Double Coordination in Small Groups

Luigi Mittone, Matteo Ploner, Ivan SoraperraComputable 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

5 .70 .50 .30 .10 -.10

4 .60 .40 .20 .00

3 .50 .30 .10

2 .40 .20

1 .30Source: Weber, 2006

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 Game2 Pareto-ranked equilibria

Two actionsT(raditional good)I(nnovative good)

Interaction Structure

Groups of 10 5 players role A5 players role B

30 repetitions with feedback1 repetition rewarded (random pick)

2 experimental treatmentsBaseline (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 butFocal point in the NW cornerWeaker risk perception for the I move

Treatment (2)

Summary

BaselinePlayers A (e.g., consumers) and Players B

(e.g., producers) must build a belief on the preferred choice of the other group

TreatmentPlayers 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 Students of the University of Trento, Italy

Computerized experiment Web-based

Average earnings $$$

Time required About 1h 30min

Results Payoffs1Number of players choosing I - Base1 (Gr 3 & 4)

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Number of players choosing I - Base1 (Gr 1 & 2)

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Number of players choosing I - Base1 (Gr 5 & 6)

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Number of players choosing I - Treat1 (Gr 3 & 4)Number of players choosing I - Treat1 (Gr 3 & 4)

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Number of players choosing I - Treat1 (Gr 5 & 6)

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•In the baseline a fast coordination on I is observed

•In the treatment coordination on I is slower (or it does not even occur !)

Results Payoffs 2Number of players choosing I - Base2 (Gr 1 & 2)

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Number of players choosing I - Base2(Gr 3 & 4)

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Number of players choosing I - Base2 (Gr 5 & 6)

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Number of players choosing I - Treat2 (Gr 1 & 2)

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Number of players choosing I - Treat2 (Gr 3 & 4)

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Number of players choosing I - Treat2 (Gr 5 & 6)

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• 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