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Mutual support in agent networks
Wan Ahmad Tajuddin Wan Abdullah Dept of Physics, Universiti Malaya, Kuala Lumpur A .K. M. Azhar Graduate School of Management, Universiti Putra Malaysia, Serdang
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Can we model social/economic systems using (extended) statistical physics?
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Agent models Agents: in free space/ on lattices/ on networks
Interactions: choices – game theoretic – strategies, memories [internal state], information [pertaining to internal state of engaged agent], learning
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Some games people play... Prisoner's dilemma on lattice
Minority game and modifications Deviant's dilemma etc
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This model Agents i, i = 1,...,N, with measure of influence (i).
Random meetings of i with j; i decides to support j or otherwise, depending on a strategy matrix (i (i,j) = 1 (i decides to support j) with probability (0.5+ |(i,)|)/(+ |(i,)|) (i,j) = 0 otherwise is noise level, is situational 6-digit binary number b5b4b3b2b1b0 current value of (i,j) (j,i) if |(i)-(j)| < (i) previously if (i) > (j) previously if |(i)-(j)| < (i) now if (i) > (j) now
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This model (cont'd) j then has increased influence,
(j) → (j) + (i,j)(i) where is a constant Agents are then ranked according to (i), and carries out reinforcement learning quantified by rank change: (i,) → (i,) + Ri' - Ri
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Computational studies
Monte Carlo simulations N = 100 200 iterations (interactions per pair) normalise each time learn for move 1 timestep ago
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a = 0.3, n = 10.0
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strategies
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strategies
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strategies
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strategies – top 10%
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strategies – top 10%
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strategies – top 10%
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influence scatter evolution
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influence scatter evolution
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support evolution
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Learn for immediate move
Learn for move 2 timesteps ago
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a = 0.1 a = 0.5
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n = 5.0 n = 20.0
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conclusions Emergence of structures/heterogeneities
Emergence of successful (?) strategies - understand rationale for strategies Phase space so far homogeneous Relate to real social dynamics?
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