Are communication failures common? We revisit a classic example of experimental coordination failure and explore, in a 2x2 design, the effects of deviation costs and loss avoidance. Our results provide additional insights into the parametric determinants of laboratory coordination failures, and successes.coordination games, Pareto-ranked equilibria, payoff-asymmetric equilibria, optimization incentives, robustness, coordination failure

Andreas Ortmann

Giovanna Devetag

English

Research Papers in Economics

     
 
 
  
  
Volume 30, Issue 2 
  
Classic coordination failures revisited: the effects of deviation costs and loss 
avoidance 
  
 
 
Giovanna Devetag  
Department of Law and Management, University of 
Perugia 
Andreas Ortmann  
Economics Department, Australian School of Business, 
University of New South Wales
Abstract 
Are communication failures common? We revisit a classic example of experimental coordination failure and explore, in 
a 2x2 design, the effects of deviation costs and loss avoidance. Our results provide additional insights into the 
parametric determinants of laboratory coordination failures, and successes.
Financial support from the Italian Ministry of Education, University and Research (MIUR) is gratefully acknowledged. We thank seminar 
participants in Amsterdam, Pisa, and Trento, and participants at the ESA 2007 Asia-Pacific annual meeting for useful comments and 
suggestions on a previous draft. The usual caveats apply. 
Citation: Giovanna Devetag and Andreas Ortmann, (2010) ''Classic coordination failures revisited: the effects of deviation costs and loss 
avoidance'', Economics Bulletin, Vol. 30 no.2 pp. 1633-1641. 
Submitted: Apr 19 2010.   Published: June 10, 2010. 
 
     1. Introduction 
 
Coordination games with Pareto-ranked equilibria have attracted major attention over the 
past two decades, as path-breaking experimental studies (Van Huyck, Battalio and Beil 
[henceforth VHBB] 1990, 1991; Cooper, DeJong, Forsythe and Ross 1990, 1992) were 
widely interpreted as suggesting that coordination failure -- here interpreted as failure to 
coordinate on the efficient equilibrium -- is a common phenomenon in the laboratory. In 
Devetag and Ortmann (2007), we argue that coordination failures are less common than 
is widely perceived (e.g., Ochs 1995 and Camerer 2003). We argue that by now it is well 
understood how coordination successes can be engineered in the lab and we formulate 
specific conjectures about the impact of deviation costs and loss avoidance (see Cachon 
and Camerer 1996 and Rydval and Ortmann 2005 for related studies). 
 
To test these conjectures, we use the original version of the median action game first 
studied by VHBB (1991). Early results on the median action game had shown both a high 
frequency of coordination failure and strong history-dependence, in that the last-round 
median always equaled the first-round median in all treatments. In our experiments, we 
test the robustness of these results by manipulating two parametric determinants related 
to the original payoff function in VHBB (1991): the presence of negative/positive payoffs 
in  the  earnings  tables;  and  the  presence  of  linear/nonlinear  deviation  costs,  i.e.,  the 
opportunity costs of deviating from the best response to a given median. The effect of the 
first determinant has been tested by Cachon and Camerer (1996), while the effect of 
lowering deviation costs has been studied by Goeree and Holt (2005) and Battalio et al. 
(2001).  However,  no  previous  study  has  systematically  investigated  the  separate  and  
joint effects of changes in these two determinants of the VHBB (1991) median action 
game. More specifically, and unlike the previous studies, we employ the same payoff 
function used in VHBB (1991) in our baseline treatment. Furthermore, we employ the 
same (large) group size and the same information conditions.  
 
2. Design 
 
In order to test our conjectures, we chose the following 2x2 design summarized in Table 
I, where Neg stands for earnings tables that contain negative payoffs and Non-lin stands 
for non-linear deviation costs: 
 
 
Table I here 
 
"A" is mnemonic for the anchor of  Table I and is identical to the key earnings table in 
VHBB (1991) while B, C, and D are our treatments.  
 
Specifically, the four earnings tables A – D look like this:  
 
                     Table A here   
Clearly, Table A features negative payoffs and non-linear deviation costs; for example, 
the opportunity cost of picking action 4 when the current median is 3 equals 5 cents, 
whereas the deviation cost rises non-linearly to 45 cents when action 6 is picked.  In B, 
negative payoffs have been eliminated by adding 1.30 to all payoffs.
1  
 
 Table B here 
               
Table C shows the results from substituting the squared term in VHBB (1991):  
 
   
€ 
π ei ( ) = aM −b M −ei [ ]
2
+c, 
 
where M = median,  i ε {1, 2,….,7}, a=0.10, b=0.05, c=0.60, with the absolute value 
(linearizing deviation costs), and by setting parameter b equal to .30.
2   
  
Table C here 
                
In D, we have only changed the last term of the payoff function in VHBB (1991) by 
substituting the squared term with the absolute value.   
 
Table D here                   
 
The elimination of the squared term results in positive payoffs.
3   
 
Negative payoffs in the original payoff table (A) appear in the upper right and lower left 
corner, which might explain the clustering of initial choices just above the secure action. 
Removing negative payoffs eliminates a potential reason for not picking the efficient 
action. Linearized deviation costs lower the opportunity costs of choices far above the 
current median, thus encouraging exploration in the direction of efficiency. Hence, our 
main hypothesis is that the absence of negative payoffs and linear deviation costs are both 
efficiency-enhancing  features;  therefore,  we  expect  to  observe  a  higher  incidence  of 
coordination  success  in  the  experimental  treatments  compared  to  the  anchor,  ceteris 
paribus. However, since in treatment C deviation costs are higher than in the baseline for 
"small" deviations, observing less coordination in C than in the remaining treatments is a 
possibility.   
 
 
 
                                                 
1   In B, deviation costs are the same in absolute terms but not in relative terms. This seems 
unavoidable. 
2   This way we recapture negative payoffs. The implied change in the size of the (now linearized) 
deviation costs seems unavoidable although we would have liked to avoid it since it was likely to affect the 
probability of coordination failure.   
3  Again unavoidably, this change relocated the secure equilibrium from Choice 3 to Choice 1.  3. Implementation 
 
Experiments were conducted with 16 groups of players in 8 sessions using a between-
subject design. We obtained 4 independent data points for each treatment. 
           
Table II here      
     
We exactly replicated the design in VHBB (1991).  Groups of 9 subjects played the stage 
game  for  a  total  of  10  rounds.  Each  session  included  18  subjects  who  were  seated 
randomly  at  computer  terminals.  The  instructions  specified  that  subjects  would 
participate in a "market" that would last for ten rounds.
4 They would be divided into two 
groups randomly by the computer program at the beginning of the experiment, and the 
group composition would remain fixed for the whole duration of the market. Payoffs 
were expressed in experimental currency units, to be converted into Euros at the end of 
the experiment. In an effort to keep the maximum potential gain in Euros constant across 
treatments, the conversion rate used in B was half that of the remaining treatments. At the 
end of each round, each subject received information about the group median for that 
round and his or her resulting individual payoff. No information was given about the 
individual choices and payoffs of the other players throughout the experiment. Before 
starting the experiment, subjects had to answer some questions to ensure that everybody 
understood how to calculate the median of a series of numbers and how payoffs were 
computed on the basis of the earnings table.  
 
4. Results 
 
Table III reports the median and mode of choices in the first round, pooled across groups 
and divided by treatment. Figure 1 reports the entire distribution of first-round choices, 
divided  by  treatment  (each  treatment  in  the  first  round  contains  36  independent 
observations).   Table IV reports the observed medians in the first and last rounds of play; 
these medians are reported separately for each group and treatment and hence add a 
temporal dimension. 
  
Turning to the first-round results, we have six observations: first, the median choice in 
treatment  A  reflects  the  typical  case  of  coordination  failure  found  in  previous 
experiments  (e.g., VHBB 1991, Cachon and Camerer 1996, Blume and Ortmann 2007). 
In contrast, in treatment D the median choice is the efficient one, confirming our key 
conjecture. Second, contrary to all other experiments that we know (see Devetag and 
Ortmann 2007), the modal choice in treatment A is the choice that induces the efficient 
equilibrium. The typical modal choice in the previous experiments, action 4 or 5, is less  
preferred in our case. Third, the efficient choice is also the modal choice for treatment D. 
In terms of the modal choice, although we do see the distribution of choices shift in the 
hypothesized direction, the hypothesized joint effect of deviation costs and loss aversion  
turns out to be statistically non-significant given our number of independent observations. 
                                                 
4   The term "market" was also used in VHBB (1991).   Essentially, the baseline results are "too good" to allow for the hypothesized effect to 
materialize in a statistically significant manner given our original implementation plans. 
Fourth,  the  surprising  results  of  treatment  A  also  affect  the  hypothesized  effects  of 
treatments  B  and  C.    Specifically,  using  a  Mann-Whitney  U  test,  we  do  not  get  a 
significant difference going from A to B, or going from A to C.  Fifth, we find highly 
significant differences going both from treatment B to D (p<.01, one-tailed), and from 
treatment C to D (p<.01, one-tailed). Sixth, as hypothesized, in treatment D, in which 
there  are  only  positive  payoffs  and  deviation  costs  are  linear  (and,  recall  footnote  2, 
somewhat lower than in treatment C), the percentage of players picking the efficient 
action 7 is the highest (55%) relative to all other treatments.   
 
Figure 1 here 
 
Table III here 
 
Table IV here  
 
The data in Table IV exhibit the inertia phenomenon that was documented in previous 
experiments. Specifically, in both rounds 1 and 10, the modal median is 6 for treatment 
A, 5 for treatments B and C, and 7 in treatment D.  
 
In summary, in the presence of only positive payoffs and linear deviation costs (our 
treatment  D),  the  modal  outcome  is  one  of  successful  coordination  on  the  efficient 
equilibrium, which is in line with our hypothesis. The data from treatment C suggest, 
quite in line with our intuition, that the magnitude of deviation costs also plays a role in 
determining coordination success, similarly to what was obtained by Goeree and Holt 
(2005)  for  a  different  group  size  and  a  different  matching  protocol.  The  data  from 
treatment B suggest, contradicting our priors, that positive payoffs alone are not sufficient 
to generate successful coordination.    
 
5. Discussion 
 
Using the original median action game first studied by VHBB 1991, we have reported 
experimental  sessions  designed  to  replicate  VHBB's  main  findings  and  to  test  our 
conjectures on the impact of deviation costs and loss avoidance. Our replication ceteris 
paribus shows higher coordination efficiency compared to the original experiment. In 
addition, by and far, our results suggest that some combination of loss avoidance and low,  
linear deviation costs is efficiency-enhancing. In effect, it seems that when going from 
treatment  A  to  treatment  D,  simply  changing  the  nonlinear  term  of  the  generating 
function used in VHBB (1991) made the difference between coordination failure and 
coordination success. Our results add to our understanding of what it takes to engineer 
coordination successes in the laboratory. 
 
  
 
References 
 
Battalio, R.C., Samuelson, L., and Van Huyck, J. (2001) “Optimization Incentives and 
Coordination Failure in Laboratory Stag Hunt Games” Econometrica  69, 749-764. 
 
Blume, A. and Ortmann, A. (2007) “The Effects of Costless Pre-play Communication: 
Experimental Evidence from Games with Pareto-ranked Equilibria” Journal of Economic 
Theory 132, 274-290.  
 
Cachon,  G.P.  and  Camerer,  C.  (1996)  “Loss-avoidance  and  Forward  Induction  in 
Experimental Coordination Games” Quarterly Journal of Economics 111, 165-194. 
 
Camerer,  C.  (2003)  Behavioral  Game  Theory.  Experiments  in  Strategic  Interaction,  
Princeton University Press: Princeton.  
 
Cooper,  R.,  D.  De  Jong,  R.  Forsythe,  and  Ross,  T.  (1990)  “Selection  Criteria  in 
Coordination Games: Some Experimental Results” American Economic Review 80, 218-
233. 
 
Cooper,  R.,  D.  De  Jong,  R.  Forsythe,  and  Ross,  T.  (1992)  “Communication  in 
Coordination Games” Quarterly Journal of Economics 107, 739-771. 
 
Devetag, G. and Ortmann, A. (2007) “When and Why: A Critical Survey on Coordination 
Failure in the Laboratory” Experimental Economics 10, 331-344. 
 
Ochs, J. (1995) “Coordination problems” in Handbook of experimental economics by J. 
Kagel and A.E. Roth, Eds.,  Princeton University Press: Princeton, 195-252.  
 
Goeree, J.K. and Holt, C.A. (2005) “An Experimental Study of Costly Coordination” 
Games and Economic Behavior 51, 349–364. 
 
Rydval, O. and Ortmann, A. (2005) “Loss avoidance as selection principle: Evidence 
from simple stag-hunt games” Economics Letters 88, 101-107.   
 
Van Huyck, J. B., R. C. Battalio, and Beil, R.O. (1990) “Tacit Coordination Games, 
Strategic Uncertainty, and Coordination Failure” The American Economic Review 80, 
234-248. 
 
Van  Huyck,  J.  B.,  R.  C.  Battalio,  and  Beil,  R.O.  (1991)  “Strategic  Uncertainty, 
Equilibrium  Selection,  and  Coordination  Failure  in  Average  Opinion  Games”  The 
Quarterly  Journal  of  Economics  106,  885-911.  
  6
 
 
Table I. Experimental Design 
 
        Neg  Pos 
 
  Non-lin               A  B 
         Lin    C  D 
 
 
 
 
 
Payoff Table A        Median value of X chosen 
        7  6  5  4  3  2  1 
Your choice of X  7  1.30  1.15  0.90  0.55  0.10  -0.45  -1.10 
      6  1.25  1.20  1.05  0.8  0.45  0.00  -0.55 
      5  1.10  1.15  1.10  0.95  0.70  0.35  -0.10 
      4  0.85  1.00  1.05  1.00  0.85  0.60  0.25 
      3  0.50  0.75  0.90  0.95  0.90  0.75  0.50 
      2  0.05  0.40  0.65  0.80  0.85  0.80  0.65 
      1  -0.5  -0.05  0.3  0.55  0.70  0.75  0.70 
   
                       
 
Payoff Table B        Median value of X chosen 
        7  6  5  4  3  2  1 
Your choice of X  7  2.60  2.45  2.20  1.85  1.40  0.85  0.20 
      6  2.55  2.50  2.35  2.10  1.75  1.30  0.75 
      5  2.40  2.45  2.40  2.25  2.00  1.65  1.20 
      4  2.15  2.30  2.35  2.30  2.15  1.90  1.55 
      3  1.80  2.05  2.20  2.25  2.20  2.05  1.80 
      2  1.35  1.70  1.95  2.10  2.15  2.10  1.95 
      1  0.80  1.25  1.60  1.85  2.00  2.05  2.00 
 
 
 
Payoff Table C        Median value of X chosen 
        7   6    5    4    3    2     1 
Your choice of X  7  1.30  0.90  0.50  0.10    -0.30   -0.70       -1.10 
      6  1.00  1.20  0.80  0.40  0.00    -0.40      -0.80 
      5  0.70  0.90  1.10  0.70  0.30    -0.10      -0.50 
      4  0.40  0.60  0.80  1.00  0.60  0.20      -0.20 
      3  0.10  0.30  0.50  0.70  0.90  0.50   0.10 
      2  -0.20  0.00  0.20  0.40  0.60  0.80     0.40 
      1  -0.50   -0.30   -0.10  0.10  0.30  0.50   0.70 
  
  7
 
 
 
 
 
Payoff Table D        Median value of X chosen 
        7  6  5  4  3  2  1 
Your choice of X  7  1.30  1.15  1.00  0.85  0.70  0.55  0.35 
      6  1.25  1.20  1.05  0.90  0.75  0.60  0.40 
      5  1.20  1.15  1.10  0.95  0.80  0.65  0.45 
      4  1.15  1.10  1.05  1.00  0.85  0.70  0.55 
      3  1.10  1.05  1.00  0.95  0.90  0.75  0.60 
      2  1.05  1.00  0.95  0.90  0.85  0.80  0.65 
      1  1.00  0.95  0.90  0.85  0.80  0.75  0.70 
 
 
 
Table II. Experiment Implementation       
 
                Treatment  
              A  B  C  D 
         Groups     4   4   4   4 
        Rounds    10  10  10  10 
 
 
 
Table III. Median and modal choice by treatment             
 
  A  B  C  D 
N  36  36  36  36 
median  6  5  5  7 
mode  7  4  7  7   
 
  Table IV. Median in the 1
st and 10
th round of play, divided by group and treatment. 
   
 
Treatment  A  A  A  A  B  B  B   B  C  C  C  C  D  D  D  D 
Group  1  2  3  4  1  2  3  4  1  2  3  4  1  2  3  4 
1st round median  5  6  6  7  5  6  5  4  5  5  5  5  5  7  6  7 
10throundmedian  6  6  6  6  5  6  5  4  5  5  6  5  7  7  7  6 
 
  
  8
 
 
Fig. 1. Distribution of first round choices in the four treatments (in percentages) 
   
 
 
  
 

Behavioral Game Theory. Experiments in Strategic Interaction,

Coordination problems” in Handbook of experimental economics by

Loss avoidance as selection principle: Evidence from simple stag-hunt games”

Loss-avoidance and Forward Induction in

Optimization Incentives and Coordination Failure in

Selection Criteria in Coordination Games:

Strategic Uncertainty, Equilibrium Selection,

The Effects of Costless Pre-play Communication: Experimental Evidence from Games with Pareto-ranked Equilibria”

When and Why: A Critical Survey

Classic coordination failures revisited: the effects of deviation costs and loss avoidance

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Classic coordination failures revisited: the effects of deviation costs and loss avoidance

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