Experiments in Behavioral Network Science 2: Some Preliminary Analysis of Kings and PawnsSummary of EventsSlide 3Slide 4Slide 5Next 6 SlidesSlide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Experiments in Behavioral Network Science 2:Some Preliminary Analysis of Kings and PawnsNetworked LifeCSE 112Spring 2007Michael Kearns & Stephen Judd2Summary 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 payof–Announced and explained the bug; restarted second set of games•19 diferent 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…3Chain of 6-CliquesIsolated Pairs Rewired Chain P.A. TreeDense P.A. Erdos-Renyi Bipartite4Chain of 6-CliquesIsolated Pairs Rewired Chain P.A. TreeDense P.A. Erdos-Renyi Bipartite5corrected!6Next 6 Slides•Each slide corresponds to one of six diferent 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$0.507P.A. tree (max ~ 0.86)8Bipartite (max 0.75)9Dense P.A. (max ~ 0.73)10Erdos-Reyni (max ~ 0.70)11Clique Chain (max ~ 0.59)12Rewired Chain (max ~ 0.66)13Competitive 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)14Competitive 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)15Cumulative 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:
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