Implementation Assignment

Background

Panini is a brand name of an Italian firm which produces collectable stickers. It started in the 1960s with its football (soccer) collections, which soon became a cultural phenomenon during the following decades.

Every year, Panini publishes a set of albums with placeholders for pictures. Each collector then purchase packs containing random stickers that she uses to fill the album.

As an example, the 2006 FIFA World Cup Panini album contains placeholders for 596 stickers representing the 32 qualified national teams. Each pack of 5 stickers were sold for CHF 0.90, which brings the overall price of filled album to a bit more than CHF 105.--, should there be no inevitable duplicates.

To expedite the filling of the albums, collectors resort to swapping stickers with their friends, which explains the cultural impact of the Panini model.

Research question

We would like to investigate how the collectors' spatial connectivity to other collectors affect  the speed at which the albums can be filled. We will consider three type of spaces:

• the Internet: each collector can exchange cards with every other collector;
• the Earth: each collector can exchange cards with his neighbors;
• the Prison: each collector is on his own and cannot exchange cards.

The question we would like to answer is what is the average cost and time to fill an album, for each type of space mentioned above, as well as how much revenue the Panini company can expect to make.

Model design

There are 225 people trying to fill their album, which is composed of 596 placeholders for stickers. Every day, the collectors trade their duplicate stickers with the collectors they are connected with. More precisely, the models works as follows.

Each time step consists of the following sub-procedures:

• All collectors purchase one pack of 5 Panini stickers for a cost of CHF 0.90, if their album is not filled yet.
• Then all collectors are activated in random order, and each collector does the following:
  1. Contact each of its neighbors
  2. Exchange the maximum number of stickers with the neighbor at the exchange rate 1:1 (for each of the neighbor's stickers the collector needs, it pays one of its duplicates the neighbor needs).

In the Internet space, each collector can interact with all the other collectors. For the Earth type of space, use a toroidal (wrap-around) grid with a dimension of 15x15 cells. Here, we define the neighborhood of a collector as its Moore neighborhood of radius 2. In the Prison topology, the collectors cannot interact with any other collector.

Assignment

Create a computer program that simulates the exchange of stickers among the group collectors. You are free to implement it in the language of your choice, but we recommend the use of Java with RePast agent-based modeling toolkit. You should answer the following questions:

• What is the average cost to fill an album for each of the spaces?
• What is the average number of time steps until an album is filled?
• For each of the spaces, how much revenue can Panini expect to make in our artificial world? Assume the empty album to be given away to collectors at no cost.

Send an overview of your findings as well as the source code of your model to Luc Girardin <girardin@icr.gess.ethz.ch> by March 18, 2008.

Extensions

If you are addicted to the Panini model, then you can try some of the following extensions:

• How does a small-world or random network affect the effectiveness?
• What is the effect of not uniformly printing stickers?
• Does the number of stickers per pack play a role?