Experiments in Behavioral Network Science 2 Some Preliminary

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

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 – – – • 19 different networks – – – – • 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 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… 2

Isolated Pairs Dense P. A. Chain of 6 -Cliques Rewired Chain Erdos-Renyi P. A. Tree Bipartite 3

Isolated Pairs Dense P. A. Chain of 6 -Cliques Rewired Chain Erdos-Renyi P. A. Tree Bipartite 4

corrected! 5

Next 6 Slides • Each slide corresponds to one of six different network generation models – • • Each row corresponds to one of three trials of networks of that type Left column: for the non-tips trial, – – • • e. g. preferential attachment trees, Erdos-Renyi, etc. 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 6

P. A. tree (max ~ 0. 86) 7

Bipartite (max 0. 75) 8

Dense P. A. (max ~ 0. 73) 9

Erdos-Reyni (max ~ 0. 70) 10

Clique Chain (max ~ 0. 59) 11

Rewired Chain (max ~ 0. 66) 12

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) 13

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) 14

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) 15

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