Experiments in Behavioral
Network Science 2:
Kings and Pawns
Networked Life
CSE 112
Spring 2007
Michael Kearns & Stephen Judd
Crucial Information
•
•
•
•
The experiments take place tomorrow, March 16, beginning at 3 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.
2
Overview
• Experiments in collective problem-solving in network settings
• As with the February 16 Coloring & Consensus experiments:
–
–
–
each participant sits at a workstation and interacts with others only through the system
each participant controls the behavior of a single vertex in a network of 36 vertices
each participant has only a local, “first neighborhood” view
•
•
You see your own vertex, your neighbors (black edges), and connections between neigbhors (red edges)
each neighbor annotated by their number of non-local, “invisible” neighbors
–
–
network structure changes from experiment to experiment
two different game types (even more closely related than Feb 16)
–
–
–
–
background and information for game players
system walk-through
compensation details
logistics, ground rules, etc.
• Our immediate agenda:
• Please ask questions if you have them!
3
Kings and Pawns, Version 1
•
•
•
•
•
Each player controls a vertex
Player action is to choose to be either a “King” or a “Pawn”
Being a King pays more highly than being a Pawn --- unless you have
a neighboring King
Furthermore, pay is accumulated continuously at a rate that
depends on your current choice and those of your neighbors
Payment rates:
–
–
–
–
•
All games will last exactly 2 minutes --- no early stopping!
–
•
•
$1 per minute for being a King with no neighboring King (“Lone King”)
$0.50 per minute for being a Pawn
$0 per minute for being a King with a neighboring King (“Fighting King”)
Again, rates are expressed per minute, but are accumulated continuously!
Unlike Coloring and Consensus, all players receiving max possible payoff no possible
19 experiments total
In principle, an individual could make $38 on Version 1
4
5
6
7
Version 2:
Kings and Pawns with “Tips”
•
•
•
Same as before, but now Kings can offer “tips” or side
payments to neighboring pawns
A Solo King can offer any fraction of its $2/minute to
neighboring pawns
This fraction will be split equally among all neighboring pawns
–
•
Payment rates:
–
–
–
–
•
•
•
no differential tips
$1/min – tips for being a Lone King
$0.50/min + tips (summed over all neighboring Lone Kings) for being a Pawn
$0/min for being a Fighting King
Again, payment accumulated continuously based on current state
All games will last exactly 2 minutes; no early stopping
19 experiments total
Individuals could again make $38 on Version 2
8
9
10
11
A Related Computational Problem
•
•
•
•
For any network or graph G, an independent set in G is a set S of vertices
such that no pair of vertices in S are connected by an edge in G
The “opposite” or dual of a clique
Maximum independent set: largest possible in G
Computationally difficult to compute a maximum independent
–
•
Relationship to Kings and Pawns:
–
–
–
•
even for centralized computation
expensive of being a Conflicting King + Pawn profit  encourages Kings to be an independent set
most profitable to be a Solo King  encourages set of Kings to be as large as possible
in particular, maximum social welfare achieved by a maximum independent set
However, play however you like!
12
Important Notes
•
•
•
•
Experiments are tomorrow (Fri March 16) at 3 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 3 PM SHARP.
–
–
–
•
You must be present for the entire session in order to receive compensation or credit
–
–
•
3 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
–
–
–
–
–
–
•
At 3:05, 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
13