1. 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

2. Can we model social/economic systems using (extended) statistical physics?

3. 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

4. Some games people play... Prisoner's dilemma on lattice
Minority game and modifications
Deviant's dilemma
etc

5. 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

6. 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

7. Computational studies
Monte Carlo simulations
N = 100
200 iterations (interactions per pair)
normalise  each time
learn for move 1 timestep ago

8. a = 0.3, n = 10.0

9. strategies

10. strategies

11. strategies

12. strategies – top 10%

13. strategies – top 10%

14. strategies – top 10%

15. influence scatter evolution

16. influence scatter evolution

17. support evolution

18. Learn for immediate move
Learn for move 2 timesteps ago

19. a = 0.1
a = 0.5

20. n = 5.0
n = 20.0

21. conclusions Emergence of structures/heterogeneities
Emergence of successful (?) strategies
- understand rationale for strategies
Phase space so far homogeneous
Relate to real social dynamics?