The timing effects (timing without observability) identified by Weber, Camerer, and Knez (2004) in coordination game experiments are caused by their fixed-matching protocol. When we use a random-matching protocol the alleged timing effects completely vanish.

Tao Li

English

Research Papers in Economics

Are there timing effects in coordination game experiments? 
Tao Li
Shanghai University of Finance and Economics
Abstract
The timing effects (timing without observability) identified by Weber, Camerer, and Knez
(2004) in coordination game experiments are caused by their fixed-matching protocol. When
we use a random-matching protocol the alleged timing effects completely vanish.
This paper has benefited from discussions with Steffen Huck, David Laibson, Al Roth, Roberto Weber, and participants in the
2006 Economic Science Association meeting. Financial support from Shanghai Pujiang Project is gratefully acknowledged.
Citation: Li, Tao, (2007) "Are there timing effects in coordination game experiments?." Economics Bulletin, Vol. 3, No. 13 pp.
1-9
Submitted: March 6, 2007.  Accepted: April 10, 2007.
URL: http://economicsbulletin.vanderbilt.edu/2007/volume3/EB-07C90001A.pdf1 Introduction
Can timing play a signi¯cant role in coordination games, even without
a®ecting the information late movers have? According to von Newmann
and Morgenstern (1947, p51), timing without observability never matters
since it is equivalent to simultaneous move. According to Camerer (2003)
and Weber, Camerer, and Knez (2004), there seems to exist a timing e®ect
in coordination game experiments which overturns von Newmann and Mor-
genstern's presumption. Our paper contributes to this research question by
showing that the timing e®ects Weber, Camerer, and Knez (2004) identi-
¯ed are caused by their ¯xed-matching protocol. When we use a random-
matching protocol the alleged timing e®ects completely vanish.
Weber, Camerer, and Knez (2004) use a variant of the following Stag
Hunt game (Table 1). In their treatment, it was common knowledge that
Row players went ¯rst, but also that Column players did not know what
Row did. Simply knowing the order of the play led pairs to move to Row's
preferred equilibrium (Q;Q). So timing without observability can help solve
this coordination problem.1
Q P
Q :9;:9 0;:6
P :6;0 :3;:3
Table 1: Stag Hunt Game
However, the identi¯ed timing e®ects in Weber, Camerer, and Knez
(2004) could be caused by their experimental protocols. Since they adopt
a ¯xed-matching protocol with full feedback on previous outcomes, the early
mover's previous-round actions are essentially revealed to the later movers.
As the matching is ¯xed and the ¯rst mover in each round is always the
same person, a previous-round Q choice from the ¯rst mover is a strong
costly signal that she would choose Q again.
We successfully replicate their results using the same ¯xed-matching pro-
tocol with feedback. When we use random matching in which the ¯rst mover
is not necessarily the same person for consecutive rounds, the alleged timing
e®ects completely vanish. We also observe no timing e®ect in the experi-
1Another pure-strategy Nash equilibrium is (P;P).
1ments using a simpler version of their game. Overall our results shed doubt
on the existence of timing e®ects in coordination games.
Section 2 reports our experimental results. Section 3 discusses the liter-
atures and implications.
2 Stag Hunt Experiments
Subsection 2.1 describes our replication of Weber, Camerer, and Knez
(2004) with the ¯xed-matching protocol and reports the treatment experi-
ments with random matching protocols. Subsection 2.2 reports corroborating
results for simpler experiments.
2.1 Weak Link Game
Weber, Camerer, and Knez (2004) use a generalized 3-person Stag Hunt game
called \weak link." The players are choosing an e®ort level between 1 and
7. The payo® is determined by own e®ort and own group's minimum e®ort.
The detailed payo® is in the following table.
7 6 5 4 3 2 1
7 1.3 1.1 0.9 0.7 0.5 0.3 0.1
6 - 1.2 1.0 0.8 0.6 0.4 0.2
5 - - 1.1 0.9 0.7 0.5 0.3
4 - - - 1.0 0.8 0.6 0.4
3 - - - - 0.9 0.7 0.5
2 - - - - - 0.8 0.6
1 - - - - - - 0.7
Table 2: Weak Link (The rows correspond to your choice. The columns
correspond to the minimum choice in your group.)
The weak link is a stag hunt game because all diagonal outcomes are
pure-strategy Nash equilibria, which are ranked according to its associated
payo®. Any equilibrium with higher payo® always comes with higher risk.
Equilibrium selection in this game is a subtle problem.
We focus upon the following two experiments they conducted: 1) Simultaneous-
move protocol, in which all three players choose simultaneously; and 2)
Sequential-move protocol, in which three players move one by one, with early
2choices unobservable. Their experimental outcomes con¯rmed their predic-
tion based upon virtual observability that subjects in the sequential treat-
ment tend to coordinate on higher-e®ort equilibrium. The average choice in
the sequential treatment is about one level higher.
Our replications were carried out in November of 2005. We conducted
experiments with undergraduates at Shanghai University of Finance and Eco-
nomics recruited from classes of various topics (including economics, business,
information technology, English, and many others). Students normally have
quite limited knowledge of modern economics. We do not allow students re-
cruited from the same class to dominate any one session. Most participants
get a payo® between $1 and $2 (1 US dollar = 8 yuan). The average length
of each session (including instructions) was about half an hour. The local
wage for a college student is at best $1 per hour.
In each session 24 subjects sat in a networked computer lab specially
designed for running economic experiments. They were subdivided into 3-
person groups and played 10 rounds together. The group was ¯xed and there
was feedback after each round. In each group the ¯rst (and respectively
second and third) mover was always the same person. Subjects in each
session played 10 rounds. This is longer than Weber, Camerer, and Knez
(2004).
The replications was quite successful. The top two curves in Figure 1 is
very close to corresponding curves in Figure 3 and 4 of Weber, Camerer, and
Knez (2004). The average choice in the sequential treatment is also about
one level higher.
We then conducted an additional treatment (timing without observabil-
ity) using a random-matching procedure in May, 2006. We used only 9
subjects (divided into 3 groups) and also allowed feedback after each round.
The result is reported in the bottom curve of Figure 1. Even for such a small
population, which tends to facilitate coordination, the average choice for the
¯rst round is only 3:3, and it keeps dropping until in the last three rounds it
is only about 1:2. The group minimum is above 1 for only two times (2 out
of 30, roughly 7%).
Note that in Weber, Camerer, and Knez (2004), with feedback, the
previous-round choice for each player is public information when they choose.
The ¯rst mover in each round is always the same person. Then the ¯rst mover
can choose high e®ort in the ¯rst round to signal her strong intention to lead
the group in the following rounds. She might lose from her choice in the ¯rst
round, which makes her signal costly and credible in a repeated game. The
32 4 6 8 10
1
2
3
4
5
6
7
period
a
v
e
r
a
g
e
 
c
h
o
i
c
e
Timing without Observability (random rematching)
Simultaneous (replication: fixed group)
Timing without Observability (replication: fixed group)
Figure 1: Weak Link Experiments
4same logic applies to the second round and etc. It is not surprising that the
¯rst mover can lead the entire group to high-e®ort equilibria. But this is
entirely a signalling e®ect in a repeated game, and not due to timing per se.
We conducted an additional experiment (not reported here) using a ¯xed-
matching procedure in which we label players as ¯rst, second, and last mover.
The real choices are made simultaneously. The label remains unchanged for
the entire experiment. Again, subjects tend to coordinate on higher-e®ort
equilibria, and the magnitude of treatment e®ect is the same as in Weber,
Camerer, and Knez (2004).
2.2 2 £ 2 Stag Hunt
For the game described in Table 1, which is a simper version of the weak link
game, we run two similar experiments (simultaneous-move protocol Stag-SIM
and sequential-move protocol Stag-SEQ). We observe no timing e®ects here
either.
The experiments were carried out in May of 2006. The procedure is
similar to what was described above except that we now have 42 subjects.
In each session 8-12 subjects played 10 rounds together. There was random
rematching and feedback after each round. The results are summarized in
the following Table 3.
P Play Q Play Total
Stag-SEQ I 73 7 80
91% 9% 100%
Stag-SEQ II 85 35 120
71% 29% 100%
Stag-SIM I 59 41 100
59% 41% 100%
Stag-SIM II 111 9 120
92% 8% 100%
Table 3: 2 £ 2 Stag Hunt
There is some variation across sessions. But it is quite obvious that
(Q;Q) failed to strongly emerge in both Stag-SEQ experiments. Overall Stag-
SEQ is rather like Stag-SIM. A one-sided Â2 test, ignoring the independence
5requirements by pooling data from the same treatment sessions, fails to reject
the null hypothesis that the proportion of P play in Stag-SIM is the same as
the same proportion in Stag-SEQ. The p value is 0:38.
3 Conclusion
Cooper et al. (1993) and Rapoport (1997) were the ¯rst to address the
timing e®ects in asymmetric coordination games (battle of the sexes). Weber,
Camerer, and Knez (2004) argue that symmetric stag hunt game is better
than asymmetric coordination games for identifying timing e®ects since in
asymmetric games moving ¯rst also makes ¯rst mover's preferred equilibrium
outcome more \focal." Their procedure yields relatively less ambiguous re-
sults.
Building upon Amershi, Sadanand, and Sadanand (1985, 1992), Weber,
Camerer, and Knez (2004) summarized the explanation for such timing ef-
fects as \virtual observability" (VO). The later mover would choose as if she
could observe the early mover's choice. The early mover would then take ad-
vantage of this tacit follower behavior by choosing her preferred equilibrium
action.
In recent years, more and more researchers acknowledged the ¯ndings of
Weber, Camerer, and Knez (2004) and their VO explanation (Muller and
Sadanand 2003, Poulsen and Tan 2004). This argument is appealing since
it ¯ts our intuition that a ¯rst mover often has an advantage. However, our
paper shows that the evidence is not yet strong.
For practical implications of our results, consider a team production prob-
lem (a weak link game). In order for the group members to uniformly exert
high e®ort, it is usually not enough to have a leader who makes a hidden
¯rst move, as was implicitly implied in Weber, Camerer, and Knez (2004).
Such a leader is e®ective only in a repeated scenario with ¯xed group mem-
bership, where history is public information. Her previous-round action can
then serve as a model to encourage other players.
4 Appendix
The following is an English translation of the original Chinese instruction
for the stag hunt game experiment in which the early mover's choice is un-
observable (Stag-SEQ treatment). Instructions for the other treatments are
available upon request from the author.
6Thank you for attending scienti¯c experiments in economics. Every par-
ticipant will get 5 yuan show-up fee. During the experiment you have the
chance to earn additional money according to the rule. At the end of the
experiment the sta® will put all your money into an envelop and hand it to
you when you leave the room one by one. Please keep quiet from now on. If
you have questions please raise your hand.
We have 12 people in this room. We will conduct 10 rounds of identical
experiments.
At the beginning of the 1st round, the computer will automatically divide
12 people into 6 groups, with 2 people in each group. The grouping is random
and anonymous (you will never know who ever played with you).
At the beginning of the following 9 rounds of experiments, the computer
will re-do the random and anonymous grouping. So it is highly unlikely that
you are grouped with the same person in each round.
In each round of the experiment, we ask you and your partner in the
same group to choose Left or Right respectively. One person is to choose
¯rst. When the second person chooses, he or she does not know the previous
choice. The early mover is randomly picked by the computer in each round.
When both persons have completed the above choices, you will be informed of
the results of the experiment, which include the ¯nal choice of your partner
and the money you earn in this round.
The money you earn in each round is determined by the following two
factors:
² your own choice
² your partner's choice
The details are shown below (monetary unit: yuan)
your choice your partner's choice your income your partner's income
Left Left 0:9 0:9
Left Right 0 0:6
Right Left 0:6 0
Right Right 0:3 0:3
Table 4: Detailed Income
Your have 3 minutes to go over the instructions before we start the ex-
periment.
7References
[1] Amershi, A., Sadanand, A., and Sadanand, V. 1985. \Manipulated Nash
Equilibria III: Applications and a Preliminary Experiment." UBC Work-
ing Paper #1222b.
[2] Amershi, A.H., Sadanand, A., and Sadanand, V. 1992. \Player Impor-
tance and Forward Induction." Economics Letters. 38 : 291C297.
[3] Camerer, C. 2003. Behavioral Game Theory, Princeton University Press.
[4] Cooper, R., Douglas V. DeJong, Robert Forsythe, and Thomas W. Ross.
1993. \Forward Induction in the Battle-of-the-Sexes Games." American
Economic Review 83 : 5;1303 ¡ 16
[5] Muller, A., and Sadanand, A., 2003. \Order of play, forward induction
and presentation e®ects in two-person games." Experimental Economics
6 : 5C25.
[6] Von Neumann, J., and Morgenstern, O., 1947, The Theory of Games
and Economic Behavior (2nd ed.) Princeton NJ: Princeton University
Press
[7] Poulsen, A., and Tan, J., \Can Information Back¯re? - Experimental
Evidence from the Ultimatum Game." Working Papers from Aarhus
School of Business, Department of Economics
[8] Rapoport, A. 1997. \Order of Play in Stratetically Equivalent Games in
Extensive Form," International Journal of Game Theory 26 : 113 ¡ 36:
[9] Schelling, T. 1960. The Strategy of Con°ict, Cambridge, MA: Harvard
University Press.
[10] Weber, R., Camerer, C., and Knez, M. (2004): \Timing and Virtual
Observability in Ultimatum Bargaining and \Weak Link" Coordination
Games", Experimental Economics, 7 (1), p. 25-49.
8

Are there timing effects in coordination game experiments?

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Are there timing effects in coordination game experiments?

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