To play the game you must submit a rectangle in the unit square. That is four numbers between 0 and 1.  The first two numbers are the xand y coordinates respectively for the bottom left corner of yourrectangle and the next two numbers are x and y coordinates respectivelyfor the upper right corner of your rectangle.

If someone plays the exact same numbers as you then you are automatically on the same “crew.”

The mark you receive on this assignment will be proportional to the area successfully claimed by your crew divided by 1.2^(n-1) where n is the number of people in your crew.

If your crew’s rectangle overlaps the rectangle of another crew then that overlapped area is disputed. To resolve how much of the disputed area your crew receives thefollowing rule is used.  The length of the perimeter of your undisputedterritory is calculated. Say it is L.  Then the number of people inyour crew is counted up.  Say it is N.  Then N/L is the density of crewfolks along the perimeter of your undisputed area.  There is a borderbetween your crew’s undisputed territory and the disputed territory.Say that border has length B.  Then the force which your crew puts intothe disputed area is
force into disputed area = B * N/L

The other crews that are disputing this area with you do a similarcalculation and which ever crew applies the greater force to thedisputed area counts the disputed area as part of their total area andeveryone else does not get to count it.

Two weird cases, (and hopefully no more but if you find one let meknow）

The first weird case is when a crew has no undisputed area. (Thesimplest way for this to happen is for one crews rectangle to becompletely enclosed within another’s). In this case the enclosed crew’soriginal perimeter is treated as their undisputed perimeter and thecalculations are then made as above.

The second weird case is when there is a disputed area, and all theother area’s that border on it are also disputed.  In this case theconflict is temporarily unresolvable, so it is left along with anyother situations, until all the resolvable disputes have been resolvedby the above rules.  The formerly disputed areas are now treated asundisputed areas making some of the formerly unresolvable conflictsresolvable.  This process is iterated through until all conflicts areresolved.

There is a fair socially optimal strategy in this game, but theremay be temptations to deviate from this socially optimal strategy.  


An alysis ofthis game will include,

• Finding the fair socially optimal strategy profile.
• Determining whether or not the fair socially optimal strategy profile is a Nash equilibrium.
• Determining whether or not this game has any(other?) Nash equilibria
• Some reasoning about how you think the class will play and why.