Neil F. Johnson, Sean Gourley, Sehyo C. Choe, David Smith Pak Ming Hui

1. Multi-Agent Populations & Networks: Competition for Limited Resources numerical simulations Binary Agent Resource models real world biology sociology See also Financial Market Complexity (Oxford University Press, 2003) theory Crowd-Anticrowd theory  analytic, ‘many-body’ description of dynamical correlations Neil F. Johnson, Sean Gourley, Sehyo C. Choe, David Smith Pak Ming Hui Oxford University Chinese University of Hong Kong n.johnson@physics.ox.ac.uk

2. histories action -1 f f d d action +1 b e b e S S c c N-agent network with resource level a a strategies reward structure 2 possible winning outcomes history at time t . . . . 0 1 updated history at time t +1 . . . . 1 0 agent memory m = 2

3. histories action -1 f f d d action +1 b e b e S S c c N-agent network with resource level a a strategies history at time t . . . . 0 1 updated history at time t +1 . . . . 1 0 agent memory m = 2

4. Complex agent-based dynamic networke.g. B-A-RBinary Agent Resource system system’s time evolution global resource level L[t] = L time … + 5 … + 1 … + 4 … + 3 … + 2 What affects the typical fluctuation size  and hence efficient use of global resource?

5. Large crowds   >> 0  wastage Wastage reduced by smaller crowds, using e.g. • stochastic strategy choice • mixed-ability population: large m and small m •  better for large m and small m agents Minority Game  no network Challet and Zhang crowd - anticrowd pairs execute uncorrelated random walks sum of variances  theory ~ numerical .. also works for general B-A-R systems typical fluctuation size coin-toss walk step-size # of walks

6. Key to collective dynamics: Heterogeneity in strategies within population  single macrostate  many microstates strategy space inter-agent network connections

7. Crowd-Anticrowd theory typical fluctuation size strategy scores small m ‘crowded’ regime no network See cond-mat/0306516 strategy allocation matrix 

8. Analytic Crowd-Anticrowd Theory vs. Numerical Simulation typical fluctuation size Thermal Minority Game Basic Minority Game  vs. m  vs.  Numerical results: Garrahan, Sherrington MG: Challet and Zhang, Numerical results: Savit et al.

9. Crowd-Anticrowd theory with network typical fluctuation size

10. Analytic Crowd-Anticrowd Theory vs. Numerical Simulation

11. Proof that minimum in wastage  can occur at lowconnectivity p Crowd-Anticrowd Theory at low p: n-mer gas e.g. 2 dimers, 4 monomers number of n-mers at given p

12. Details of Crowd-Anticrowd theory . . .

22. m1= 3 m2= 6

23. Multi-Agent Populations & Networks: Competition for Limited Resources numerical simulations Binary Agent Resource models real world biology sociology See also Financial Market Complexity (Oxford University Press, 2003) theory Crowd-Anticrowd theory  analytic, ‘many-body’ description of dynamical correlations Neil F. Johnson, Sean Gourley, Sehyo C. Choe, David Smith Pak Ming Hui Oxford University Chinese University of Hong Kong n.johnson@physics.ox.ac.uk