1. Gönül Doğan, Marcel van Assen, Jan Potters Tilburg University
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

2. 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
Broadly speaking, a “link” is what makes possible a particular bilateral

3. 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?

4. 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

5. 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

6. 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

7. 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
Standard predictions: assuming selfish preferences , full rationality, and (subgame perfect) equilibrum

8. Standard predictions Equilibrium predictions for link formation
Link cost 0: triad
Link cost 40: dyad
160-40
80-40

9. Hypotheses of standard model
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

10. 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 FS -
equity

11. 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 Euros

12. Experimental design

13. 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
p = .001

14. 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)
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

15. 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
Pseudo R² = 0.142, Wald ² = 56.6 p< .001

16. 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)
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 !

17. 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
Pseudo R² = 0.142, Wald ² = 56.6 p< .001

18. 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
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
.007

19. 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

20. 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
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

21. 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

23. 1. Effect of cost on number of links

24. 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

25. 1. Effect of cost on number of links

26. 3a. Effect of link costs on seller offers

27. 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