I. INTRODUCTION

The present model is about two factors affecting movie attendance of members of a delimited peer group. First are the "tastes" of individuals-how people (heterogeneously) evaluate the intrinsic attributes of movies that cause them to see movies independently of others. Second is the effect of "buzz" on movie attendance. Buzz in turn has two components: what people who saw the movie say about it, and how many people saw the movie (e.g., The English Patient, Star Wars-numbers give reason for seeing a movie even if it's no good). That is, buzz contains an issue of movie quality as conveyed by peers (which of course implies that buzz is indirectly influenced by those individuals' heterogeneous reactions to the same movie), and of the "faddishness" of a movie.
 
 

II. THE MODEL

The model is implemented as a learning classifier system. This allows representation of a large number of agents (100 in our initial trials), each of which makes a decision (about movie attendance in our case) in response to its environment. Part of its environmental message, in turn, is composed of the decisions of other agents. A classifier system specifies a collection of decision rules, which map environmental conditions into decisions. A decision rule is then one and the same with the agent it represents.

• The interactive component of this model is that part of an agent's environmental condition is itself a function of the decisions of other agents. For simplicity, we model each agent as having three possible decisions: "see the movie and like it," "see the movie and dislike it," and "don't see the movie." (Note that for convenience in implementation, an agent does not actually know which decision it makes when going to see the movie, as by assumption people don't see movies they know they won't enjoy. Rather, the enjoyment is determined probabilistically for agents who see the movie.) An agent's enjoyment of the movie is reported to all other agents, who are more likely to see the movie if peers who have seen it like it. Agents are also more likely to see a movie if a large number of peers have seen it, regardless of their enjoyment. This is the "fad effect" or, more appropriately, the "English Patient effect."

• The intrinsic, non-interactive (at least not directly) aspects of the movie are common in the environment faced by each agent. In this model, the intrinsic aspects are: the "type" of movie (here comedy or drama, but easily generalizable to multinomial and/or multidimensional type spaces such as star power or director); the report of critics (either favorable or unfavorable); and whether the movie is likely to be crowded (either crowded or not). Type and critical reviews are fixed at the start for a given movie, but crowdedness can vary over time, to account for the fact that movies are generally more crowded on opening weekend. See below for more on the disconnect between crowdedness and whether any agents have seen the movie. This is certainly a restriction and eliminates movies like Life is Beautiful that get more crowded well into their releases, as a result of the buzz. Certainly the model's parameters could easily be altered to allow for movies that become more popular into their releases, but it must be taken as exogenous. Learning classifier systems allow for heterogeneous reactions to the same movie on the part of different agents because the decision rule used is can be made probabilistic; this is to be interpreted as a decision with a component that is random to an outside observer.

The model assumes away problems of budget constraint, transportation, distance to theater, theater characteristics, and especially problem of finding a date. Movie budgets could actually be included, by assuming different people require much more favorable conditions for a movie before they become very likely to see it.

Agents do not evaluate the gamble they face over movie attendance in an expected utility sense. Agents can face negative expected utility from attending--e.g., if conditional on seeing the movie they are extremely likely to dislike it in a certain condition--and still attend. The interpretation is as a sort of bounded rationality, if an admittedly somewhat ad hoc one.

It is possible for "crowds" to be big even though no agents see the movie, or even if all agents have seen the movie. The interpretation is that a group of agents represents a group of friends, not the entire moviegoing population (even in a given area). Also note that agents infer nothing about the movie quality from the size of the crowd.
 
 

III. IMPLEMENTATION

In this section we explain some important features of learning classifier systems and some specifics of our implementation.

In a classifier system information flows from the environment to the agent through its detectors, which decode the information into one or more messages, usually represented in binary strings whose values are members of the alphabet {0,1}. These messages activate zero, one or more classifier rules at any given time, and out of these matching classifiers, an auction takes place to determine the current winner, which posts its action in the environment through the effectors.  The classifier rule consists of two parts: <condition>:<action>.

All matching classifiers make bids according their strength  i.e, according to how successful they have been. The winner can be chosen by selecting the one offering the highest bid or by adding some normally distributed, zero-mean noise with a specified noise deviation bidsigma into its deterministic bid, called effective bid -ebid.

When starting the program we provide a seed (a real value between 0 and 1) which initializes the random number generator. In the next section, we provide results of runs with different seed values.

This is a rudimentary description to acquaint the reader with the basic idea. For more on learning classifier systems and complete descriptions of the parameters used, refer to chapter 6 of David E. Goldberg's Genetic Algorithms in Search, Optimization and Machine Learning (Reading, MA: Addison-Wesley, 1989).
 

Representation

The environmental message and the condition part of the classifiers are both represented in a bit string of length 6, where the classifier's string is part of the alphabet {0,1,#}. The # is a "don't care" symbol matching both, a 0 or a 1 in the incoming message. The action is a string one bit long which takes any of the same three values.

The environmental message provides the following to the classifier's condition part:

• Movie attributes. Specify the type of movie in question: comedy (1) or drama (0).
• Critics. Reports that are either favorable (1) or unfavorable (0), but are not given by friends (i.e. they are sources of public information such as magazines, newspapers, etc.). This variable is represented randomly with equal probability of having it 0 or 1.
• Opinion of peers. The average of the friend's opinions.
• The number of friends who have actually seen the movie. It takes two bits for the classifier rule to represent the percentage of friends who have seen the movie. It ranges from 0-24, 25-49, 50-74, 75-100%, and it is represented as 00, 01, 10 and 11 respectively.
• Crowd. We have arbitrarily defined it as being "big" during the first 1/4 of the time span of the experiment (resembling the firsts few weeks of the release of a movie), and "small" after that period.

• 0 when the agent saw the movie and did not like it
• 1 when it saw it and liked it
• # when did not see it.

The number of agents in the model is set to be 100, but it can easily be replaced by any other number. We though 100 represents most of the space of possibilities. Results of runs with different seed values and either with noise or without it are given in the following section.
 
 

IV.  RESULTS

Although we performed several simulations, we are only presenting results of some of them. These seeds were selected because they show the range of effects of adding random noise; also within a noise treatment they show the sensitivity of results on the seed. For other seeds, the effect of adding noise lies somewhere between these results. Within a noise treatment, there is a strong non-monotonicity with respect to changes in seed.

Each example consists of 100 agents, each making an attendance decision and giving a report about the movie. Viewers who see the movie and like it are listed as "happy viewers," and viewers who see it and don't like are denoted "unhappy viewers."
 

Happy Viewers           = 38        //  Agents who saw and liked the movie
Unhappy Viewers      =  30       //   Agents who saw and disliked the movie
Total Viewers             = 68        //   Add Happy plus Unhappy viewers
Did not see it               = 32        //    Chose not to see the movie

The following are just a few examples of the types of rules that fired during the simulation:
 

Rule	Matching Environmental State	Action / Decision
101111:0	Comedy / Bad Critics / Peers liked it /  75-100% friends have seen it / it is crowded	Went-disliked it
#1110#:#	Does not care about type /  Good Critics / Peers liked it / 50-74% friends have seen it / does not care about crowds	Did not go
101101:1	Comedy / Bad Critics / Peers liked it / 50-74% friends have seen it / it is crowded	Went - liked it

The ratio of happy viewers to unhappy viewers is 1.27.

Happy Viewers          =   43
Unhappy Viewers      =  30
Total Viewers             =   73
Did not see it               =   27

Type of classifier rules that fired:
 

Rule	Environmental State	Action / Decision
100001:0	Comedy / Bad Critics / Peers did not like it /  0-24% friends have seen it / it is crowded	Went-disliked it
101001:1	Comedy /  Bad Critics / Peers liked it / 0-24% friends have seen it / it is crowded	Went - liked it
111011:0	Comedy / Good Critics / Peers liked it / 25-49% friends have seen it / it is crowded	Went-disliked it

The ratio of happy viewers to unhappy viewers is 1.43.

Happy Viewers          =   59
Unhappy Viewers      =  28
Total Viewers             =   31
Did not see it               =   41

Type of classifier rules that fired:
 

Rule	Environmental State	Action / Decision
#0##0#:1	Does not care about type / Bad Critics / Does not care about peers /  Cares only if 0-24% or 50-74% have seen it / does not care about crowds	Went-liked it
100011:1	Comedy /  Bad Critics / Peers disliked it / 25-49% friends have seen it / it is crowded	Went-liked it
100001:0	Comedy / Bad Critics / Peers disliked it / 0-24% friends have seen it / it is crowded	Went-disliked it

The ratio of happy viewers to unhappy viewers is 2.1.

Happy Viewers          =   68
Unhappy Viewers      =  38
Total Viewers             =   30
Did not see it               =   32

Type of classifier rules that fired:
 

Rule	Environmental State	Action / Decision
101101:#	Comedy / Bad Critics / Peers liked it /  50-74% friends have seen it / it is crowded	Did not go
111001:1	Comedy /  Good Critics / Peers liked it / 0-24% friends have seen it / it is crowded	Went - liked it
111011:0	Comedy / Good Critics / Peers liked it / 25-49% friends have seen it / it is crowded	Went-disliked it

The ratio of happy viewers to unhappy viewers is 1.79.

General Comments

The results show in each case that for a given seed, adding random noise to a rule's effective bid dampens the "fad effect" of a movie. In every case, however, the results and associated dynamics also show a clear duality of influence on movie demand--namely, the buzz created by peers who see a movie early, and the influence of movie attributes independent of the buzz.
 

Dynamics

Preliminary observations of the results gave us some insight about changes in the agents' opinions about the movie and their desire to go and see it. For example, early viewers tend to see the movie and enjoy it: viewers after the first few to see and enjoy the movie tend to have similar environments (e.g., crowdedness and number of peers who have seen the movie). The same decision fires because of its success early on in this environment. As the environment changes over time, that advantage is dampened and the rule of "see the movie and dislike it" tends to get chosen. The emerging pattern is that the satisfied viewers, as a proportion of those who have decided to see the movie, starts out fairly close to 1. Over time that proportion declines to anywhere from 2/3 to 1/2, depending on parameters.  Moreover, this pattern was evident in the No Noise treatments. When random noise was added to effective bids, even early on the ration of satisfied viewers to all viewers tended to be close to 1/2, as expected.

The punch line is that people who see a movie early tend to be excited about it, and are captured in our model as satisfied viewers. Essentially, there is a selection bias operating on early viewers. Later viewers, however, are later viewers for a reason--they are not so excited about the movie and tend to be less satisfied with it. (We note the important caveat that the model does not allow for repeat viewing: there is no Leonardo DiCaprio in our world.)
 
 

V. EXTENSIONS AND FUTURE WORK

Several extensions have already been described above. For example, we could easily make the "type space" of the movie multinomial and multidimensional. For example, a "Leonardo DiCaprio effect" could be easily included by expanding the length of the bit string representing environmental messages.

In addition, the initial probability that a decision rule is the one to fire under a particular condition is the same for each possible decision rule. This could be relaxed by altering the initial strength associated with each decision rule. This latter extension is a simple way to implicitly represent preferences in the learning classifier system framework. Alternatively, preferences could be included as part of the environmental conditions. The latter route is worth exploring, because its explicitness is more satisfying.

For a multi-movie setting, the action space of the model could be easily generalized to size n3. The conditions space could also be generalized, to account for heterogeneity in tastes for comedies, the weight of movie critics, and movie budgets. In principle, the multi-movie model could be calibrated with actual data, enabling recommendations of conditions which are favorable for release of a certain type of movie. In addition, for movies with a particular release date (e.g., summer, when many other movies are out there), the model could recommend characteristics a movie should have (e.g., star power).

Although classifier systems and genetic algorithms are complementary to each other, in the present model the genetic action is disabled, meaning that it does not evolve new rules as time progresses -it only uses preexisting ones. The genetic algorithm is built in the system, so it would be very interesting to run simulations and observe the effect evolution would have in the patterns of the agents' preferences.