Experiments in Behavioral
Network Science
Networked Life
CSE 112
Spring 2007
Michael Kearns & Stephen Judd
Crucial Information
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The experiments take place tomorrow, Feb 16, beginning at 5 PM sharp.
Please arrive a few minutes early.
The location is 207 Moore. Find out how to get there well in advance.
Go to the bathroom before you arrive.
You are responsible for showing up if you’re on the list. No excuses.
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Overview
• Experiments in collective problem-solving in network settings
• Now in their third year
– early efforts: pen-and-paper in-class exercises for several problems
– have gradually become more systematic and ambitious
– last year: graph coloring system, hefty cash payouts, scientific paper
• Directly related to almost all class themes
– we’ll discuss (and you will analyze) the results in due course
• Our immediate agenda:
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background and information for game players
system walk-through
compensation details
logistics, ground rules, etc.
• Please ask questions if you have them!
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The Graph Coloring Game
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Each player controls a vertex
Player action is to choose a color from a fixed set
Graph is properly colored if:
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Cellphone ringtones; specialization within an organization; scheduling
Player “goal”:
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choose a color that is different from those chosen by all neighbors
Minimum number of colors required:
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for every edge, vertices at each end are different colors
called the chromatic number of the graph
all coloring experiments will use exactly this many colors
Brief comments on coloring:
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notoriously difficult computational problem (even centralized or approximate)
k-clique forces at least k colors, but constraints can be much more subtle
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A Properly Colored Graph
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A Not Properly Colored Graph
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The Consensus Game
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Somewhat the “opposite” of coloring
Each player controls a vertex
Player action is to choose a color from a fixed set
This time, goal is for all players to choose the same color
Player “goal”: choose a color that is the same as those chosen by all neighbors
A basic problem of coordination or deciding on a convention
Minimum number of colors required: 1
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but to create a challenging coordination problem, we’ll give you many
Brief comments on consensus:
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trivial centralized computational problem
and the system will prevent trivial solutions (first button, conventions…)
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A Solved Consensus Game
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An Unsolved Consensus Game
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Purpose of Studies
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We are interested in how people solve problems on networks...
– As a group
• “collective dynamics” --- coordination is important
• search & navigation (Travers&Milgram, Kleinberg, Watts,…)
• other problems?
– With each person seeing only a small part of the graph
• confusion due to limited view is important
– Without coordinated, centralized strategies
– Under differing network structures
• course theme: how does network structure influence outcomes?
– Under varying problem types
• start with coloring and consensus; later sessions will examine other problems
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Graphs and Subgraphs
• Graph (a.k.a. Network)
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set of nodes, set of edges that join some pairs of them
the nodes adjacent to a given node are “neighbors”
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one given node + all its neighbors
all the edges between those nodes
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will not have global views of the network!
will also show you how many “other” neighbors your neighbors have
• First Neighborhood Subgraph
• In all experiments, players will have first-neighborhood views
• Rationale: “Maximum” plausible info available to individuals
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Example of a
First-Neighborhood Subgraph
subgraph
overall graph
(of n8 and all its neighbors)
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A Player’s View: Example
subgraph
display
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Player’s View: Details
• Names of nodes have been removed
– your neighbors will always be anonymous
• The node the player controls is labeled “you”
• Edges that connect to the larger graph:
– have been removed
– # of them shown in the node with a “+”
• Edges from “you” to neighbors are black
• Edges between your neighbors are red
• Location of a node on the page indicates nothing!
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Global Aspects of Game Design
• Global Graphs:
– always connected
– edges chosen randomly according to some generative model
– details purposely withheld for now
• 1 node ↔ 1 player
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as many nodes in the overall graph as there are players
each node has one controllable property
each player controls exactly one node
players are assigned to nodes in random, unbiased fashion
• Game is always solvable
– there is a solution where everyone can get paid on every game
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Details of User Interface
• Player View
– a graph of several nodes and edges, peculiar to you alone
• first-neighborhood subgraph of one big network, in which you control one
node. Your node is labeled with “you”.
• You DO NOT see the whole network!
– each node will take on a color.
• Actions
– several colored buttons; just click on them to change color
– each button click will cause YOUR node to change color within 200
milliseconds. If it does not change, either the game is finished, or it
is suspended, or there is a system problem.
– if a problem persists, please raise your hand and tell us.
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Player Interface
• status bars
• graph panel
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• button
Status Bars
• game progress bar:
• game status bar:
measure of global progress
what’s happening
• elapsed time bar:
• your current payoff:
• payoff definition:
game ends when bar completes
your pay if game ends NOW
just words to remind you
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Progression of a Single Game
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Your view appears; no buttons work
Supervisor says something; you ask questions
Supervisor starts the game; buttons become live
Players click, timer runs, solution detector runs
Game stops; buttons inactive again
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time ran out
global solution found
supervisor suspended it due to some problem
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Any time a global solution is reached, game automatically ends
• Game panel disappears
• Ending a game:
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global solution: no “conflicts” anywhere in the network
coloring: all edges have different colors
consensus: all vertices have same color
All games end automatically after 3 minutes (180 seconds)
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elapsed time progress bar shows how much has passed
will also call out countdown warnings
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Progression of Entire Session
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Logging people onto workstations
Quick review + demo game
18 Coloring games, each with different network
18 Consensus games, each with different network
Exit survey
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Compensation Details
• Participants will be financially compensated
• Compensation will be in accordance with performance
– thus, different participants may receive different amounts
• Compensation given only for “completed” games
– completed games: global solution found or 3-minute limit reached
– no compensation for games with system problems, protocol violations, browser
breakdowns, power failures, misbehavior, acts of God, etc.
• For each completed game, individual payoffs are:
– coloring:
• $2 if game ends and you are a different color than all neighbors
• $0 if game ends and you have the same color as one or more neighbors
– consensus:
• $2 if game ends and you are the same color as all neighbors
• $0 if game ends and you have a different color than one or more neighbors
• Note: Payoffs are “selfish” or “local” despite global objective
• Max individual payoff: $2 x 36 games = $72
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• Compensation will be distributed on a later date; details TBD
Some Aspects of Play
• Communication
– No communication is permitted except through the system
• this will be strictly enforced and taken seriously
– You have no formal way of discussing things with your neighbors,
and no way of describing the state of the graph you see.
– Your neighbor can see your color, just as you can see theirs
• Changeability
– you can change the color of your node as often as you want
– there is no cost to changing or pausing
– payoff is calculated only on the final state
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Important Notes
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Experiments are tomorrow (Fri Feb 16) at 5 PM
Experiments will take place in the workstation lab of 207 Moore.
Please find out how to get there well in advance
We will begin seating for the experiments at 5 PM SHARP.
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You must be present for the entire session in order to receive compensation or credit
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7 PM end time is only approximate
If you can’t stay for the entire session, don’t come and let us know NOW
There will be various ground rules you are expected to follow
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At 5:05, we will stop giving credit for participating.
Don't be late.
GO TO THE BATHROOM BEFORE YOU ARRIVE
No talking, except to raise hand an ask questions of proctors
No other attempts at communication with other participants
No doing anything with the computers except as instructed
Pay full attention at all times: no reading material, iPods, etc.
TURN YOUR CELL PHONES OFF
Best model for how to behave: Pretend this is a final exam
Violations will result in dismissals without compensation or credit
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