EVOLUTION OF ECONOMIC ENTITIES CONTROLLED BY INTERACTING AGENTS UNDER VARYING SPATIOTEMPORAL ECONOMI

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EVOLUTION OF ECONOMIC ENTITIES CONTROLLED BY
INTERACTING AGENTS UNDER VARYING
SPATIO-TEMPORAL ECONOMIC CONDITIONS

• Marcel AUSLOOS1 Paulette CLIPPE1
• Janusz MISKIEWICZ2 Andrzej PEKALSKI2
• 1 SUPRATECS, B5, University of Liège,
  Euroland
• 2 Institute of Theoretical Physics, University
  of Wroclaw, Poland

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REFERENCES (published work) (1)

• M.Ausloos, P.Clippe, and A.Pekalski, "Simple
  model for the dynamics of correlation in the
  evolution of economic entities under varying
  economic conditions",
• Physica A, 324 (2003) 330-337
• (http//arXiv.org/abs/nlin/0210041)
• M. Ausloos, P. Clippe and A. Pekalski,
  "Evolution of economic entities under
  heterogeneous political/environmental conditions
  within a Bak-Sneppen-like dynamics",
• Physica A 332 (2004) 394-402
• (http//arXiv.org/abs/physics/0309007)
• J. Miskiewicz and M. Ausloos, "A logistic map
  approach to economic cycles. (I). The best
  adapted companies",
• Physica A 336 (2004) 206-214
• (http//arXiv. org/abs/cond-mat/0401147)

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REFERENCES (published work) (2)

• M. Ausloos, P. Clippe and A. Pekalski, "Model
  of macroeconomic evolution in stable regionally
  dependent economic fields",
• Physica A 337 (2004) 269-287.
• (http//arXiv. org/abs/cond-mat/0401144)
• M. Ausloos, J. Miskiewicz, and M. Sanglier,
  "The durations of recession and prosperity
  does their distribution follow a power or an
  exponential law?",
• Physica A 339 (2004) 548-558
• (http//arXiv.org/abs/cond-mat/0403143)
• M. Ausloos, P. Clippe, J. Miskiewicz, and A.
  Pekalski, "A (reactive) lattice-gas approach to
  economic cycles",
• Physica A 344 (2004) 1-7
• (http//arXiv.org/abs/cond-mat/0402075)

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Table of content

• Title and references
• General considerations
• Basic model
• Parameters
• Results concentration, fitness, cycles,
• Cases of best fitted companies
• Cycles and chaos
• Cases of delayed policy implementation
• Cycles and chaos

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Considerations

• Delocalization globalization processes!
• Time and space varying economic conditions?
• Berlin wall effect change in volume
• Role of agent interactions
• connect macro-economy to micro-model
• Economic cycles ?
• Chaotic behaviours?
• Control parameters

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(initial) Model

• The world is a lattice with square symmetry
• With different (all equal in size) regions 3 !
• West wonderful ! Exist company concentration c
• Each company is a scalar number f 0,1
• If not fit w.r.t. (s F) gt company disappears
• Companies must move one step at a time
• and interact
• Business plan b merging or creating spin-off
• N.B. Berlin wall effect change in volume

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Algorithm

• Choose initial concentration c(0) in I, II, III
• Give some random f value to each company
• Check if company survives under conditional
  probability
• If company can move, move it
• Look for partner merge with probability b
• create spin off with probability 1-b

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Delocalization Number of firms in regions I,
II, III vs. t, for s ... and F0.3, 0.5, 0.6
0.9
0.4
1.7
1.3
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Time for invasion
Different s regimes?
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Globalization Average fitness in regions I,
II, III vs. t, for s and F0.3, 0.5, 0.6
0.9
0.4
1.3
1.7
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Delocalization c(x t) for F 0.5, 0.4,
0.3




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Cycle for F0.4, 0.5, 0.6 when s 1.75
...
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Asymptotic fitness vs. s for F 0.3, 0.5, 0.6
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Normalized asymptotic values (b) Total
asymptotic number of born firms
Selection Pressure s gt Phase Transition
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Cases of best fitted companies cycles and chaos

• Mean field approximation
• Sort of lattice gas reaction diffusion model
• Predator-prey model evolution equation
• gt one parameter business plan b
• Whence study Lyapunov exponents for finding
  stability, cycling, chaos
• ( Relaxation time studies)

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Lyapunov exponent(s)
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Merging probability phase diagram
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Relaxation time vs. merging probability
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Cases of delayed policy implementation cycles
and chaos

• Consider that in the logistic map,
• i.e. high order (Verhulst) evolution equation,
• the environmental factor value (r 1-x(t) is NOT
  taken into account in the immediate next time
  step
• but at a later T time, i.e. as if r(t-T)
• or as if r 1-x(t-T)

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Evolution equation
where
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Best fitted companies asymptotic stability
c(t T) - role of initial concentration
T4
T3
T12
T5
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Best fitted companies - role of time delayed
information
T3
T2
T5
T12
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Conclusions

• Simple microscopic (agent based) model for
  macroeconomy questions
• Role of local (economic) field conditions
• Role of local (competitive) conditions
• Role of initial conditions
• Role of time delay policy implementation

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Parameters

• lattice type (could be off-lattice treatment)
• region sizes and numbers
• initial concentrations
• company is defined by one scalar number f
  !!!!!
• selection pressures s (and sequences)
• local field constraints F (and sequences)
• types of motion (and sequences)
• types of company interactions (and sequences)
• business plan priorities b !!! (and sequences)
• evolution equations for f (and sequences)