Behavioral Experiments in a
Network Formation Game
Prof. Michael Kearns
Networked Life
Spring 2010
Basic Game Purpose: Unanimity
• Each player can choose to be Red or Blue.
• Each player has a set of neighbors, and can see
•
•
the color choice of those neighboring players.
If you all agree within one minute on the same
color choice, you all get paid; if not, you all get
nothing.
Everyone can pay to acquire new neighbors.
Local and Remote Vertices
• your immediate neighbors are shown in a
conventional
network diagram.
• other (remote)
vertices are
represented in
the lower left.
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Neighborhood Representation
• You and your color are represented by a
doubly-circled node with “YOU” on it.
• All other visible vertices are your neighbors,
each labeled with its total degree.
• There are 36 players (vertices) in total.
• An edge will be shown in light gray between
you and each of your neighbors.
• A darker edge is drawn between neighbors
who are themselves neighbors.
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Neighborhood Representation
• YOU
• 13 neighbors
• one has
degree 19
• one has
degree 4
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Remote Vertex Representation
• Any vertex not your immediate neighbor is
represented in the lower left.
• The display has 2 axes: Distance & Degree.
• Distance is the length of the shortest path
between you and it; Degree is the number
of neighbors it has.
• Every remote vertex appears as a white
ball on the Distance-Degree grid.
• If a white ball has a “*” inside, it means
there are 2 or more such vertices.
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Remote Vertex Representation
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Player Actions
• You can change your color at any time.
• You can purchase an edge at any time
(unless you have exhausted your budget).
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Changing your Color Choice
• click one of the color buttons.
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Buying an Edge
1. Consider the distance and degree, and
choose a white ball.
2. Click and release it.
3. An edge will be constructed and a new
vertex will appear and grow in your local
network, which will adjust to display it.
4. Edges cannot be rescinded. Their cost
cannot be returned.
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Buying an Edge (example)
• this player is purchasing
a link to a vertex at
distance 2 and of degree 4
• the ball will highlight in
yellow until released
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Failing to Buy an Edge
•
•
Sometimes, your selection will not be
honored:
1. If you have no remaining budget
2. If your selection is no longer valid
The first vertex to request an edge gets
charged for it. If you ask for an edge that
someone else just bought, you won’t have
to pay for it.
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Seeing other’s Actions
• As soon as a neighbor changes colors, your
display will change to show it.
• If someone buys an edge to you, your display
will change to reflect it:
- by adding them to your neighborhood, and adjusting
the layout
• If one of your neighbors buys an edge, your
display will change to reflect it:
- by incrementing his degree
- by showing the new edge, if it is to another neighbor
• Remote vertices may increase their degree or
decrease their distance to you
- grid representation will be updated accordingly
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Initial Conditions
• When you first start, your vertex will have no
color (white), and all others will appear white
too.
• You must choose a
color before you will
be shown the other
vertices’ colors.
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Other Elements of the GUI
game status bar
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Other Elements of the GUI
elapsed time bar (full width is 60 seconds)
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Other Elements of the GUI
potential payoffs
(was $1 for red and $4 for blue
before buying 3 edges @ $0.10 each)
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Other Elements of the GUI
budget bar
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Overview of the Evening
• There will be 99 “rounds”, each 1 minute long.
• Each round is unrelated to all other rounds.
• You get assigned to nodes randomly.
• Your neighbors change randomly on each
round; you do not know who they are.
• In some rounds, we will start with the empty
network (no edges); in others, there will be
some initial, “free” network already in place.
• Your take-away pay is the sum of what you
make in each round.
• There will be an exit survey when games end.
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