1. Experiments in Behavioral Network Science 2: Some Preliminary Analysis of Kings and Pawns Networked Life CSE 112 Spring 2007 Michael Kearns & Stephen Judd

2. 2 Summary of Events Held 2 x 19 Kings and Pawns experiments First 19 with simpler, no-tips mechanism Second 19 with tips by kings permitted –Glitch in this interface! –When a King, sometimes had to click on Pawn to discover payoff –Announced and explained the bug; restarted second set of games 19 different networks –Each run once under no-tips and tips mechanisms – 1 network of 18 isolated pairs –3 preferential attachment trees –3 denser preferential attachments –3 Erdos-Renyis –3 bipartite networks –3 trials of chain of 6-cliques –6 chains of 6-cliques with 20% random rewiring Questions –Did the tips influence behavior and performance? –Did network structure influence behavior and performance? –Many, many others…

3. 3 Chain of 6-CliquesIsolated PairsRewired ChainP.A. Tree Dense P.A.Erdos-RenyiBipartite

4. 4 Chain of 6-CliquesIsolated PairsRewired ChainP.A. Tree Dense P.A.Erdos-RenyiBipartite

5. 5 corrected!

6. 6 Next 6 Slides Each slide corresponds to one of six different network generation models –e.g. preferential attachment trees, Erdos-Renyi, etc. Each row corresponds to one of three trials of networks of that type Left column: for the non-tips trial, –number of Kings vs. time (blue curve) –number of fighting Kings vs. time (red curve, always less than blue curve) Middle column: same as left, but for tips trial Right column: average rate of pay per player per minute vs. time, –non-tips: black –tips: green –computed as (#kings - #fighting kings)x$1 + (#pawns)x$0.50

7. 7 P.A. tree (max ~ 0.86)

8. 8 Bipartite (max 0.75)

9. 9 Dense P.A. (max ~ 0.73)

10. 10 Erdos-Reyni (max ~ 0.70)

11. 11 Clique Chain (max ~ 0.59)

12. 12 Rewired Chain (max ~ 0.66)

13. 13 Competitive Ratio (=total payoff/max possible in network): non-tips (x) vs. tips (y) (1: PA trees; 3: Dense PA; E: Erdos-Renyi; B: Bipartite; 0: Clique Chain; 20: Rewired Chain; P: Pairs)

14. 14 Competitive Ratios in Order of Experiments: non-tips (cyan), tips (magenta) (1: PA trees; 3: Dense PA; E: Erdos-Renyi; B: Bipartite; 0: Clique Chain; 20: Rewired Chain; P: Pairs)

15. 15 Cumulative and Max Instantaneous Competitive Ratios in Order of Experiments: cumulative (two leftmost bars in each group of four); instantaneous (rightmost two bars) (1: PA trees; 3: Dense PA; E: Erdos-Renyi; B: Bipartite; 0: Clique Chain; 20: Rewired Chain; P: Pairs)

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