Behavioral Experiments in a Network Formation Game

Prof. Michael KearnsNetworked Life

Spring 2010

• 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.

Basic Game Purpose: Unanimity

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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 Edges cannot be rescinded.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 purchasinga 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 budget2. 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.