Double Coordination in Small
Groups
Luigi Mittone, Matteo Ploner, Ivan Soraperra
Computable and Experimental Economics Laboratory –
University of Trento, Italy
IAREP/SABE - World Meeting 2008
Roma 4 September 2008
Motivations and Related
Literature (1)


Coordination has been studied exclusively in
single groups (BoS, WLG, Minimum Game,
etc.).
Many interesting situations in which two
groups of people must coordinate their
actions on two levels:
• two groups of stakeholders in a firm,
• two departments of the same firm,
• consumers and producers of goods with
network externalities, etc.
Motivations and Related
Literature (2)
A crossroad between two streams of
literature: coordination failures and
network externalities
 Network externalities considered
within the problem of introducing a
new product
 Coordination failures in large groups:
the weak link coordination game

Technology Adoption and
Network Externalities
 Katz
and Shapiro (AmEcRew 1985,
JourPolEc 1986)
 Liebowitz and Margolis (JourEcPersp
1994)
Katz and Shapiro (1986)
p.822-823
Katz and Shapiro (1986)
Network Externalities



Network consumption externalities require that
at least one specific attribute, using the
Lancaster’s Theory of Consumption
terminology, is almost perfectly homogeneous
Supply side competition is therefore restricted
to the other attributes (first of all price)
The common attribute works as an entry barrier
for the newcomers.
Network Externalities



Network externalities as a public good
Need for coordination to produce a Pareto
efficient solution.
The specific case when the consumers must
coordinate themselves to switch from a
traditional product (already characterized by
network externalities) to an innovative one
(which we assume can produce even stronger
positive externalities due to the use of a more
innovative technology)
Coordination in
Experimental Games
WEBER (AmEcRew 2006)
 BORNSTEIN et al (Games&EcBehav 2002)
 COOPER et al (AmEcRew 1990)

COOPER et al (1990) p. 218
We study a class of symmetric,
simultaneous move, complete
information games called
coordination games. This term refers
to games which exhibit multiple Nash
equilibria which are Pareto-rankable.'
That is, all players are better off in
one equilibrium relative to another
yet may be unable to explicitly coordi-
nate their strategies to
achieve the preferred
outcome. When this
occurs, a coordination
failure arises.
WEBER (2006)
BORNSTEIN et al (2002)
Weak link coordination game
 Coordination failure in large groups
(experimental)
 Competition between groups
 Progressive increase in the size of the
group

Weak Link Coordination Games
Player’s
choice
Minimum choice of all players
7
6
5
4
3
2
1
7
.90 .70
.50
.30
.10 -.10 -.30
6
.80
.60
.40
.20
.00 -.20
.70
.50
.30
.10 -.10
.60
.40
.20
.00
.50
.30
.10
.40
.20
5
4
3
2
1
Source: Weber, 2006
.30
Two Groups, Two Goods,
Double Coordination
One group are the “consumers”
 One group are the “producers”
 Positive network externalities for both
groups
 Multiple Nash equilibria


Not a weak link game
One innovative good
 One traditional good

Interaction Structure
 Coordination
2
Game
Pareto-ranked equilibria
 Two
actions
 T(raditional
good)
 I(nnovative good)
Interaction Structure

Groups of 10
5 players role A
 5 players role B


30 repetitions with feedback


1 repetition rewarded (random pick)
2 experimental treatments
Baseline (two different payoffs structures)
 Treatment (two different payoffs
structures)

Baseline(1)



Symmetric game
2 Nash equilibria
 All players choose I; All players choose T
Dominant strategy is to choose what the majority of the members
of the other group chooses (independently from one`s own
group)
Treatment (1)




Asymmetric game
2 Nash equilibria
 All players choose I; All players choose T
Dominant strategy for role A is to choose what the majority of
role B chooses
Dominant strategy for role B is to choose what the majority of
role B chooses
Baseline(2)

Same properties of Baseline 1 but


Focal point in the NW corner
Weaker risk perception for the I move
Treatment (2)
Summary

Baseline


Treatment


Players A (e.g., consumers) and Players B
(e.g., producers) must build a belief on the
preferred choice of the other group
Players B (e.g., producers) have a greater
power in determining the equilibrium
In setting (2) option I is less risky than in (1)
setting
Predictions

Baseline


Due to the simmetry of the incentives across groups
and to the “balanced” payoff structure of the two
matrices we expect a fast convergence towards one
of the two equilibria.
Treatment

Players B can pull towards one of the two goods
• If no coordination at the beginning then the choice of majority
of Bs will attract the other players in the game

In (2) more global coordination on I,I than in (1)
Procedures and Participants

60 Participants


Computerized experiment


Web-based
Average earnings


Students of the University of Trento, Italy
$$$
Time required

About 1h 30min
Results Payoffs1
Number of players choosing I - Base1 (Gr 5 & 6)
Number of players choosing I - Base1 (Gr 1 & 2)
5
4
4
4
B
7
5
3
1
9
7
9
r2
r2
r2
r2
r2
r1
5
Round
Number of players choosing I - Treat1 (Gr 5 & 6)
Number of players choosing I - Treat1 (Gr 3 & 4)
Number of players choosing I - Treat1 (Gr 3 & 4)
r1
3
Round
r1
r1
9
7
r2
5
r2
3
r2
9
1
r2
r2
7
r1
3
1
5
r1
r1
r1
r9
r1
r7
r5
r3
r1
9
7
r2
5
r2
3
r2
1
r2
9
r2
7
r1
5
r1
3
r1
r1
r1
1
0
r9
0
r7
0
r5
1
r3
1
r1
1
Round
A
2
1
2
3
r1
B
r9
A
r1
2
3
r7
B
r5
A
r3
3
n° players
5
n° players
5
5
5
4
4
5
Round
Round
•In the baseline a fast coordination on I is observed
•In the treatment coordination on I is slower (or it does not even occur !)
7
5
3
1
9
r2
r2
r2
r2
9
Round
r2
r1
5
7
r1
r1
1
3
r1
r9
r1
r7
r1
9
r2
5
3
1
9
7
5
7
r2
r2
r2
r2
r1
r1
r1
r1
r1
3
0
1
0
r5
B
r3
n° players
A
2B
1
r9
r2
9
r2
7
r2
5
r2
3
r2
1
r1
9
r1
7
r1
5
r1
3
r1
1
r9
r7
r5
r3
r1
0
3
A
1
r7
1
2
r5
2
A
3
B
r3
3
r1
n° players
4
n° players
n° players
Number of players choosing I - Base1 (Gr 3 & 4)
Results Payoffs 2
Round
4
4
7
5
3
1
9
7
5
9
r2
r2
r2
r2
r2
r1
7
9
r2
r2
5
r2
1
9
7
3
r2
r2
r1
r1
r1
9
r2
7
r2
5
r2
3
r2
1
r2
9
7
3
5
Round
r1
r1
r1
r1
1
r1
r9
r7
r5
r3
r1
7
9
r2
r2
3
5
r2
r2
1
r2
9
r1
7
r1
3
5
r1
r1
r1
1
0
r9
0
r7
0
r5
1
r3
1
r1
1
5
B
3
A
B
2
1
3A
r1
2 B
r9
A
r1
3
r7
2
5
r5
3
5
r3
n° players
4
Number of players choosing I - Treat2 (Gr 5 & 6)
n° players
5
r1
Round
Number of players choosing I - Treat2 (Gr 3 & 4)
Number of players choosing I - Treat2 (Gr 1 & 2)
Round
B
3
r1
7
9
r2
5
r2
3
r2
1
r2
7
5
9
r2
r1
r1
3
r1
1
r1
r9
r1
r7
r5
r3
r1
7
5
3
1
9
7
5
9
r2
r2
r2
r2
r2
r1
r1
r1
r1
r1
3
0
1
0
r9
0
r7
1
r5
1
r3
1
A
B
r1
2
A
r1
2
3
1
B
r1
A
r9
2
3
r1
3
r7
4
r5
4
r3
4
n° players
5
n° players
5
r1
n° players
5
Round
n° players
Number of players choosing I - Base2 (Gr 5 & 6)
Number of players choosing I - Base2(Gr 3 & 4)
Number of players choosing I - Base2 (Gr 1 & 2)
Round
• When the risk of choosing I is low all the people immediately coordinates
on the Pareto Dominant equilibrium
Preliminary Conclusions
A very high rate of coordination compared
to the coordination levels reported in the
literature
 Slower coordination in Treatment(1) when
compared to Baseline(1)
 Need for a more detailed individual level
analysis
