Diapositiva 1

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Coevolution and complex fitness landscapes
Juan G. Diaz Ochoa
Institute for theoretical physics Bremen
University
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• How emerges cooperation in a system? (elements of
  the system can be agents)
• The cooperation depends on the statistics of the
  system..... Or depends on individual
  characteristics of the elements?
• Non-selfish behavior assures large individual
  fitness. But cooperation between elements
  increases the fitness of the elements into the
  cooperators cluster.

Game theory as paradigm

• Elements have advantage if they could remember
  previous interactions gt correlation to previous
  interactions.... Or, is possible that not only
  memory, but a kind of individual choice, can
  increase the fitness of the elements?

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I. Formalism
Prisoners dilemma
B
A
D
C
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II. Model
...
X(t)
X(t-1)
St
M. Nowak et al., Nature, 359, 826 (1992)
are the movements in the past..
(t)
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II. Model
Rational choice
Preference vector for each agent
Grid of elements with periodic boundary
conditions.
E.A.D. Hammock et al., Science, 308, 1630
(2005) E. Ramirez et al. Physica A, 374, 369
(2007)
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III. Results
Memory distribution no preferences
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 Test Stochastic systems with a deterministic
limit a finite population.
III. Results
Mixed strategies
Auto correlation function
Cooperators as a function of the time
Individual realizations follow a Langevin equation
Gaussian noise
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III. Results
Distribution of total number of cooperators in
for rigid and flexible interaction matrices.
Cooperators as a function of time (large number
of memories)
Slower grow of envy when matrices are flexible
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III. Results
Number of elements with memory M

Change in the amplitude of the distribution
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IV. Conclusions

• The population of different memories may fit with
  a Levy function.
• Non symmetric games introduces changes in the
  evolutive behavior of elements with different
  memory. There is also a slower drift to
  cooperation.

Coevolutive processes can be a mix of rational (a
selection of better fitness functions) and an
irrational process (response according to
information stored in a memory).