Agent Based Simulation

Rather than implement mathematically-based simulations, the Worldwide Web Instructional Committee (WWWIC) develops agent-based simulations. In general, there are three kinds of agents employed in these simulations.

1) Atmosphere Agents,

lending local color and a measure of authenticity, to the environment. These agents are largely designed for their entertainment value. In Dollar Bay these include a Fire Inspector, a Juggler, a Beat Cop, and so forth.

2) Infrastructure Agents,

contributing in a meaningful way to the "play" of the game. These agents are essential to the pedagogical goals of the educational environment. In Dollar Bay these include the Customers who effect economic demand, to a lesser extent, the Employees who control the day-to-day workings of each synthetic retail establishment, and the agents who supply wholesale goods, direct advertising services, provide banking and so forth.

3) Intelligent Tutoring Agents

monitor, mentor, and remediate the human learners in the performance of their roles. The tutoring agents are being developed as sub-topic experts who have access to problem solving experiences, context sensitive help and advice, conceptual and procedural tutorials, stories of success and failure within their particular sub-topic, and conversational networks for learner interaction.

Economic Environments: Dollar Bay (and Blackwood)

WWWIC economic environments (Dollar Bay and Blackwood) are networked, multi-player, simulation-based, interactive multi-media, educational games. The pedagogical domain is micro-economics, in particular, retailing.  The teaching goals revolve around the strategic importance of "targeting" specific customer groups in order to gain competitive advantage in the retail marketplace.

Similar to the WWWIC science-based simulations, these games provide a simulation that rewards analytical problem solving -- the business equivalent of the scientific method.

Economic models are typically built on the idea of demand and supply functions

where economic entities maximize their welfare when the market achieves equilibrium. These are mathematical models filled with rigor, but difficult to create, maintain, modify, or debug.

Agent-based economic models develop rational agents as heterogeneous individuals with divergent theories.

They allow us to relax assumptions about perfect rationality, rational expectations, and perceptual maximization of expected utility.

To date, agent-based models have been used in the social sciences to explore patterns of spatial segregation, the evolution of cooperation, the emergence of money, cultural evolution, market processes, electoral politics, state formation, and group stability.

The Model of Consumer Decision Making

The Dollar Bay economic model assumes rational, cost-minimizing consumers

Therefore, consumers consider travel costs, search costs, service benefits, and product quality as well as price when making buying decisions.

Dollar Bay models the entire consumer population by defining it in terms of cluster groups (CG).

The concept of cluster groups is similar to the idea of psychographic segmentation, employed by many advertisers and marketers. Psychographic segmentation is the classification of a population into groups which share similar values, attitudes, and lifestyles (Rice, 1988; Piirto, 1990). The premise is that persons with similar values and lifestyles will have similar buying behavior.

Psychographic segmentation is a growing method in marketing, for it promises insight into the emotional and lifestyle factors, which motivate consumer's buying behavior. A cluster group (consumer group) is a coherent segment of the population where the members are alike in age, income, life narrative, interests, values, and lifestyles. As a consequence the members of a cluster group have similar consumer behavior.

The Dollar Bay game uses product classes and models as its level of representation

A model represents a particular good for sale, and

a product class is used to describe the market for an entire class of goods. 

All models in the same product class compete with each other while no models in different product classes compete. 

In the Dollar Bay game, a product class contains all information on each consumer's attraction for a particular product. 

The representation of any particular product is composed of:

1)   Average potential demand (APD).

2)   A percentage number for each cluster group's relative level of interest compared to the overall all potential demand (PD).

3)   A dollar amount for unit search cost (USC) for each cluster group.

4)   A unit transportation cost for each cluster group, unit service benefit (USB) and unit quality benefit (UQB) the cluster group receives from the store and/or product.

5)   All possible features of the product, price sensitivity (PS) of cluster groups.

6)   A maximum dollar amount (MAX) and a minimum dollar amount (MIN).

Based on the information stored in the product class representation,

the Customer agents decide the amount of a particular product, at what price, from which stores they would buy.  

The individual purchasing decisions of these agents implement the economic activity of Dollar Bay.


In Dollar Bay there are 20 distinct cluster groups.


Working Class: middle aged couples with children,  renters


White Collar Singles: young singles,  renters,  upwardly mobile


College students.

Table 1: Sample Cluster Groups

There are seven small towns in the region that comprises Dollar Bay. 

Each of these towns has its own particular flavor, composed of very different populations mixes. 

For example there is Copper Harbor, mostly made up of college students and professors,

or Silver River, home to most of Dollar Bay's young professionals. 

The population for the three example cluster groups in Silver River is:


Working Class

1255 persons


White Collar Singles

4123 persons


College Students

1185 persons

Table 2: Sample Cluster Groups as Population on Product

A model represents a particular good for sale,

while a product class is used in this implementation to describe the market for an entire class of goods. 

For example, the furniture model "Econo Sleeper" is a bed possessing certain features and quality level. 

While the product class "bedroom furniture" contains data about the market for all beds,


Cluster Group Name










Working Class










White Collar Singles










College Students









Table 3: The product Class Definition for Bedroom Furniture

Product Class Definition

The product class definition is the heart of the Dollar Bay simulation. 

It contains all information on consumers’ likes and dislikes for a given product. 

Dollar Bay uses the explicit data about consumer preferences stored in the product class definition to generate consumer behavior. 

Based on the information stored in the product class representation, consumers decide

1)   how much of a product they want to buy,

2)   which stores they buy from and

3)   how much they can afford to spend. 

By changing the data in the product class definition, one changes the consumer behavior generated

by the simulation (see Table 3).

A product class definition contains firstly a number for the average potential demand (APD),

which is the average number of persons who will be want to buy the product over a given time. 

All other information is stored in a table,

with all the cluster groups on one axis and all the features and consumer values on the other. 

Each column is a dimension of the consumers’ decision making. 

The values underneath represent the value of the cluster groups. 

In the product class definition, each cluster group has a percentage number for  their relative level of interest compared to the overall average potential demand (I). 

So cluster groups with high interest in a product class will have a percentage number over 100% while those with low values will be below 100%. 

These numbers were based loosely upon market research information obtained from Simmons demographic data (Simmons, 1993). 

For each cluster group a dollar amount is given for unit search cost (USC). 

The unit search cost is the cost for a group to gain information about a particular store per unit of distance between store and consumer. 

The greater the distance between store and buyer the more expensive it is for a consumer to learn about what the store is selling and at what prices. 

This unit search cost is used to simulate advertising.

Unit transportation cost (UTC) is the unit cost to each cluster group of getting to a store and getting the product back home. 

Some cluster groups are more mobile than other and therefore have lower transportation costs. 

For example, retired persons have very high transportation cost, while families with homes, who own cars, have much lower transportation costs. 

The product class definition also contains data about benefits that products or stores may offer. 

The product class definition gives values for unit service benefit (USB)

The unit service benefit is a dollar amount a cluster group is willing to pay for a unit of added service. 

and unit quality benefit (UQB).

The unit quality benefit is the dollar amount a cluster group is willing to pay for a unit of added quality. 

Both of these benefits will be subtracted from the price of a model in calculating the overall consumer's real cost. 

Also contained in the product class definition is an enumeration of all the possible features a model of this class may have. 

For example a bed may be a springed bed or a waterbed. 

In Dollar Bay furniture has the features of size, type, and quality. 

Models have the features enumerated in their product class definition. 

Different features are valued differently by different consumer groups. 

For each feature enumerated, the product class definition contains each cluster group's value for that feature in dollars. 

This is the amount a cluster group will pay for that feature. 

Some features may be so disliked by a particular cluster group that they have a negative value for them,

which means players would need to offer a lower price than for a product without the feature, in order to make them want to buy it. 

The product class definition also contains data about cluster group sensitivity to price

in the form of a percentage number called price sensitivity (PS). 

This percentage tells how sensitive a group is compared to an average price sensitivity,

where 100% means that a cluster group has average price sensitivity,

and a lower number means that the cluster group is less concerned about getting the best buy.

Finally, product class definitions also contain two numbers for each cluster group which represent how much they can afford to spend: 

a maximum dollar amount (MAX), which is the price at which no one in the cluster group can afford to buy the product and

a minimum (MIN), which is the price at which everyone in the cluster group can afford to buy the good. 

All these values will be used to calculate consumers' decision making.


Model Definition

A model represents a particular item that players sell – it is an instantiation of the abstract product class. 

Each model has a pointer to its parent product class definition, along with its name, feature settings, manufacturers suggested retail price (MSRP), and an iconic picture. 

Three models created for the Dollar Bay game are shown in Table 4. 


Model Name

Econo-Sleeper 500

Super Sleeper 1200

Ultra Waveless 900

Model Description

“a econo priced, low quality spring-bed”

“a high priced, excellent quality spring-bed”

"a high-priced, excellent quality waterbed”






Quality: Low (=0)

Quality: High (=3)

Quality:High (= 3)


Kind = spring

Kind = spring

Kind = water

Table 4: Three Models of the Bedroom Furniture Product Class

Tom's furniture store, hoping to attract bargain hunters, sells only the Econo-Sleeper 500 for $310, while

Bob's tries to attract up-scale clients with the Super Sleeper 1200, selling for $800, and the Ultra Waveless 900 selling for $700.



Dollar Bay models the effect of advertising by

first determining the search cost, to a consumer group, of finding out if a particular store sold a desired item

and at what price they sold it – if that store did not advertise. 

This is found by multiplying the cluster group's unit search cost (USC), found in the product class definition (Table 3),

by the unit distance between store's town and consumer's town. 

Advertising reduces that search cost by some percentage. 

The amount an ad reduces this search cost is called the percentage search cost reduction (RSC).

Different advertising reaches different consumers. 

Dollar Bay models an advertisement by giving, for each cluster group, a percentage number for the reduction in search cost. 

Different advertisements in different media and different sizes have different percentage numbers (Table 5):


Cluster Group Name

Leisure Section, Quarter Page, RSC

Sports Section, Quarter Page, RSC


Working Class




White Collar Singles




College Students



Table 5: Quarter Page Print Ads


Bob's takes out a quarter page advertisement in the Leisure section while

Tom’s takes out a quarter page advertisement in the sports section. 

For the working class cluster group, a quarter page advertisement in the leisure section reduces search cost 8%,

while one in the sports section reduces search cost 5%. 

A quarter page ad in the sports section reduces college students’ search cost 20%,

while one in the leisure section only 5%.

The Dollar Bay game supports several forms of media.


Each turn, the virtual consumers decide what they want to buy,

how much, and from whom. 

The model of consumer decision-making has four main steps:   

Each group of customers decides how much of a particular product they want to buy.

They decide which stores they like best.

They visit stores, searching for the product.

If they find it, they decide whether to buy it


Step 1. The Level of Consumer Interest in a Product.

First, each cluster groups’ potential demand (PD) in each product is determined. 

The server obtains this by looking at the population representation and the product type definition. 

A particular cluster groups’ level of interest is calculated by taking the population in each cluster group

and multiplying it by the percentage potential market of that group for that product.  The formula for potential demand is:

PD= P * I * ADM  


PD   = potential demand

P    = population

I    = demand index

ADM  = average demand.

This is repeated for each cluster group in an area, and then for all areas in Dollar Bay.  

For example, the potential weekly demand for beds for three sample cluster groups living in Silver River are shown in Table 6:


Cluster Group Name

Potential  Demand (PD)


Working Class



White Collar Singles



College Students


Table 6: Potential Demand

That is, there are 223 White Collar Singles (cg2) in Silver River who want to buy beds every week plus 75 college students and 23 working class families.

Step 2. Real Cost to Cluster Groups is Calculated.    

Next, each cluster groups’ real cost is calculated for all products for sale in a product type. 

Real cost is calculated with the following formula:

RC = P + TC + SC - (SB + FB).


RC = real cost

P  = price

TC = transport cost

SC = search cost

SB = service benefit

FB = feature benefit.

The transport cost is calculated by:

TC =  2 * UTC * D(S,C);


TC     = transportation cost

UTC    = unit transport cost for the cluster group

D(S,C) = distance from store to cluster group neighborhood.

In Table 3, the UTC for white-collar singles is $10 – this represents the notion that college students have less personal resources and less cars than many other cluster groups and therefore view transportation as more costly.  Thus, college students are much more likely to shop in their own areas.

The search cost are calculated:

SC = RSC *(USC * D(S,C) ^2)


SC     = search cost to cluster group

RSC    = % reduction in search cost from ads by store

USC    = unit search cost to cluster group

D(S,C) = distance between store and cluster group.

The service benefit is calculated as:



SB  = service benefit of store to cluster group

USB = unit service benefit of cluster group

SL  = service level set by store (an integer from 0 to 4).

In Dollar Bay there are three levels of quality:  basic, good, and high. 

These three levels are represented with the set [0,1,3]. 

The working class cluster group may have an $80 unit quality benefit UQB (see Table 3). 

While white-collar singles have a UQB of $120.

Super Sleeper 1200 beds are high quality (quality = 3). 

Working class families will see this as a $240 discount

while white-collar singles will see it as a $360 discount. 

Therefore white-collar singles will be willing to spend $120 more for the bed,

since high quality is more valued by them. 

In this way, Dollar Bay models the different values and tastes important to different consumer group decision-making.  A model may have any number of features.  This allows us to make products, which are more and more complex, with any number of features which effect consumers’ decision-making.


Cluster Group Name

Tom's Econo-Sleeper 500

Bob's Super Sleeper 1200

Bob's Ultra Waveless 900


Working Class





White Collar Singles





College Students




Table 7: The Real Cost to the Three Example Cluster Groups Living in Dollar Bay,

for the Three Kinds of Beds for Sale in the Two Stores

Step 3. Percentage Distribution of Sales Based on Real Cost

Next, consumer group sales are distributed based on real cost to the cluster group. 

The lower a model’s real cost relative to other models real cost to a cluster group,

the greater that model's share of the overall demand for that cluster group. 

This is done with a simple distribution formula:

PSD = ( 100% / n) + PS (ARC - PRC).


PSD = percentage sales distribution for a store.

PS  = price sensitivity of a cluster group for a product class

n   = number of stores in a particular market.

ARC = average real cost for all models sold by all stores in a product class,

PRC = a single players real cost to a cluster group.

This formula returns a percentage of the total demand of a cluster group for a product a store's particular model has won.  If all stores were to offer the same model at the same price in the same location with the same service level, then they would split the demand evenly between them.  For the example we are working on it comes like this:


Cluster Group Name

Tom's Econo-Sleeper 500

Bob's Super Sleeper 1200

Bob's Ultra Waveless 900


Working Class





White Collar Singles





College Students




Table 8: Percentage of Total Demand Assigned to Each Model  for Sale in Each Store

Step 4. Consumer Group Determines How Much They Can Afford

In the last step, each cluster group determines how much of their desire for a product they can afford

to actually satisfy.  This is done with the following formula:

AFD   = 100% + (100% (min- price)/(max - min))


AFD   = percentage of a cluster group that can afford a particular price

price = actual price of a model

min   = the price at which all members of a cluster group can afford the model (Table 3).

max   = the price at which no members of a cluster group can afford the model (Table 3).

Generally the wealthier a consumer group, the higher the min and max numbers will be. 

For the beds’ product class, Table 3 shows that the maximum for white-collar singles is $800 and the minimum is $200. 


Cluster Group Name

Tom's Econo-Sleeper 500

Bob's Super Sleeper 1200

Bob's Ultra Waveless 900


Working Class





White Collar Singles





College Students




Table 9: Percent Affordability in Dollar Bay Per Cluster  Group, Per Store, Per Model of the Bed Product Class

Therefore the most any white-collar single will pay for a bed is $800, though very few will. 

Any white-collar single is willing to pay $200 for a bed. 

Therefore, even if players’ stores have a monopoly, they can often increase sales by decreasing prices.

Dollar Bay calculates total sales by multiplying potential demand

in each cluster group by affordability and market distribution. 

These steps are repeated for all cluster groups in all towns over the entire region of Dollar Bay.


Cluster Group Name

Tom's Econo-Sleeper 500

Bob's Super Sleeper 1200

Bob's Ultra Waveless 900


Working Class





White Collar Singles





College Students










Table 10: Total Sales in Dollar Bay by Cluster Group, Per Store,  Per Model of Bed