based on “the number of times a participant successfully reached awinning number (the first time they had a chance to do so) divided by the
number of chances they faced” (Hanaki et al., 2022, p.4). In addition, we
implemented an attention check question in which participants are asked tounselect their answer in a question like the risk-taking question for GPS.
We define a dummy variable passAC that takes a value of 1 if participants
correctly answered the question.
We conducted six sessions of Experiment 2 in February and March 2023
(See Table V.1 in Online Appendix V for further details). We recruited
156 subjects from a subject pool at the Institute of Social and Economic

28

Research, Osaka University. Each subject experiences eight trials in a session, which consists of four consecutive trials of Tree treatment and Cycle
treatment, respectively (within-subject design).23 The treatment order iscounterbalanced as the 78 subjects receive the Tree treatment first and theremaining 78 subjects receive the Cycle treatment first. Just as in Experiment 1, subjects’ roles are randomly determined at the beginning of theexperiment and fixed during the experiment. At the beginning of a newtrial, a new group of three players are randomly formed while respecting the
subjects’ roles.

6

Results of Experiment 2

We again focus on payoffs and prices. The results of additional analyses, suchas the frequency of successful trades and the number of trades are reported
in the Online Appendix V.

6.1

Payoffs

The mean payoff of players is presented in Table 4. An originator earns alarger payoff (104.92) than buyers (47.54) in Tree. Among the buyers, alast buyer earns 56.13 on average, which is larger than a first buyer earns on
average (38.95) and is significantly different with p−value < 0.01.24 In Cycle,
the mean payoff of an originator is 78.97 on average, which is statistically23

We could not repeat the trial for 16 times as in our Experiment 1 because it tookmuch longer to run the experiment with a continuous double auction than Experiment 1,
which was based on a simultaneous move game. One of the 8 trials is selected randomly atthe end of the experiment and participants are paid based on the points they obtained in
the chosen round at 40 JPY = 1 point, in addition to the 500 JPY participation fee. The
exchange rate between the point and JPY along with the participation fee are identical tothat for Experiment 1.
24
The p-values in this subsection are after controlling for individual-level fixed effects
with subject-level cluster-robust standard errors.

29

Table 4: Mean Payoff of Players in the Additional Experiment
Treatment
Tree
Cycle

Originator104.920(26.906)
78.972(24.747)

PooledBuyerFirst Buyer

Last Buyer

47.540(18.588)
60.514(21.923)38.948(14.029)50.698(23.488)

56.133(18.651)
70.330(14.780)

Note: Standard deviations in parentheses.

significantly smaller than in Tree (p − value < 0.01). And buyers earnmore (60.51). Among buyers, a first buyer earns 50.70 on average, which issignificantly larger than in Tree (p − value < 0.01). A last buyer earns 70.33
on average, which is significantly larger than in Tree (p − value < 0.01).
The higher payoffs of the last buyer in Cycle than in Tree indicate that thecontinuous double auction has indeed enhanced competition between the twosellers in Stage 2 of Cycle. Furthermore, unlike Experiment 1, a first buyer
earns less than a last buyer earns in Cycle (p − value < 0.01). First buyers
earning less than the last buyer in both Tree and Cycle indicates the twobuyers may be over-competing in Stage 1, as we will see later.

6.2

Price

The distribution of observed prices in Stage 2 for Cycle (top) and Tree (bottom) is illustrated in Figure 4 accompanied by the levels predicted by thetheoretical prediction (0 for Cycle and 50 for Tree, see detailed discussion in
Online Appendix IV). The mean price in Cycle is 29.67, which is statisticallysignificantly smaller than that in Tree, which is 43.87 (p − value < 0.01).25
25

Here and below, we report p-values based on the session-level cluster-robust standard
errors. See Column 3 in Table 5.

30

Note: Red: theory. 0 for Tree and 50 for Cycle.

Figure 4: The Distribution of Prices in Stage 2 in the Additional ExperimentCompetition induced by the continuous double auction lowers Stage 2 prices
considerably, although the prices in Cycle are still higher than what the theory predicts (p − value < 0.01). Thus, we continue to observe a limited effectof competition similar to those reported in Dufwenberg and Gneezy (2000);
Baye and Morgan (2004).
The distribution of observed prices in Stage 1 is shown in Figure 5. Contrary to the case in Stage 2, the mean Stage 1 prices, 62.79 in Cycle and61.96 in Tree, are very similar (p − value = 0.557, see Column 1 in Table 5),although the theoretical prediction suggests that the two values should beconsiderably different (10 for Cycle and 55 for Tree). The mean Stage 1 pricein Cycle is statistically significantly higher than the level predicted by thetheoretical prediction (p − value < 0.01). The mean State 1 price in Tree isalso significantly higher than the theoretical prediction (p − value = 0.015).
While the mean Stage 1 prices are higher than the theoretical predictions
both in Tree and Cycle, for Cycle, it is even higher (p − value < 0.01) thanthe “pseudo-equilibrium Stage 1 price” based on the mean Stage 2 prices,

31

Note: Red: theory. 10 in Cycle and 55 in Tree.

Figure 5: The Distribution of Prices in Stage 1 in Experiment 2
50.05.26 Recall that, in Experiment 1, the mean Stage 1 price in Cycle waslower than the “pseudo-equilibrium Stage 1 price” (see Section 4.4), whichsuggests that the enhanced competition between the two buyers inducedby the continuous double auction has resulted in too-high prices in Stage 1.
Retrospectively, after considering the widely observed overbidding in auctionsin the experimental literature (see, e.g., Kagel, 1995; Kagel and Levin, 2016),
this may not be too surprising.
Result 5: While the enhanced competition between the two sellers inducedby the continuous double auction lowers the Stage 2 prices in Cycle,
it raises the Stage 1 prices in both Cycle and Tree. As a result, theStage 1 prices in Cycle are not significantly lower than those in Tree.
We also examine the learning effects. We perform an identical regression analysis as in Experiment 1 (Table 2). Table 5 provides the regression
26

Note that the buyers must be indifferent between buying in two stages. Thus we
C
C
C
C
C
solve for price (pC
1 = 100 − x1b ) such that x1b + δ(1/2)x2s = δx2b using x2s = 29.67 andC
x2b = 70.33.

32

Table 5: Regression Results for Price in Experiment 2
Dependent Variable
Price
Stage 1

Stage 2Model 1Model 2Model 1Model 20.827
(1.317)-−14.196∗∗∗(3.227)-43.867∗∗∗(3.077)−11.777∗∗(4.192)−4.929(2.477)−0.48(2.425)44.107∗∗∗(3.724)329
0.1535329
0.1658Latter-Const.

61.958∗∗∗(1.897)−0.739(2.024)3.096(3.711)−2.306(2.452)63.129∗∗∗(2.751)

Observations
R2

389
0.0008389
0.0044Cycle
Cycle × Latter-∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Cluster-robust standard errors (session level) in
parentheses.

results.27 The result for Stage 2 in Column 4 demonstrates that while the coefficient of Latter is insignificant (−0.480, p − value = 0.851), the sum of thecoefficients of Latter and Cycle × Latter is significantly negative (−5.409,
p − value < 0.01), implying that a further price drop occurs in Cycle assubjects experience more trials. Given that the price level predicted by thetheoretical prediction is 0, this implies that learning reduces the deviationfrom the theoretical prediction in Stage 2. Contrarily, in Stage 1 (Column2), we do not identify any learning effect in both treatments. Not only is thecoefficient of Latter insignificant (−2.306, p − value = 0.390), but also thesum of Latter and Cycle × Latter is insignificant (0.710, p − value = 0.685),
indicating that the price level remains unchanged, even after subjects gain
27

As the number of trials in each treatment is four in Experiment 2, Latter takes a valueof 1 if the trial lies in the third or fourth trial.

33

experience in Stage 1.
The abovementioned results indicate that the enhanced competitive environment in Cycle brought about by the continuous double auction lowers
prices to a certain extent, and further price falls are expected toward the level
implied by the theoretical prediction in Stage 2. However, the Stage 1 priceremains unchanged contrary to the theoretical prediction and the situation
is not resolved with learning. Thus, we explore other factors that sustain thedeviation from the theoretical prediction in Stage 1.

6.3

Subject Personal Traits

Observing that the competitive environment in Stage 2 in Cycle does notpush the price down to the level predicted by the theoretical prediction anddoes not account for the high price in Stage 1 in Cycle, we explore otherfactors that prevent the price from falling. The personal traits of subjects,
such as lack of certain cognitive abilities or existence of other-regarding preferences, might prevent the prices from falling. Table 6 reports the descriptive
statistics of these personal traits. As noted above, GPS measures are standardized within our sample.
Let us start with Stage 2. In Section 4.5, we found evidence that thelast buyers’ fairness considerations resulted in their higher willingness to pay
when the transactions were done with the originator rather than the reseller
in Experiment 1. We also found that this higher willingness to pay did not
result in higher prices. In Experiment 2, however, the last buyers cannot
tell whether the originator or the reseller is submitting the best asks. Thus,
they cannot act differently depending on which potential buyer is currently
submitting the best asks. As a result, the realized prices are not significantly

34

Table 6: Personal Traits of Subjects
Variable

Sample size

Mean

s.d.

156
156
156
156
153
155
151
153
152
150
155
156

5.180
1.974
0.440
0.923
−0.001
0.000
0.004
0.005
−0.0020.003−0.000−0.000

1.205
1.016
0.309
0.267
0.791
0.984
0.758
0.804
0.824
0.853
0.984
0.984

CRT
matrix
BI
passACGPS patienceGPS procrastination
GPS risktaking
GPS posrecip
GPS regrecip
GPS altruism
GPS trust
GPS subj math skills

different between transactions with the originator and the reseller.28
To address whether individual traits can explain the deviation from thetheoretical prediction, we regress the Stage 2 prices on the personal traits for
all players in the game (i.e., last buyer, first buyer, and originator). Table 7
displays the regression result, in which the first column includes the coefficients for the last buyer’s personal traits, the second column indicates thatfor the first buyer, and the third indicates that for the originator.
As shown, most cognitive abilities are not significantly related to the price.
The coefficient for GP S procrastination of the last buyer is significantly
negative (−2.638, p − value = 0.013). Accordingly, the ability to resist atendency to procrastinate lowers the Stage 2 price towards the equilibrium
level. However, the mechanism behind it is unclear. Although the coefficientfor BI of the originator is negative, it is only marginally significant (−6.345
with p−value = 0.061). In addition, while GP S risktaking of the first buyer
28

p − value = 0.497 based on regressing the Stage 2 price on the originator dummy (thattakes a value of 1 when the transaction is between the originator and the last buyer, and0 otherwise) and a constant.

35

Table 7: Regression Results for Subjects’ Personal Traits and Stage 2 Pricein Cycle

CRT
matrix
BI
passACGP S patience
GP S procrastination
GP S risktaking
GP S posrecip
GP S regrecip
GP S altruism
GP S trust
GP S subj math skills
Const.
Observations
R2

2nd stage price
Last buyer First Buyer Originator
1.322-1.101-1.245(1.155)(0.549)(0.938)1.840-0.194-0.881(1.324)(2.039)(0.751)-3.087-2.965-6.345*(4.255)(4.509)(2.631)
0.664
1.365
2.539
(4.519)(2.773)(1.918)-4.805-0.688-0.996(2.629)(2.314)(0.865)-2.638∗∗0.083-0.722(0.703)(0.820)(1.190)1.830-0.719*0.286(1.376)(0.330)(0.901)-3.609∗∗-1.170-2.683(1.396)(0.786)(2.381)
1.191-1.543-0.375(1.930)(1.683)(0.782)5.650∗
0.769
0.835(2.229)(1.140)(0.966)-1.1280.140-0.471(1.889)(0.320)(1.815)-2.868-0.6860.946(2.052)(1.445)(1.615)∗35.432 (14.290)
139
0.425

∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.

36

is negative, it is also only marginally significant (−0.719 with p − value =0.081).
As for the impact of other-regarding preferences on the Stage 2 price,
the coefficient for GP S altruism of the last buyer is positive (5.650) but
only marginally significant (p − value = 0.052). Thus, altruistic last buyers
may accept higher prices, which could be causing the deviations from thetheoretical prediction. Conversely, the coefficient for GP S posrecip of thelast buyer is significantly negative (−3.609, p−value = 0.049), implying thatthe last buyer’s positive reciprocity lowers the price. However, the argumentthat it brings about the equilibrium behavior is not convincing.
Let us now turn to Stage 1 prices. Table 8 displays the regression results for Stage 1 prices. As shown, most cognitive abilities do not havea significant influence on the price determination. Only the coefficient for
GP S subj math skills of the originator is significantly different from 0, andthe value is positive (3.220, p − value < 0.01). Accordingly, the lack of mathskills of the originator lowers the Stage 1 price toward the equilibrium level.
However, an argument that a lack of cognitive skill is conducive for optimal
behavior is not convincing. Similarly, although the coefficient for matrix ofthe last buyer is positively marginally significant (3.358, p − value = 0.053),
the lack of fluid intelligence leading to optimal behavior is unlikely. Accordingly, although we found some evidence that certain measures of cognitive
ability are related to price determination, we could not identify the cause ofdeviation from the theoretical prediction among them. Instead, high ability
in certain players increases the deviation from the theoretical prediction.
The effect of other-regarding preferences is also inconclusive. Amongthese regressors, only the GP S altruism of the originator is significantly
related to price. The coefficient is −5.069 (p − value = 0.028), which implies

37

Table 8: Regression Results for Subjects’ Personal Traits and Stage 1 Pricein Cycle

CRT
matrix
BI
passACGP S patience
GP S procrastination
GP S risktaking
GP S posrecip
GP S regrecip
GP S altruism
GP S trust
GP S subj math skills
Const.
Observations
R2

1st stage price
Last buyer First Buyer Originator-1.531-0.1130.676(2.039)(1.255)(1.092)
3.358∗
1.670
1.068(1.335)(1.980)(1.124)-1.047-1.293-0.254(5.948)(0.852)(5.783)-1.1570.015
3.010(2.442)(6.110)(7.302)-0.1850.828-0.868(1.776)(1.685)(1.360)1.711-1.326-2.142(1.776)(1.685)(1.360)-2.004
1.126
2.622(3.262)(0.744)(2.280)
1.311
1.955
4.247
(2.192)(3.256)(3.279)2.493-0.2381.430(1.340)(1.450)(2.560)-1.086
1.420-5.069∗∗(1.324)(2.001)(1.653)0.417-1.788-1.469(1.550)(2.439)(1.450)-0.797-0.2923.220∗∗∗(2.784)(2.180)(0.781)54.757** (18.530)
139
0.315

∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.

38that altruistic originators tend to accept lower Stage 1 prices. Although thealtruism of originators brings the price closer to the level implied by thetheoretical prediction, interpreting this to suggest altruism is leading to an
equilibrium outcome is not convincing.
Overall, we cannot identify any convincing obstacle to optimal behavior
in Stage 1 in Cycle among the cognitive abilities and other-regarding preferences. Rather, contrary to our speculation, we find that a high cognitive
ability in a certain player increases the deviation from the theoretical prediction, and the existence of other-regarding preferences in a certain player
reduces this deviation. Further and most importantly, we do not find any
significant effect of the ability for backward induction on the price. None of
the coefficients for BI in the regression result is significantly different from 0,
indicating that it does not play a substantial role in the price determinationin Stage 1, despite it being the critical premise of the theoretical prediction.

6.4

Risk-Taking Attitude and Patience

One concern is that the Stage 1 price remains high if the first buyer is lesswilling to take risk than the last buyer. Among the two buyers, buyersthat are less risk-tolerant could accept a high price in Stage 1 and securea certain amount of payoff. Such behavior could be a potential cause of
the deviation from the theoretical prediction. If this is the case, the buyerthat demonstrates a greater willingness to take risk tends to be the buyer
in Stage 2 (i.e., the last buyer). Moreover, the difference in prices between
Stages 1 and 2 tends to be large if the difference in the risk-taking attitudes
between the two buyers is also large.
To examine whether this is the case, we perform the following two analyses. First, we compare GP S risktaking between the last buyer and the first39

Table 9: Risk-Taking Attitude and Price Differences Between the Two Stages
Dependent Variable
ST 1.P rice − ST 2.P rice
−0.988(1.160)33.162∗∗∗(1.065)

Diff. of GP S risktaking
Const.
Observations
R2

168
0.0028∗p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.

buyer. The result is that the two variables are not statistically significantly
different (p − value = 0.261, t-test allowing for unequal variances), implyingthat the first buyer does not take less risks. Second, we regress the differencein prices between Stage 1 and 2 on the difference of GP S risktaking between
the buyers (last buyer’s price - first buyer’s price). Table 9 displays the regression result. Contrary to speculation above, we do not find a significant
correlation between the two variables (p − value = 0.433). Accordingly, we
cannot confirm that the difference in risk-taking attitudes between the twobuyers accounts for the high Stage 1 prices.
We also examine whether a similar story holds for patience. Of the twobuyers, the less-patient buyer could accept a higher price in Stage 1. First,
we compare the GP S patience of the two buyers, but do not identify asignificant difference between them (p − value = 0.224, t-test allowing forunequal variances). Second, we regress the difference in the prices between
Stage 1 and 2 on the difference of GP S patience between the two buyers.
Table 10 displays the regression result. As shown, we do not reveal any
significant correlation between the two variables (p − value = 0.174). Thus,40

Table 10: Patience and Price Differences Between the Two Stages
Dependent Variable
ST 1.P rice − ST 2.P riceDiff. of GP S patience

2.037(1.286)33.642∗∗∗(1.059)Const.
Observations
R2

167
0.0137∗p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.

we obtain no evidence that a difference in patience between the two buyers
accounts for the higher price in Stage 1.
Result 6: We do not observe clear and convincing relationships between
personal traits and experimental outcomes, except for the degree of
altruism being positively correlated with Stage 2 prices.

7

Conclusion

This study experimentally examines the trading of information goods within
networks. Information goods are copyable; hence, a buyer can become aresale competitor to existing sellers once the good is purchased and if resalechannels are available in the network. We examine whether competition
through reselling lowers the prices of the good in line with the theoreticalprediction.
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 com41

petition between the originator and the reseller in the network could lower
prices. According to the theoretical prediction, 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 resellingin their future transactions. In the other treatment, Tree, there is no cycle
path in the network and the resale of the good is therefore not possible. The
originator can then enjoy monopoly power and post higher prices.
In Experiment 1, we find that the prices observed in Cycle are inconsistent
with the theoretical prediction 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, theextent of this is very small in magnitude compared with the theoretical prediction. In addition, and again contrary to the theoretical prediction, theprices in the first transaction tend to be higher in Cycle than in Tree.
Furthermore, learning does not resolve the discrepancy between the theoretical prediction and the data in Cycle as the Stage 1 prices carry signsof further price increases according to the buyers’ bidding behavior. On thecontrary, in Tree, the bidding behavior suggests signs of further decreases inprices toward the level implied by the theoretical prediction.
As discussed in Section 4.4, the observed prices in Stage 1 of Cycle, although inconsistent with their theoretical prediction, are consistent with participants 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 Stage 2 prices fall.
Potential reasons for Stage 2 prices in Cycle remaining high include: (1)a lack of competition between the originator and the reseller, and (2) the
participants’ other-regarding preferences. For the latter, we find evidence42that the last buyers are willing to pay higher prices to the originator than
to the reseller in Stage 2. For the former, it is possible that the bargaining protocol we employed in our Experiment 1, namely, the Nash demand
game, softened the competitive pressure in Stage 2 in Cycle. To test thisconjecture, we conduct an additional experiment (Experiment 2) by employing a continuous double auction as the bargaining protocol. As expected,
the enhanced competition between the two sellers in Stage 2 of Cycle lowers
prices substantially. However, the observed prices are still higher than thetheoretical prediction.
Furthermore, the enhanced competition between the two buyers in Stage 1
raises prices in both Tree and Cycle. In Cycle, it raises the prices even above
the “pseudo-equilibrium price” implied by the mean observed price in Stage 2.
As a result, the Stage 1 prices in Cycle are not significantly different fromthose in Tree. This result is again inconsistent with the theoretical prediction.
Individual characteristics such as cognitive ability, willingness to take risks,and patience do not consistently explain our results. As for other-regarding
preferences, we find evidence that the altruism of the last buyers seems tokeep Stage 2 prices high.
Of course, it is possible that two players are just insufficient for competition to overcome the effect of other-regarding preferences. For example, in
Dufwenberg and Gneezy (2000), when the number of players is three or more,participants quickly learn to compete more aggressively in a Bertrand competition experiment. However, as we observed in Experiment 2, enhanced
competition can also result in overpricing during earlier stages. Therefore,
the overall impact of competition among more than two players on prices inthe early stages is not ex ante clear. Hence, conducting experiments with alarger number of players would be a fruitful avenue for future research.

43

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48

Online Appendix
I

Summary of the data

Table I.1 summarizes the sessions.
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

First Treatment
Cycle
Tree
Cycle
Tree
Tree
Cycle

We briefly summarize the data by overviewing the sample size, share of
successful trials, and the frequency of negotiations. The data contains 752
trials of three-person games, which consist of 2,077 rounds of negotiations in
total. Of the 752 trials, 623 trials (82.8%) were successful in that both buyers
obtained the good. Among the remaining 129 trials, no buyer obtained thegood in 57 trials, and only one buyer obtained the good in 72 trials. We referto 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 acrossTable I.2: 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

1

Table I.3: 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.

the two treatments. As displayed in Table I.2, the percentage of trials inwhich two whole transactions are successfully established for all three players is 82.2% and 83.5% in Tree and Cycle, respectively. The two values do notdiffer statistically significantly (p − value = 0.159 in Online Appendix I.2).
Similarly, the percentage of trials in which at least one transaction is done is
93.1% in Tree, which does not differ significantly from that in Cycle, whichis 91.8% (p − value = 0.343 in Online Appendix I.2). These results suggest that we do not need to be concerned with the unevenness of sample
failure across the two treatments due to sudden failure amid ongoing negotiations. A detailed discussion and statistical analysis are presented in Online
Appendix I.2.
Table I.3 presents summary statistics of the number of negotiations pertrial 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 Online Appendix I.3).
For the percentiles displayed in Table I.3, there is little difference up to
the 75th 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 75th percentile in Tree.
We might expect that the speed of learning about the optimal plays of the2

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 acrossthe treatments. Our analyses, reported in Online Appendix I.3, confirm thatthe number of negotiations decrease as our subjects gain experience in Cycle.
In Online Appendix I.3, we also compare the numbers of negotiations acrossStages 1 and 2, but we do not find a significant difference.

I.1

Order Effect

As the treatments are reverse ordered among our subjects by dividing themroughly 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(66 subjects starting from Tree, and 75 from Cycle) could be a source ofpotential 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 1 if the subject is assigned to the session thatstarts with Tree, otherwise 0. This variable captures the existence of an
overall order effect. Cycle is a dummy variable that takes a value of 1 if
the trial belongs to Cycle, otherwise 0. T reeF irst × Cycle is the cross termof T reeF irst and Cycle, whose significance would indicate the presence ofdistinct 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 I.4, with the resultsfor Stage 1 prices in the first and second columns and those for Stage 2 in
3

Table I.4: Order Effect in Prices
Dependent Variable
Price
Stage 1Model 1Model 2Model 1Model 2

−3.136(2.945)-−2.736(1.888)-49.532∗∗∗(0.845)−2.569(2.264)−0.311(1.061)−1.766∗(0.737)50.418∗∗∗(1.099)623
0.0217623
0.0324Cycle-

Const.

54.551∗∗∗(1.424)−2.339(2.661)−1.617∗(0.784)2.276∗∗∗(0.358)53.426∗∗∗(1.248)Observations
R2695
0.0297695
0.0387

T reeF irst
T reeF irst × Cycle

Stage 2-∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.

the third and fourth columns. Although the coefficient for the cross term
Cycle × T reeF irst is marginally significant (p − value = 0.094 < 0.1), any
coefficients associated with the term T reeF irst do not significantly differ
from 0 in both Stages 1 and 2 for both Models 1 and 2 with a significancelevel of 0.05. Thus, the data suggests some order effects may exist; however,
the evidence for this suggestion is not statistically meaningful.

I.2

Likelihood of Successful Trials

This subsection documents the statistical comparison of the likelihood of
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 a successful trial on the four explanatory variables4(i.e., Cycle, Latter, Cycle × Latter, and a constant). Cycle is a dummy
variable that takes a value of 1 if the trial belongs to Cycle, otherwise 0.
Latter is a dummy variable that takes a value of 1 if the trial lies in the latter
half of each treatment (i.e., 5th to 8th trials), otherwise 0. This captures theoverall learning effects across the treatments (unless a negatively significant
treatment-specific learning effect exists in Cycle). Cycle × Latter is the crossterm of Cycle and Latter, and this captures any additional impact on thelearning effect specifically appearing in Cycle. The statistical significance ofthe variable indicates that the learning effects differ across the treatments(i.e., the existence of treatment-specific learning effects). The learning effectin Tree is captured by the coefficient of the term Latter, and that in Cycle by
the sum of the coefficients of the terms Latter and Cycle × Latter. We also
report the result of a regression in which only two regressors are included(i.e., Cycle and a constant) to gauge the treatment effect over all trials.
The regression results are presented in Table I.5. The results for the wholetransaction 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 0 (p − value = 0.159), indicating that the likelihood of success 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 notdiffer statistically significantly from 0 (p − value = 0.195), indicating that atreatment-specific learning effect does not exist. Indeed, the results of theinsignificant coefficient of Latter (p−value = 0.569) and the insignificant sumof the coefficients of Latter and Cycle × Latter (F-test, p − value = 0.269)
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 third5

Table I.5: Likelihood of Successful Trials
Dependent Variable
Success
Whole transactions
Stage 1 transaction
Model 1Model 2Model 1Model 20.013
(0.008)-−0.013(0.013)-0.931∗∗∗(0.009)−0.016(0.021)
0.005(0.035)0.000(0.017)0.931∗∗∗(0.014)752
0.0006752
0.0007

Latter-Const.

0.822∗∗∗(0.024)−0.011(0.016)0.048(0.032)−0.027(0.044)0.835∗∗∗(0.020)Observations
R2

752
0.0003752
0.0013

Cycle
Cycle × Latter-∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.

column does not statistically significantly differ from 0 (p − value = 0.343).
The coefficient of Cycle × Latter in Model 2 in the fourth column does notdiffer statistically significantly from 0 (p − value = 0.885). 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 = 0.877).
These results suggest that the likelihood of a successful trial does not differ
between 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.

6

I.3

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 like the analysis for the likelihoodof successful trials in Online Appendix I.2, 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 I.6 displays the regression results. As shown in the first and thirdcolumns, the coefficients for Cycle differ statistically significantly from 0
on the negative side, indicating that the overall number of negotiations issmaller in Cycle (p − value < 0.01 for both), as first suggested in Table I.3
in Section I.
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 marginally significantly different from 0 (0.414, p − value =0.096 < 0.1). However, the existence of a learning effect in Cycle is lessclear as the sum of the coefficients for Latter and Cycle × Latter is near
0 (F-test, p − value = 0.657), which implies less possibility that a learning
effect exists in Cycle. Indeed, the coefficient for Cycle × Latter is significantly negative (−0.473, p − value = 0.037 < 0.05). Similarly for the firsttransaction basis, we identify a significant treatment-specific learning effectas the coefficient for Cycle × Latter in the fourth column has a significant
7

Table I.6: Number of Negotiations
Dependent Variable
Number of Negotiations
Whole transactions
Stage 1 transaction
Model 1Model 2Model 1Model 2−0.487∗∗∗(0.101)-−0.255∗∗∗(0.061)-

1.783∗∗∗(0.062)−0.094(0.077)−0.321∗∗(0.095)0.155(0.103)1.707∗∗∗(0.070)623
0.0146623
0.0204Latter-Const.

3.579∗∗∗(0.114)−0.253(0.132)−0.473∗∗(0.168)0.414∗(0.202)
3.376∗∗∗(0.092)

Observations
R2

623
0.0173623
0.0237

Cycle
Cycle × Latter-∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.
Limited to trials with whole transactions among the three players.

negative value (−0.321, p − value = 0.020 < 0.05). However, the coefficientfor Latter is not significant (p − value = 0.193), along with the sum of thecoefficients for Latter and Cycle × Latter (p − value = 0.246), suggesting
the presence of learning effects themselves is unclear.
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 1 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 of a regression

8

Table I.7: Comparison of the Number of Negotiations across Stages
Dependent Variable
Number of Negotiations
Tree
Cycle
Model 1Model 2Model 1Model 20.129
(0.093)-0.035(0.095)-

1.529∗∗∗(0.056)−0.103(0.075)0.273(0.159)−0.166∗∗(0.052)
1.613∗∗∗(0.061)628
0.0003628
0.0046

Latter-Const.

1.783∗∗∗(0.062)−0.038(0.077)0.104(0.176)0.155(0.103)1.707∗∗∗(0.070)Observations
R2

618
0.0000618
0.0069SecondST
SecondST × Latter-∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.
Limited to trials with whole transactions among the three players.

including only two regressors, SecondST and a constant.
The regression results are presented in Table I.7. 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 = 0.727) nor are the coefficients for the
cross term SecondST × Latter (p − value = 0.146) and SecondST (p −value = 0.227). These results suggest that the numbers of negotiations do
not change significantly across the stages, despite the considerable differencein negotiation structure in Cycle.

9II

Bid and Ask

We obtained little evidence of subjects learning to play according to thetheoretical prediction based on our analysis of prices. However, as prices are
determined jointly by bids and asks, this may mask the effect of learning.
We thus turn our attention to bids and asks separately.

II.1

First Bids and Asks in Stage 1

We particularly focus on the bids and asks proposed in the first negotiationsof each trial because they carry uncontaminated information. The first bids
and asks are proposed before the player observes any behavior of the otherplayers in the trial29 . Thus, they are considered to directly reflect the player’s
initial prospects for the prices in the trial.30 Here we focus our analysis on
the first bids and asks in Stage 1.
Figure II.1 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-effects model in which thesubject-level individual heterogeneity is controlled for by individual fixed effects. In addition, we employ cluster-robust (subject-level) standard errors
29

Recall that players are randomly rematched into groups of three at the beginning ofeach trial, but while maintaining their roles.
30
One concern is that first bids and asks also reflect the individual heterogeneity ofplayers, such as negotiation style. For this reason, we control for individual differences in
the following regression analysis.

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

Figure II.1: Dynamics of the First Bids and Asksfor the hypothesis tests. As before, we also report the result of a regression
including only two regressors: Cycle and a constant.
Table II.8 presents the regression results for the first bids and asks inStage 1. The first column in Table II.8 indicates that the first bids in Tree arelarger than in Cycle by 2.302 (p−value = 0.024). The second column displays
the regression result to address the presence of learning effects. The value ofthe coefficient of Latter is −3.289, which is significantly different from 0 (p −value < 0.01), indicating that the first bids in Tree have a strong downward
trend as observed in Figure II.1. For Cycle, the value of the coefficient of thecross term Cycle × Latter is 4.227, which is significantly different from 0 (p −value < 0.01). This indicates the presence of a treatment-specific learning
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. Although this11

Table II.8: 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 (subject level)in parentheses.

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 astatistically significant positive upward trend in Cycle, as shown in Figure II.1
(p − value = 0.038, Table II.9). The first bids exhibit treatment-specificlearning in opposite directions across the two treatments.
Unlike the first bids, we do not observe any treatment-specific learning
for the first asks. The third column in Table II.8 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.
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
12Table II.9: 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 (subject level)in parentheses.

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 II.2. 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 on
the same four explanatory variables to the earlier regression analysis of prices(i.e., Cycle, Latter, Cycle × Latter, and a constant). Table II.10 presents
the regression results. In the second column, we observe a treatment-specificlearning effect as the coefficient of the cross term Cycle × Latter is 0.191 andis significant (p−value = 0.023). According to these results, the first negotiations in Cycle are more likely to be successful in later trials by approximately
19% than in Tree.
The abovementioned findings consistently suggest that buyers become13Red: Cycle. Blue: Tree

Figure II.2: Share of Successful Negotiations in the First Trials
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.
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 learned gradually, 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 seem

14

Table II.10: Likelihood of Success in the First Negotiations
Dependent Variable
Success
Model 1Model 20.064∗∗(0.024)-Latter-Const.

0.527∗∗∗(0.029)−0.032(0.029)0.191∗∗(0.059)−0.096∗(0.043)0.574∗∗∗(0.036)

Observations
R2752
0.0041752
0.0134Cycle
Cycle × Latter∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01. Cluster-robust
standard errors (session level) in parentheses.

to 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.

II.2

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, the next question would be whether the sellers competingin Stage 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 first
asks and the first bids in Stage 2. The regression models are identical to those15

Table II.11: 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 (subject level)in parentheses.

used 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 II.11. 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).31 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.
However, unlike the case of the first bids in Stage 1, we do not reveal
learning effects for the first asks in Stage 2. The fourth column of Table II.11
shows that the coefficient of the term Latter is not significantly different from
31

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

16

0 (p − value = 0.770). The coefficient of the cross term Cycle × Latter isalso not significant (p − value = 0.619), nor is the sum of the coefficients ofCycle × 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 asksin 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 transactions in Stage 2. It isthen 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, like 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 shownin the first column of Table II.11, 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 that arecompeting only feel some urge to complete, although the reason behind it
remains puzzling.

II.2.1First Asks in Stage 2

We observe that the first asks in Stage 2 differ significantly across the two
experimental treatments. We could then consider the possibility that thisdifference arises because of the distinct roles of the sellers initially assignedin 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

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

Figure II.3: First Asks in the Second Stages
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 II.3. As displayed, the asks of originators
are smaller than those of resellers in the early trials; they then converge toan almost identical level.
However, we do not statistically confirm a significant difference between
them even in the early trials. Table II.12 presents regression results to address
the difference of the Stage 2 first asks between the two sellers. In Model 1 (seethe first column), the coefficient for Originator is not significantly different
from 0 (p − value = 0.343), indicating that the overall mean does not differ
between the two types of sellers. Even for the early trials, the coefficient for
Originator in Model 2 (see the second column), which captures the differencein the early trials in the regression model specification, is only marginally18

Table II.12: 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 (subject level) in parentheses.

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.

19

III

Case for Risk-averse Players

As in Section 4.4, the observed Stage 1 price is lower than the pseudoequilibrium Stage 1 price by 10.69. Here we show that this difference can be
explained by the players’ risk aversion.
To address this, we modify Eq. (4) 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
(III.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.,1x1−γ ). Substituting the values for the observed prices into pC
u(x) = 1−γ
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 (e.g., Abdulkadri and Langemeier,2000).

20

IV

Theoretical Analyses of Experiment 2

Here we present the theoretical predictions for Experiment 2.

IV.1

Stage 2 in Cycle

There are two sellers, Player 1 and the player who won the good at Stage 1,
who are denoted as s1 and s2 , respectively.
T
The strategies for the sellers and the buyer are pC
2si ∈ [0, 100], p2b ∈ [0, 100](i ∈ [1, 2]). Their payoff functions are

xC
2si =





100 − pC

2






 1 {100 − pC }
2

C
C
C
if pC
2b ≥ p2si and p2si < p2sj (j 6= i)
C
C
C
if pC
2b ≥ p2si and p2si = p2sj (j 6= i)

2

C
C
if pC
2b < min{p2si , p2sj }(j 6= i)




δxC

2si






0

xC
2b =

C
C
if pC
2sj < p2b < p2si (j 6= i)100 − pC

C
C
if pC
2b ≥ min{p2s1 , p2s2 }



δxC
2b

C
C
if pC
2b < min{p2s1 , p2s2 }2

The Bertrand competition among sellers determines the price to satisfy
CCC
pC
2 = x2si = 0. Thus, x2s1 = x2s2 = 0, x2b = 100, and p2 = 0.

IV.2

Stage 1 in Cycle

There are two buyers, Players 2 and 3, who are denoted as b1 and b2 , respectively. The strategies for the seller and the buyers are pC
2s ∈ [0, 100],21

pC
2bi ∈ [0, 100] (i ∈ [1, 2]). Their payoff functions are:

xC
1s =

xC
1bi =




pC + 1 δxCCCif max{pC
1b1 , p1b2 } ≥ p1s



δxC
1s

C
C
if max{pC
1b1 , p1b2 } < p1s

1

2

2s




1
C

100 − pC
1 + 2 δx2s






 1 {100 − pC + 1 δxC } + 1 δxC
2

1

2s

2

2

C
C
C
if pC
1bi ≥ p1s and p1bi ≥ p1bj (j 6= i)

2b



C


δx2b





δxC
1bi

C
C
C
if pC
1bi ≥ p1s and p1bi = p1bj (j 6= i)
C
C
if pC
1bi < p1s ≤ p1bj
CC
if max{pC
1bi , p1bj } < p1s

The Bertrand competition among buyers determines the price to satisfy
C
C
C
C
xC
1bi = δx2b = 100δ. Thus, x1s = 100(1 − δ), x1b1 = x1b2 = 100δ, andpC
1 = 100(1 − δ).

IV.3

Stage 2 in Tree

The strategies for the seller and the buyer are pT2s ∈ [0, 100], pT2b ∈ [0, 100].
Their payoff functions are:xT2s =

xT2b =




p T
2

if pT2b ≥ pT2sδxT2sotherwise
100 − pT

if pT2b ≥ pT2sδxT2botherwise2

22

where pT2 =T
pT
2b +p2s.
2Every strategy (pT2b , pT2s ) satisfying 100 − pT2 ≥ δxT2b ,pT2 ≥ δxT2s is an equilibrium. Their equilibrium payoffs are, for any α ∈ (0, 1)
xT2s =δxT2s + α{100 − (δxT2b + δxT2s )}xT2b =δxT2b + (1 − α){100 − (δxT2b + δxT2s )}Thus, xT2s = 100α, xT2b = 100(1 − α), pT2 = 100α.

IV.4

Stage 1 in Tree

There are two buyers, Players 2 and 3, who are denoted as b1 and b2 , respectively. The strategies for the seller and the buyers arepT1s ∈ [0, 100],
pT1bi ∈ [0, 100] (i ∈ [1, 2]). Their payoff functions are:xT1s =

xT1bi =

pT + δxT

if max{pT1b1 , pT1b2 } ≥ pT1sδxT1sif max{pT1b1 , pT1b2 } < pT1s

2s

1





100 − pT1







 1 {100 − pT1 } + 1 δxT2b
2




δxT2b





 T

δx1b
i

2

if pT1bi ≥ pT1s and pT1bi ≥ pT1bj (j 6= i)
if pT1bi ≥ pT1s and pT1bi = pT1bj (j 6= i)
if pT1bi < pT1s ≤ pT1bj (j 6= i)if max{pT1b1 , pT1b2 } < pT1s

The Bertrand competition among buyers determines the price to satisfy
xT1bi = δxT2b = δ100(1 − α). Thus, xT1s = 100{(1 − δ) + α(1 + δ)}, x1b1 =x1b2 = δ100(1 − α), pT1 = 100{1 − (1 − α)δ}.

23

IV.5

Equilibrium Price

The equilibrium prices are as follows:pC
1 =100(1 − δ)(IV.1)

pT1 =100(1 − (1 − α)δ)(IV.2)pC
2 =0(IV.3)

pT2 =100α(IV.4)TC
In our benchmark case (δ = 0.9 and α = 0.5), pC
1 = 10, p1 = 55, p2 = 0 and

pT2 = 50.

24

V

Summary of the Experiment 2 data

Table V.1 reports the sessions of Experiment 2
Table V.1: Sessions for Additional Experiment (Experiment 2)
Subject
27
27
24
27
24
27

February 27, 2023 (morning)
February 27, 2023 (afternoon)
February 28, 2023 (morning)
February 28, 2023 (afternoon)
March 2, 2023 (morning)
March 2, 2023 (afternoon)First Treatment
Tree
Cycle
Cycle
Tree
Tree
Cycle

In this section, we present further details of the data, which contains 414
trials of three-person games,32 which consists of 1,188 rounds of negotiations
in total.

V.1

Likelihood of successful trials

Among the 414 trials, 329 trials (79.5%) were successful for whole transactions, and 389 trials (94.0%) were successful for at least Stage 1 transactions. The likelihood of successful trials across the two treatments is presented in Table V.2. The percentage of successful trials in Tree and Cycle is72.8% and 86.1%, respectively. The two values are insignificantly different
32

Two trials are excluded from data analysis as at least one subject in both trials
disconnected due to Internet trouble.

Table V.2: Share of Successful Trials for Experiment 2

Treatment

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

Tree
Cycle

0.728
0.861

0.918
0.962

25

Table V.3: Likelihood of Successful Trials for Experiment 2
Dependent Variable
Success
Whole transactions
Stage 1 transaction
Cycle

Model 1Model 2Model 1Model 20.132
(0.074)-0.044(0.037)-0.917∗∗∗(0.029)0.050(0.028)−0.011(0.035)0.011(0.041)
0.912∗∗∗(0.032)414
0.0086414
0.0088Latter-Const.

0.728∗∗∗(0.059)0.140(0.089)−0.015(0.049)−0.014(0.048)0.735∗∗∗(0.074)

Observations
R2414
0.0269414
0.0277

Cycle × Latter-∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.

(p − value = 0.135 in Column 1 in Table V.3). Similarly, the percentage ofpartially successful trials is 91.8%, which does not differ significantly from
96.2% in Cycle (p − value = 0.291 in Column 3 in Table V.3). We also examine learning effects with the identical analysis employed in Experiment 1(Table I.5); however, we do not confirm any learning effect as presented
in Columns 2 and 4 in Table V.3. Both coefficients of Latter are not significantly different from 0 (p − value = 0.780 for whole transactions andp − value = 0.793 for Stage 1 transactions) as well as the sums of the coefficients of Latter and Cycle × Latter (F-test, p − value = 0.519 for wholetransactions, and F-test, p − value = 1.000 for Stage 1 transactions).

26

Table V.4: Number of Negotiations per Trial for Experiment 2

Treatment

Mean

St. Dev.

Pctl(25)

MedianPctl(75)

Pctl(95)

Max

Tree
Cycle

3.620
2.581

2.081
1.189

2
2

3
2

4
3

7
5

20
12

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

V.2

Number of negotiations

The number of negotiations per trial for each treatment is presented in Table V.4. The average number of negotiations in Tree is 3.620, whereas that in
Cycle is 2.581. These are statistically significantly different (p−value = 0.018
in Table V.5). As observed in Table V.4, the number of negotiations tends tobe larger in Tree. We also examine learning effects with the identical analysis as performed in Table I.6; however, we do not confirm any statisticallymeaningful learning effect in the results presented in Table V.5. In Tree, bothcoefficients of Latter are not significantly different from 0 (p − value = 0.267
for whole transactions in Column 2 and p − value = 0.166 for Stage 1 transaction in Column 4). In Cycle, we find only marginally significant learning
effects in the sums of the coefficients of Latter and Cycle × Latter for bothof whole transactions and Stage 1 transactions (p − value = 0.084 in Column
2 and p − value = 0.060 in Column 4).
Across stages, the number of negotiations is larger in Stage 2 than that inStage 1 in Tree as indicated by the significant positive coefficient of SecondST(0.86, p − value < 0.01) in Column 1 in Table V.6 where we performed
identical analysis as that in Table I.7. Contrarily, the number could besmaller in Stage 2 than in Stage 1 in Cycle, although the difference is only
marginally significant (p − value = 0.054 in Column 3). As for learning

27

Table V.5: Number of Negotiations for Experiment 2
Dependent Variable
Number of Negotiations
Whole transactions
Stage 1 transaction
Model 1Model 2Model 1Model 2

−1.039∗∗(0.298)-0.073(0.191)-1.38∗∗∗(0.096)

0.039(0.173)0.072(0.147)0.2(0.123)
1.28∗∗∗(0.101)329
0.0015329
0.0181

Latter-Const.

3.62∗∗∗(0.224)−0.916∗∗(0.246)−0.242(0.303)0.44(0.352)
3.4∗∗∗(0.163)Observations
R2329
0.0894329
0.0986

Cycle
Cycle × Latter-∗

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.
Limited to trials with whole transactions among the three players.

effects, we do not observe any significant learning effect in Tree (p − value =0.166 for the coefficient of Latter, and F-test, p − value = 0.464 for the sumof the coefficients of Latter and SecondST × Latter in Column 2). In the
result of Cycle presented in Column 4, we do not find significant learning
effect in the sum of the coefficients of Latter and SecondST × Latter (Ftest, p − value = 0.393), however, we find only marginally significant effectin Latter (p − value = 0.060).

V.3

Order Effect

As the treatment order is counterbalanced among our subjects by dividingthem in exactly half, the order effects should not appear at the aggregate
level. However, documenting the order effects in our data would be mean-

28

Table V.6: Comparison of the Number of Negotiations across Stages forExperiment 2
Dependent Variable
Number of Negotiations
Tree
Cycle
Model 1Model 2Model 1Model 20.86∗∗∗(0.087)-−0.324∗(0.129)-1.453∗∗∗(0.131)−0.154(0.084)−0.346∗(0.171)
0.272∗(0.112)
1.32∗∗∗(0.100)358
0.0362358
0.0499Latter-Const.

1.38∗∗∗(0.096)0.84∗∗∗(0.096)0.04(0.299)0.2(0.123)
1.28∗∗∗(0.101)

Observations
R2300
0.0751300
0.0801

SecondST
SecondST × Latter-∗
p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.
Limited to trials with whole transactions among the three players.

ingful. We perform an identical regression analysis as that in Experiment 1(Table I.4) and the results are presented in Table V.7. None of the coefficients associated with T reeF irst are statistically significant. Although thecoefficient of T reeF irst × Latter in Column 4 is a large negative value, it
is only marginally significant (F-test, p − value = 0.073). Thus, while order effects might exist in our data, they do not appear to be statisticallymeaningful.

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Table V.7: Order Effect in Prices for Experiment 2
Dependent Variable
Price
Stage 1Model 1Model 2Model 1Model 2

−3.481(2.623)-3.015(2.153)-34.548∗∗∗(0.594)7.153(4.716)−9.612∗(4.236)−8.887∗∗∗(0.439)39.766∗∗∗(0.939)329
0.0070329
0.1735

Cycle-

Const.

64.146∗∗∗(2.094)−2.244(3.771)−2.356(2.431)1.906(2.183)63.133∗∗∗(3.174)

Observations
R2

389
0.0148389
0.0172T reeF irst
T reeF irst × Cycle

Stage 2∗-

p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.
Cluster-robust standard errors (session level) in parentheses.

30