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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