Experiments in Behavioral Network Science 2: Kings and Pawns Networked Life CSE 112 Spring 2007 Michael Kearns & Stephen Judd

2 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.

3 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) Our immediate agenda: –background and information for game players –system walk-through –compensation details –logistics, ground rules, etc. Please ask questions if you have them!

4 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: –$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! All games will last exactly 2 minutes --- no early stopping! –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

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8 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 –no differential tips Payment rates: –$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

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12 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 –even for centralized computation Relationship to Kings and Pawns: –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!

13 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. –At 3:05, we will stop giving credit for participating. –Don't be late. –GO TO THE BATHROOM BEFORE YOU ARRIVE 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 –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