Decision Patterns and Information Availability in
the Beer Distribution Game
Jonas Kunze, Yalin Giindiiz
Universitat Karlsruhe(TH), Karlsruhe, Germany
Contact author: jonas.kunze@em.uni-karlsruhe.de
July 7, 2006
Abstract
In this article we present results of different experiments with the
Beer Di ion patterns and the effect
of varying information on the decision quality. Besides the known de-
cision patterns such as the ordering heuristic presented by Sterman
(1989) and the well investigated bullwhip effect in the Beer Distribu-
tion Game, we make two other observations. First, as an extension to
ribution Game focusing on de
available studies, we suggest that decision behavior could be explained
by policies that change over time. Second, a non linear relationship
between the anchor and the de s presented and contrasted to
the linear heuristic. Information scems to play an important role in
the decision making process, but the effect is not necessarily positive.
This could be explained by coordination problems. Overall, the com-
plexity of the Beer Distribution Game raises various questions about
the experimental design.
n
1 Introduction
In the late 1950s, in order to introduce the mechanics of System Dynamics
in a role-playing setting, the Beer Distribution Game (BDG) was devel-
oped.This is a simulation game where each of the players is responsible for
meeting the incoming orders in a supply chain. The BDG has proven to
be an important tool in the spread of System Dynamics methodology, in-
fluencing many researchers and executives (Sterman (2000)). Especially for
researchers, it provided an important experimental setup for understand-
ing, analyzing and simulating dynamic systems (Sterman (1989), Sterman
(1992); Senge (1994)). There have been alternative application areas of
BDG where it has been used
(Geyer-Schulz (1998)) and as a b:
Donohue (2002)).
The Beer Distribution Game has a simple and nice system dynamics
model setup where the orders flow through the supply line. The inventories
and the supply lines are the stocks of the system. As in all System Dy-
namics models, these stocks show a quantifiable level of either a physical
or non-physical variable, such as inventory, cash, headcount, or customer
satisfaction. In the BDG setting, the variable of interest for the players is
the inventory and supply line stocks, which are ideally tried to be mini-
mized because of inventory and backlog costs. The dynamic structure of the
System Dynamics model is achieved through the flows in the system; while
stocks represent the state of system elements, flows show how things are
changing. In this sense flows revise and update the stock values: they can
denote actions such as producing, hiring/firing, selling, or delivering. In the
BDG setup, flows in the system refer basically to incoming order flow, and
outgoing shipment flow!. The players therefore maintain system balancing
behavior through control of the supply line and inventory (Sterman (2000),
pp-684-694).
Overall, the System Dynamics Modeling of the real world systems pro-
vides a powerful way of representing a problem faced everyday: In a dy-
namic decision making setting, typically, decisions are taken in order to
manage/regulate the level of stocks (i.e. inventory) through affecting the
inflows and outflows to the stocks per unit time (ie. producing, deliver-
ing). The desired level of inventory and the desired supply line are auxiliary
variables in the system, which are individually decided by the players in
a dynamic environment. In this study we focus on decision patterns, and
the effects of information availability on the basis of the experimental BDG
setup. The dynamic decision making tasks that the players face in manag-
ing the stock levels are examined in the light of previous literature. First
addressed by Tversky and Kahneman (1974), anchoring and adjustment has
been an important behavioral policy to estimate an unknown quantity by
a reference point. We observe that the system balancing behavior that the
players aim to achieve might result in a non-linear relationship between an
anchor and the ordering decision. Further, we show that ordering policies
might change in time. Information availability has importance in decision
making, but the effect is not necessarily positive, which can be explained
through coordination problems.
complex problem in artificial intelligence
sis for different experiments (Croson and
‘For a stock-flow diagram of the BDG see Sterman (1989).
The study is organized as follows: In section 2 the BDG is described in
detail. In section 3 the experiments and the obtained datasets are described,
while section 4 focuses on the analysis of the datasets. Section 5 gives a short
outlook.
2 The Beer Distribution Game
The BDG was developed as a board game. Usually, four players form a
group and are members of a linear supply chain (retailer, wholesaler, dis-
tributor, and factory). There exists only a unique good (here: beer kegs),
which is shipped downstream, i.e. from the factory, over the distributor
and wholesaler, to the retailer. The number of goods shipped depends on
the previous order that was placed by the downstream member, i.e. there
exists an upstream flow of orders. All supply chain members have a stock
(inventory) where goods are stored until they are used to fulfill an incoming
order.
On the market side of the supply chain, there is a customer that orders a
unique good from the retailer. These orders are a predefined function, which
we will call the demand function. On the supply side of the supply chain,
there is a source with a 100% service level which serves all orders that were
placed by the factory. Sometimes, the factory has a production limit. This
is put into the play by announcing that the factory is only able to order up
to a fixed number of goods.
The transmission and processing of an order as well as the shipment of
the ordered goods takes time. By using a discrete time structure, rounds are
introduced into the game. Generally, each order needs two rounds to reach
the supplier (next upstream member) and another two rounds are needed
until the shipment arrives in the stock. Every round, one non-negative order
decision must be taken by every player in the supply chain. For more details
on the exact state transition, see Sterman (1989).
Up to now, the structure of the BDG has been described. But another
question is essential for decision making: What is the information to which
players have access? If the word ”information” is taken in a broad sense, it
includes information about the structure (number of team members.
time lag, etc.), about the system state (number of goods in retailer’s stock,
number of goods ordered by the wholesaler two rounds ago, etc.), about
the demand function (stochastic information, actual realization), and about
the other players’ decision making (communication allowance). Generally,
structural information is provided. In the traditional board game, beer kegs
size of
were symbolized by little counters. If pl shipment infor-
mation became public knowledge. Orders, to the contrary, were symbolized
by cards where a number was written. This information was hidden until
ved on one table,
the order reached the next upstream team member. Communication was
usually forbidden.
Before using the BDG in an experimental setting for the current study,
the structural and informational characteristics of a certain BDG was es-
tablished. Furthermore, some terminology was changed to achieve a more
neutral view on the decision task. First, the “beer” terminology was taken
out. Instead of beer kegs, only goods were shipped. Second, the industrial
production and distribution connotation was excluded by renaming retailer,
wholesaler, distributor, and factory to dealer 1, dealer 2, dealer 3, and dealer
4.
When talking about the experiments, we use the following terminology
(after Davis and Holt (1993)): A participant of the experiment is called
subject. In a session, a group of subjects plays the game. Each ion
has a certain treatment describing a specific configuration of experimental
variables, such as information and incentives.
3 Datasets
In this section we describe two different datasets that have been acquired in
experiments with the BDG at the Universitat Karlsruhe (TH).
The first dataset results from a preliminary experiment that was con-
ducted in February and March 2004. 60 students participated in a total of
6 sessions. The decision task was to act in a supply chain with two players
forming one group, and the demand function and the system initialization
was as described in Sterman (1989). Two repetitions of the game were
played with 30 rounds each.
The second dataset is from a lab experiment that was conducted in
March 2005 and in which 87 students participated in 6 sessions. Some
experimental design changes were made in order to achieve a more general-
izable result. Each supply chain consisted of 3 subjects. Furthermore, the
demand function was now a uniform distributed process between 0 and 10
(U0, 10]) and stochastic information was provided to the subjects. After a
training game of 8 rounds, the main game was played and lasted at least
30 rounds. Beginning with round 30, there was a 20% probability that the
actual round was the last round. This method was chosen to eliminate end
game effects. Therefore, the number of rounds in the sessions differs between
[ Dataset l 1 l 2 ]
From Preliminary Lab
Experiment: Experiment:
Group size 2 3
Groups 30 29
Information || Local vs. Classic | Local vs. Classic
Rounds 2x 30 rounds Training: 8 r.
30-37 rounds
Table 1: Characteristics of the datasets
30 and 37.
The research questions of the experimental studies focused on the in-
formational availability (Table 1). The first dataset’s experiment had two
treatments which differed in the information about the system state. In one
treatment (“local information”) only information about the actual stock,
the incoming orders and the incoming shipment were presented. The other
treatment (“classic information”) provided the information that could be
gathered by players sitting at a table, where beer kegs are symbolized by
little boxes that were moved around. Therefore, all shipments as well as
the stock of all players were public knowledge. The experiment of dataset
2 was an extension of the preliminary experiment and also focused on the
comparison between “local” and “classic” information.
It has to be noted that experimental control varied across the experi-
mental studies. In the preliminary study, only small incentives were present
and the end game effect was not addressed. In the lab experiment, signifi-
cant incentives were present, intelligibility of the instructions and the screen
layout were improved.
4 Analysis
In this section we first describe observed patterns in the decisions and discuss
the use of an anchored linear order heuristic to describe these patterns.
Then, we compare the results of the conducted experiments and discuss a
coordination problem hypothesis to explain the results.
4.1 Patterns in Decisions
The existing studies focus on total transaction costs to compare the per-
formance of different supply chains (Steckel et al. (2004), Kaminsky and
Simchi-Levi (1998)) or they adopt an ordering heuristic to identify behav-
ioral patterns (Sterman (1989), Croson and Donohue (2003), Croson et al.
(2004)). In the following analysis of the dataset from the lab experiment we
make two observations that call for an extension of the ordering heuristic
presented in Sterman (1989).
The ordering heuristic by Sterman (1989) assumes that the decision
maker orders the non-negative sum of three variables. These are namely,
(i) the expected loss (expected incoming order), (ii) the difference between
desired and actual stock, and (iii) the difference between desired and actual
supply line. To describe the decision maker’s behavior the author introduces
some parameters to the ordering heuristic that are fitted to explain the de-
cisions in the best possible way. Two inherent assumptions of this way to
describe decision making are consistency and linearity?. Consistency de-
notes that the personal parameters in the heuristic are kept constant for all
rounds, whereas the linearity assumption indicates that the order decision
is the weighted sum of the three mentioned variables and that an increase
in one of these would lead to a corresponding increase in the order decision.
4.1.1 Consistency in Decisions
Observation of subjects’ decision making leads to the impression that sub-
jects do not make their orders in a consistent way during the game. It rather
seems that decision making could be well described by order policies that
change from time to time. Although we will not formalize these thoughts
sufficiently to make statistical significance tests, we present the decision
making of 5 subjects from the lab experiment. In the following figures, for
29 rounds, the decision, the incoming order, and the decision time for each
round is depicted. For the selected cases, these variables give a good im-
pression about possible order policies that might have been employed by the
subject.
Subject 7 In Figure 1 the decision making for subject 7 is depicted. From
rounds 1 to 6 the decisions are always lower than the incoming orders. From
round 8 on, the decisions are basically 5, except for rounds 13 and 14.
Furthermore, the decision time is depicted and shows some outliers at rounds
2In the cases when the ordering heuristic predicts a positive number.
ion behavior occur some
4 and 11. Interestingly, the noticed changes in deci:
rounds after these outliers in decision time.
30 t T T T
Incoming Orders "a
ecision
25 b. [
Decision Time
Units
a
i
15
Round
30
Figure 1: Decisions of Subject 7 (Lab Experiment)
Subject 17 The behavior of subject 17 is shown in Figure 2. It can be
divided into two parts. In the first half of the rounds, a constant number
of goods is ordered for several rounds. When this number changes, long
decision times occur (round 3 and 8). From round 13 on, no clear order
policy can be concluded from visual inspection of the presented variables.
But if we include stock development, it can be seen that the over-ordering
until round 13 resulted in an excessive stock of at least 30 goods from round
13 on. Therefore, the missing clear order policy could be explained by a lost
interest in the game from round 13 on. The low decision times support this.
70
i i E T i Incoming Orders a.
60 -- 4 * “ * + Decision —=—
i Decision Time ——-x
50 + : b }
g 40;
5 sok
20 | oe
10 600K
L. we 4
ys a
‘ PO fg oP Be
oO 25 30
Figure 2: Decisions of Subject 17 (Lab Experiment)
Subject 18 In Figure 3 the time saving aspect of a simple strategy can
be seen. In 18 out of 29 decisions, the subject orders exactly the number
that has been ordered by his downstream group member (incoming orders).
The decision time is extraordinarily low.
20 T
Incoming Orders
cision
45 | Decision Time
2
= 10}.
=)
& |:
oO
oO 30
Subject 44 In Figure 4, a clear scheme is observed for the first 15 rounds.
Every time the decision taken differs from the number of incoming order:
there occurs a peak in the subjects decision time. From round 15 on, this
pattern is lost.
35 T T T r
Incomtg Orders =e
30 F Decision 4
Decision Time --
25 F- m: “|
2 20 F- vas A i + ot
3 ish Jett. lena : 4
ae
10 p-%: Bm Bomhg B- gOS 7
_ . - f ee a
6 eee eee Pow J
é : : : : :
i) 5 10 15 20 25 30
Round
Figure 4: Decisions of Subject 44 (Lab Experiment)
Subject 82 For subject 82 (Figure 5) we have a similar finding as for
subject 44. After a long planning phase (long decision times in the first 3
rounds), the subjects continuously orders 5. There is one exception in round
12 accompanied by a long decision time and some changes in the last rounds.
These changes might be motivated by the stock development, as the stock
is larger than 15 units from round 26 on.
30
y Incoming Orders a.
25 b. Decision —a
Decision Time —-x-/
20 [. H
2
= 15st
5
10 f ose
5b
0 aa oi
0 15 20 25 30
Round
Figure 5: Decisions of Subject 82 (Lab Experiment)
4.1.2 Linearity Assumption
If linearity holds, then a linear relationship between the incoming orders
(loss rate) and the decision is reasonable. To investigate this relationship
we looked at dataset 2. First of all, we checked what is the best linear trend
that could be found. We ran a linear regression with a fixed point in (0,0)
and minimized squared errors. The gradient with minimum square errors
0.825. This observation suggests that an incoming order of 5, would result
in an average order decision of 5 x 0.825. The analysis below has been
undertaken for both 0.825 and 1, as the perfect linear slope. However, as
the results did not change significantly, only the section with the linear slope
of 1 is presented.
We then counted the total amount of (incoming order,de:
ion) pairs
for every possible combination. For instance, if one subject in an arbitrary
session had an incoming order of 6 and decided to order 8, we increased the
count for the pair (6,8) by one. The results are the absolute frequencies of
these pairs and they are depicted in Figure 6. In total there are 2,491 pairs.
Visual inspection shows that two squares of high frequency exists: A (0-
5,0-5) square and a (5-10,5-10) square. In contrast to a linear relationship
s that
ss in the decision
between incoming orders and decisions, we introduce the hypothes
specific points (anchor points) have a special attractiven
making pro
To investigate our hypothesis we use the chi-square goodness of fit test.
. These anchor points are observed to be 0, 5, and 10.
To apply the test, we need to define probability distributions that gives each
Figure 6: Frequency of Pairs of Incoming Orders - Decision Pairs
incoming order-decision pair a probability. As the decision is taken after
having received the incoming order, we only need to define a conditional
probability.
For the linear relationship, we assume that the decision is normally dis-
tributed. The mean value jz is equal to the incoming order and the standard
deviation o will be estimated from the sample. For each incoming order from
0 to 10 we have run a chi-square test. The results are depicted in Table 2
and show that the observed data does not fit the normal distribution. For
any incoming order the normal distribution assumption has to be rejected,
even if the confidence interval is 99.99%.
To test our hypothesis, we need to construct a probability function that
puts special weight on the anchor points 0, 5, and 10. Therefore, we propose
the following probability distribution to observe an anchor a € {0,5, 10},
given the incoming order to be a:
? if|a—a2|<1
probpw(a/x) 3 —7(la—2|-1) if 1 < |a—a| and ja—2| <6
0 else
The resulting distribution for the three anchor points is depicted in Figure
7. Using this probability distribution to explain the data would not work,
as it only puts probability weights on the anchor points. Therefore, we
use a linear combination of the normal distribution and the anchor points
distribution. For each linear weight from 0 to 0.5 we have run chi-square
10
Incoming Number of o Categories ? distributed
Orders observations _ (est.) test statistic
0 276 3.369 9 219.384
i 123 3.406 8 43.562
2 159 2.957 9 85.569
3 215 2.548 9 93.290
4 205 2.590 10 103.838
5 636 2.639 10 470.192
6 206 2.732 9 41.604
7 183 2.946 9 39.924
8 175 3.499 9 68.329
9 105 3.699 8 30.157
10 208 4,224 9 114.368
Table 2: Results of Chi-Square Test (Normal Distribution)
i) =
Po) =
sl
08 p(0)
2 06
3
3
3
a 0.4
0.2
0
0123 4 5 67 8 9 10
Incoming Order
Figure 7: Probability to Observe an Anchor Point
ay
tests for all possible incoming orders, and calculated the average p-values
for the rejection of the hypothesis that the observations follow the mixed
distribution.The results for the different linear weights are depicted in Figure
8. Note that the p-value for every chi-square test assuming the normal
distribution is lower than 0.001%. The highest average p-value, is found if a
0.016 T T T T T T
0.014 }-
‘Avg. error prob.
0.012 }-
0.01 F
0.008 |.
0.006 }.
0.004 }-
0.002 }-
)
i i
0 0.05 0.4 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Percentage of Point-Wise Anchoring Heuristic
Figure 8: Average Error Probability for Different Linear Combinations
linear weight of 24% is given on the anchor points distribution. The results
of the chi square test of this mixed distribution are presented in Table 3.
Two of the chi-square test statistics(incoming order being 1 and 9) have a
p-value that is higher than 5%, and another test statistic(incoming order
equal to 4) has a p-value higher than 1%. These findings show that the
fitting quality is increased by including the point-wise distribution that only
puts probability weight on the anchors.
Another observation that puts emphasis on the importance of the anchor
and multiples of it is found in dataset 1. The game initializes with 12 units in
each stock and 4 units have been ordered in the past 4 rounds. The demand
function rises from 4 to 8 units in the fifth round. Therefore, especially even
numbers and multiples of 4 might have a special attractiveness for decision
makers. In Figure 9 the frequencies of each decision taken is depicted.
To summarize this section, we investigated two characteristics of decision
making in the BDG. First, decision making is not always consistent during
the whole game. Changing situations may lead to a complete change in
the order policy. Often, these changes are preceded by long decision time.
Second, experimental setup suggests anchor points. These anchor points
have a special attractiveness for decision makers.
12
Incoming Number of o Categories ? distributed p-value
Orders observations _ (est.) test statistic [%]
0 276 3.369 8 74.781 <0.0001
1 123 3.406 8 12.183 9.4705
2 159 2.957 8 27.864 0.0232
3 215 2.548 9 62.710 <0.0001
4 205 2.590 9 20.052 1.0140
5 636 2.639 10 95.238 <0.0001
6 206 2.732 9 48.916 <0.0001
7 183 2.946 8 35.022 0.0011
8 175 3.499 8 24.621 0.0885
9 105 3.699 7 12.219 5.7268
10 208 4,224 9 63.629 <0.0001
Table 3: Results of Chi-Square Test (Mixed Distribution)
1200 T T T _ T T T T T
1000 F 4
800 + 4
>
5
3 600 F 4
s
(3
400 - 4
200 + I 4
all l fla i naa
2
8 10 12 14° 16
Decision
Figure 9: Frequencies of Decisions (Dataset 1)
18
4.2 Effect of Changes in Information Availability
To investigate the effect of the different information availability settings
(classic vs. local), we make use of both datasets. In Figure 10 the distribu-
tion of the group costs for each treatment are depicted. These are the sum
of group costs for the entire time horizon. It can be seen that the group
costs of the treatment with local information are lower. For a more precise
discussion of the results see Kunze (2004).
watt PTH
Information
0 200 400 600-800-1000 1200 1400 16001800
Group costs
Figure 10: Group Costs in the Preliminary Experiment
The interesting finding that less information about the system state leads
to better results, may be explained by an overall coordination problem. In
order to achieve a supply chain with low transaction costs, participants
need to coordinate their strategies. Coordination in the BDG is difficult
to achieve as communication is prohibited. Therefore, decision makers look
at the signals they receive from their group members (e.g. incoming orders
from the downstream player, service level of the upstream player). With
these signals decision makers choose a strategy that hopefully work well with
the other players’ strategies. In the classical treatment, a lot of shipment
information is available. Therefore, the decision maker receives more signals
and his strategy selection task gets more complex. In other words, more
information allows more strategies and therefore makes the coordination
problem more complex. On the other hand, more information will surely
provide a better understanding about the system state and a more precise
guess about the other group members’ strategies.
To see whether this interesting finding holds for a supply chain with
groups of size three, the lab experiment was conducted. For this experiment,
the demand function was a uniform process between 0 and 10. In order to
compare the two treatments, one realization of the random process was used
two times, once in each of the two treatments. For six demand realizations,
the group in the local information treatment produced lower costs than the
group in the classic information treatment, while the opposite was true for
the remaining eight demand realizations. Although there appears to be a
14
Treatment 1 1 1 2 2 2
Session 1 3 5 2 4 6 |
Avg. round time [se 54.1 | 52.7 | 53.4 |) 33.1 | 38.1 | 39.8
Std. deviation 21.8 | 15.7 | 15.7 || 10.2 | 9.4 | 11.1 |
Avg. dec. time [sec] |} 23.6 | 24.6 | 23.7 |] 16.0 | 17.9 ] 19.2
Std. deviation 15.8 | 14.1 | 17.5 | 10.1 | 11.3 | 11.4 |
Table 4: Round and decision times for the lab experiment
contrary trend to the results of the preliminary experiment, a pairwise test
does not show significant differences between the treatments.
There are at two potential explanations to the fact that the groups in
the classical treatment did not perform as bad as they did in the preliminary
experiment. First, the coordination problem hypothesis could be wrong and
there is actually no effect of the different informational patterns on decision
making behavior. Second, the hypothesis could be right but the changes
in the experimental setup counterbalance or interact with the coordination
problem in an unforeseen way. A particularly strong possibility is that the
different realizations of the demand function might have produced run length
effects.
The first explanation is rendered unlikely by the fact that although group
costs do not show a significant difference, the decision time of the subjects
does. In Table 4 the round and decision times are depicted for dataset 2.
Decision time is the time that a subject needs to type in his or her order
decision and to verify it by clicking on the “Okay” button. Rounds wer
chronized across teams, i.e. a round finished when all subjects of the sess
herefore, round time is the time that all subjects
had the actual system state information on their screen. Round time as well
as for decision time are significantly higher in the classical treatment than
in the local information treatment. This observation supports the intuition
that the classical treatment demands more cognitive capacities as it offers
more information to the decision maker.
The second possible explanation, which is the counterbalancing effect,
seems more realistic, but two questions arise that have not been investigated:
Is the effect of the treatment variable (information) independent of the effect
of the realization of the demand function? Is the effect of the treatment
variable independent of the group size?
It can be concluded that information about the system state likely has an
influence on the decision making process. If more information is available,
made their decisions.
15
the decision making task is more complex and a higher decision time is
needed. The unintuitive finding of the preliminary experiment, i.e. that
groups with more knowledge about the system state perform worse than
groups with less knowledge, was explained by the coordination problem
hypothesis, but could not be replicated in the lab experiment. It remains
unclear whether this is due to the changes in experimental setup.
5 Conclusion
Experiments with the BDG reveal interesting facts about the decision mak-
ing proc
servations: First, people seem to change their decision making process from
Looking at overall patterns in the decision, we made two ob-
time to time. Second, if an anchor is present, certain anchor points have a
special attractiveness for deci:
Two experiments were used to evaluate the influence of information
sion makers.
about the system state on group performance. The results of the two exper-
iments are contradictory, pointing to the importance of experimental setup.
There might be a po:
pects (such as group size and demand function) and informational design
‘ible interaction between various structural design as-
aspects. Furthermore, the interdependencies between decisions within a
game complicate the issues even more.
These findings point to a general problem when doing experiments in dy-
namic decision problems. The possible complex interactions between struc-
tural, informational and dynamic aspects make it difficult to test a certain
research question with the BDG. These interactions should be subject for
further research in the field of experiments with dynamic decision making
problems.
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