experiments in behavioral network science 2: some preliminary analysis of kings and pawns networked...
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![Page 1: Experiments in Behavioral Network Science 2: Some Preliminary Analysis of Kings and Pawns Networked Life CSE 112 Spring 2007 Michael Kearns & Stephen Judd](https://reader030.vdocument.in/reader030/viewer/2022032706/56649d775503460f94a58b8a/html5/thumbnails/1.jpg)
Experiments in Behavioral Network Science 2:
Some Preliminary Analysis of Kings and Pawns
Networked LifeCSE 112
Spring 2007Michael Kearns & Stephen Judd
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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…
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Chain of 6-CliquesIsolated Pairs Rewired Chain P.A. Tree
Dense P.A. Erdos-Renyi Bipartite
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Chain of 6-CliquesIsolated Pairs Rewired Chain P.A. Tree
Dense P.A. Erdos-Renyi Bipartite
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corrected!
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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
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P.A. tree (max ~ 0.86)
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Bipartite (max 0.75)
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Dense P.A. (max ~ 0.73)
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Erdos-Reyni (max ~ 0.70)
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Clique Chain (max ~ 0.59)
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Rewired Chain (max ~ 0.66)
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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)
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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)
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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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