The effect of link cost on the
formation and outcome of buyer-seller
dyads and triads
Gönül Doğan, Marcel van Assen, Jan Potters
Tilburg University
1
Introduction


Importance of links
 Often agents can exchange only if they establish a
relationship or link between them
 labor markets, housing markets, procurement
The set of links (“network”) may exert a strong
influence on the outcome
 It affects the bargaining power of potential trading
partners (e.g., Corominas-Bosch, 2004)
 1 seller – 1 buyer versus 1 seller – 2 buyers
2
Introduction

This raises two questions
 Which links do actually form and how is this
affected by the costs of linking?
 E.g., do linking costs prevent the occurrence of
unequal, competitive networks?
 Are the outcomes of bargaining affected by the
linking costs (conditional on the network)?
 E.g., do fairness considerations interact with the
linking costs?
3
Introduction

We use experiments to address these questions
 Focus on the simplest, non-trivial seller-buyer
networks: dyads and triads
 Link formation
 Bargaining
 Two treatments: zero vs positive link costs
 Main results
 link costs reduce the occurrence of triads
 link costs have an direct impact on the bargaining
outcomes
4
Related experimental literature


Link formation
 Falk and Kosfeld (2003), Deck and Johnson
(2004), Callander and Plott (2005), Goeree, Riedl
and Ule (2005), Berninghaus, Ehrhart, Ott, and
Vogt (2007)
 Do not have endogenous interaction over the
network
Effect of bargaining power
 Roth, (1991), Güth, Marchand, and Rulliere
(1997), Grosskopf (2003), Fishbacher, Fong and
Fehr (2003), Charness, Corominas-Bosch, and
Frechette (2007)
 Do not have endogenous linking
5
The game



One “seller” and two “buyers”
Stage 1: Link formation
 Seller and buyers offer links simultaneously
 Links are bilateral
 A link is necessary for trade
Stage 2: Bargaining
 Seller can form agreement with one buyer only
 3 round of alternating offers bargaining with a
shrinking pie: from 240 to 160 to 80
6
Standard predictions

SPE predictions for bargaining
 0-link network; everyone gets 0
 1-link network: seller offers 80 points to linked
buyer; linked buyer accepts
 2-link network: seller offers 0 points to buyers;
buyers accept
(0)
seller
buyer 1
(0)
buyer 2
(0)
(160)
seller
buyer 1
(80)
(240)
seller
buyer 2
(0)
buyer 1
(0)
buyer 2
(0)
7
Standard predictions

Equilibrium predictions for link
formation
 Link cost 0: triad
(240)
seller
buyer 1
(0)

buyer 2
(0)
(120)
seller
Link cost 40: dyad
80-40
buyer 1
(40)
160-40
buyer 2
(0)
8
Hypotheses of standard model
1.
2.
3.
4.
Link cost decreases the number of links
Seller’s offer is higher in dyad than in triad (both
with link cost 0 and link cost 40)
Seller’s offer and buyers’ acceptance thresholds are
independent of link cost (conditional on being in a
dyad or triad)
Buyer is better off and seller is worse off with link
cost 40 than link cost 0
9
Alternatives for hypothesis 3


Social preferences (Fehr Schmidt, 1999)
a. Link cost decreases seller offer in dyad
b. Link cost has no effect in triad
Equity theory (Homans, Selten)
a. Link cost has no effect in dyad
b. Link cost decreases seller offer in triad
Effect of link cost on seller offer
1 link
2 links
Standard
0
0
FS
-
0
equity
0
10
Experimental design








Experiment at CentERLab, using z-Tree
105 student subjects, assigned to 35 groups of three
Random but fixed assignment of roles
30 periods with fixed groups
Full information feedback about choices and payoffs
Two treatments: Cost 0 (16 groups), Cost 40 (19
groups)
Lasted between 1:30 to 2:30 hours
Average earnings 18.60 Euros
11
Experimental design
12
1. Effect of cost on number of links

Cost significantly decreases the number of links
Frequency distribution of number of links (%)
0 links
1 link
2 links
Average # links
Cost 0
0.8
30.2
69.0
1.68
Cost 40
1.8
76.8
21.4
1.20
p
.17
<.001
<.001
p = .001
13
2. Effect of number of links on seller
offers
 First round offers by seller are significantly higher in
dyad than in triad
 both for Cost 0 and Cost 40
Average offer per round
First
Second
Third
1 link
2 links
p (first)
1 link
2 links
1 link
2 links
Cost 0
75.60
65.13
<.001
66.96
84.80
23.60
11.25
Cost 40
95.15
60.41
.001
59.89
75.18
26.49
20.00
p
.023
.809
.245
.414
.633
.800
14
2b. Effect of links on buyer acceptances

Buyers accept more offers with 2 links than with 1
link.
Probability of acceptance
Coefficient
p
Constant
-1.21
.008
Offer
0.04
.000
2-Links
0.82
.041
Link cost 40
-0.22
.586
Link cost  2-links
-0.38
.440
Period
.033
.008
Pseudo R² = 0.142, Wald ² = 56.6 p< .001
15
3a. Effect of link cost on seller offers

First round offers are
 significantly higher with link cost in a dyad
 insignificantly lower with link cost in a triad
Average offer per round
First
Second
Third
1 link
2 links
p (first)
1 link
2 links
1 link
2 links
Cost 0
75.60
65.13
<.001
66.96
84.80
23.60
11.25
Cost 40
95.15
60.41
.001
59.89
75.18
26.49
20.00
p
.023
.809
.245
.414
.633
.800

This rejects standard theory, but also inequality
aversion and equity theory !
16
3b. Effect of link cost on buyers’
acceptance
 Costs do not significantly effect probability of
acceptance
Probability of acceptance
Coefficient
p
Constant
-1.21
.008
Offer
0.04
.000
2-Links
0.82
.041
Link cost 40
-0.22
.586
Link cost  2-links
-0.38
.440
Period
.033
.008
Pseudo R² = 0.142, Wald ² = 56.6 p< .001
17
4. Effect of link cost on net payoffs
Seller is significantly worse off with link cost 40
 in line with prediction
Buyer is significantly worse off with link cost 40
 contrary to prediction


Average net payoffs per period
Seller
Buyers
average
1 link
2 links
average
1 link 2 links
Cost 0
151.5
113.6
165.0
34.6
37.0
33.3
Cost 40
82.1
80.1
75.9
18.1
28.0
-7.2
p
<.001
.002
<.001
<.001
.007
<.001
18
Discussion


Why do buyers not (try to) coordinate on 1-link
network when there are link costs?
Why do link costs increase offers in 1-link network?
And why not in 2-link network?

Loss aversion

Quantal Response

Reference point

Bolton Ockenfels
19
Conclusion




Linking cost reduce the number links

as predicted
The ‘competiveness’ of the network (triad versus
dyad) exerts a strong influence on bargaining

seller reduces offers; buyers accept more

as predicted
Link costs influence bargaining outcomes directly !

seller offers are higher in dyad but not in triad

contrary to prediction
Buyers do not benefit from link costs

contrary to prediction
20
Conclusion

General implication
 Interaction over a network cannot simply be
taken as given when studying the effect of linking
costs on the formation of the network
21
22
1. Effect of cost on number of links
Average link offer
1,00
0,95
0,90
0,85
Cost-0 Buyers
0,80
Cost-0 Seller
0,75
Cost-40 Buyers
0,70
Cost-40 Seller
0,65
0,60
0,55
0,50
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29
Period
23
Effect of cost on the number of links

Seller significantly reduces link offers with linking
costs, buyers do not.
Average link offers per period
seller
buyers
Cost 0
0.87
0.94
Cost 40
0.61
0.97
p
< .001
.485
24
1. Effect of cost on number of links
Average number of links
2
1,8
1,6
Cost 0
Cost 40
1,4
1,2
1
1
5
10
15
20
25
30
period
25
3a. Effect of link costs on seller offers
Average First Round Seller Offer
100
95
90
85
80
75
70
65
60
55
50
Cost-0 One Link
Cost-40 One Link
Cost-0 Tw o Links
Cost-40 Tw o Links
2
5
8
11
14
17
20
23
26
29
Period
26
Results on bargaining rounds

Cost significantly delays agreement when two links.
Percentage of acceptances in the first round
1 link
2 links
Cost 0
0.58
0.93
Cost 40
0.78
0.79
p
.175
.015
27