Agents in Economic Markets and Games
135
used an extra variable called election which helped compare results with rational expectations of firms. This was similar to the expected strategy used in
the coevolutionary approach compared to actual played strategies. Arifovic [9]
argued that the fluctuating behavior eventually converging to the equilibrium
is not possible by standard approaches like least square methods, previously
used in traditional economic theories. Dawid [47] supported the argument by
saying that “genetic algorithm learning yielded qualitatively similar aggregate
behavior than a population of human agents. The match is not perfect since
the amplitude of oscillations decreases faster in genetic algorithms compared
to the other approaches, such as least square learning method, these results
are very satisfying.”
Altavilla et al. [6] experimented with heterogeneous firms and compared
the results to the Bertrand model. Friedman [70] supported the idea that
players in reality behaved as if they have formulas in their heads. “It is only
a short step from these examples to the economic hypothesis that under a
wide range of circumstances individual firms behave as if they were seeking
rationally to expected returns”. Price [152] compared the evolution of price
in Cournot and Bertrand models.
TABLE 6.2: Evolving Cournot characteristics for each firm.
Objective
Find the maximum profit that can
be earned when competing with other
firms.
Strategy representation
Quantity production represented as binary string of 9 bits can be converted
into a numeric value.
Fitness case
Profit of the firm.
Selection scheme
Fitness proportionate roulette wheel selection.
Mutation rate
0.01, 0.03, 0.1
Crossover rate
0.1, 0.5, 0.7
Length of simulation
500
Number of runs averaged 20
The output the firms produce is represented as a string of binary digits.
This allows the genetic operations, like crossover and mutation, to be performed easily on a numerical value. For example, 000100010 = (0 × 2
8 ) + (0 ×
2
7 ) + (0 × 2
6 ) + (1 × 2
5 ) + (0 × 2
4 ) + (0 × 2
3 ) + (0 × 2
2 ) + (1 × 2
1 ) + (0 × 2
0 ) = 34.
The crossover and mutation rates help introduce variety in the population
of strategies in the database. These can be introduced with different rates
to allow divergence in the strategy population, at the same time preventing
strategies from converging before all strategies have been tried.
Figure 6.10 depicts each firm having a strategy base which is maintained
in the firm’s memory. The strategy base looks like a database table with the
135
used an extra variable called election which helped compare results with rational expectations of firms. This was similar to the expected strategy used in
the coevolutionary approach compared to actual played strategies. Arifovic [9]
argued that the fluctuating behavior eventually converging to the equilibrium
is not possible by standard approaches like least square methods, previously
used in traditional economic theories. Dawid [47] supported the argument by
saying that “genetic algorithm learning yielded qualitatively similar aggregate
behavior than a population of human agents. The match is not perfect since
the amplitude of oscillations decreases faster in genetic algorithms compared
to the other approaches, such as least square learning method, these results
are very satisfying.”
Altavilla et al. [6] experimented with heterogeneous firms and compared
the results to the Bertrand model. Friedman [70] supported the idea that
players in reality behaved as if they have formulas in their heads. “It is only
a short step from these examples to the economic hypothesis that under a
wide range of circumstances individual firms behave as if they were seeking
rationally to expected returns”. Price [152] compared the evolution of price
in Cournot and Bertrand models.
TABLE 6.2: Evolving Cournot characteristics for each firm.
Objective
Find the maximum profit that can
be earned when competing with other
firms.
Strategy representation
Quantity production represented as binary string of 9 bits can be converted
into a numeric value.
Fitness case
Profit of the firm.
Selection scheme
Fitness proportionate roulette wheel selection.
Mutation rate
0.01, 0.03, 0.1
Crossover rate
0.1, 0.5, 0.7
Length of simulation
500
Number of runs averaged 20
The output the firms produce is represented as a string of binary digits.
This allows the genetic operations, like crossover and mutation, to be performed easily on a numerical value. For example, 000100010 = (0 × 2
8 ) + (0 ×
2
7 ) + (0 × 2
6 ) + (1 × 2
5 ) + (0 × 2
4 ) + (0 × 2
3 ) + (0 × 2
2 ) + (1 × 2
1 ) + (0 × 2
0 ) = 34.
The crossover and mutation rates help introduce variety in the population
of strategies in the database. These can be introduced with different rates
to allow divergence in the strategy population, at the same time preventing
strategies from converging before all strategies have been tried.
Figure 6.10 depicts each firm having a strategy base which is maintained
in the firm’s memory. The strategy base looks like a database table with the