Artificial Economic Agents with Heterogeneous Cognitive Capacity and Their Economic Consequences: St

1
Artificial Economic Agents with Heterogeneous
Cognitive Capacity and Their Economic
Consequences Study Based on Agent-Based Double
Auction Market Simulations

• Shu-Heng Chen
• National Chengchi University,
• Taipei, Taiwan

Tina Yu Memorial University Of Newfoundland,
Canada
2
Contents

• Cognitive Capacity of Economic Agents
• Modeling Agents with Heterogeneous Cognitive
  Capacity using Genetic Programming
• An Agent-Based Artificial Double-Auction Market
• Market Simulation Results
• Analysis and Discussion
• Concluding Remarks

3
Modeling Human Cognitive Capacity

• In Experimental Economics, there is a growing
  trend to include intelligence as an explicit
  control variable in market simulation.
• In this way, the simulation results would allow
  us to explore the emergent outcomes of the
  interaction of human agents with heterogeneous
  intelligence.
• In agent-based computational economics, not much
  work has been done in this area.

4
Software Agents Engineering

• Most software agents in agent-based market
  simulation are homogeneous in their cognitive
  capability, which does not reflect the
  characteristics of human agents in real markets.
• We believe that the design of software agents
  withheterogeneous intelligence is an import next
  step to investigate the emergentcomplexities in
  agent-based computational economics.

5
Genetic Programming

• Genetic programming (Koza, 1992) is an
  evolutionary computation paradigm that can be
  applied to machine learning.
• In GP, A learning strategy is represented as a
  program parse tree.

6
Genetic Programming Learning Process
7
Parent Selection Methods

• Tournament selection (size n)
• Randomly select n strategies from the population
• The strategy with the best fitness (e.g earned
  profit) is the winner.
• Fitness proportionate selection
• The probability of a strategy to be the winner is
  its fitness divided by the total fitness of all
  strategies in the population.

8
Mutation Operation
9
Sub-tree Crossover Operation
10
The GP Intelligent Agent

• Each agent is represented as a GP system.
• An agents intelligence is defined by the size of
  the GP population.
• The population size represents the working memory
  capacity of the agent.
• An agent with a larger population size has a
  larger working memory capacity to store and
  process new strategies, hence can be argued to be
  more intelligent.

11
Working Memory and Intelligence

• Various Experimental Economics studies have
  reported that there is a positive relationship
  between working memory and human intelligence
• Devetag and Warglien, 2003
• Cornelissen,Dewitte and Warlop, 2007
• Devetag and Warglien, 2008
• Design GP agents with different population size
  to represent economic agents with heterogeneous
  intelligence seems to be a suitable approach to
  conduct economic market simulation.

12
The Artificial Double Auction Market

• Based on the Santa Fe Token Exchange
• Clearinghouse DA
• Time is discretized into alternating bid/ask and
  buy/sell.
• Bid/ask buyers and sellers submit the prices
  they are willing to buy and sell for a commodity.
• Buy/sell the highest bid and the lowest ask are
  matched and the mid-point price is used to carry
  out the transaction.

13
The DA Market Design
14
GP Buyer Vs. Truth-teller

• A GP buyer has the ability to learn from its past
  experiences.
• It maintains a population of trading strategies.
• On each day, a strategy is randomly selected to
  conduct the auction on that day.

• A truth-teller trader always gives the assigned
  price at every auction.
• For a buyer, this is the highest token value it
  currently owns.
• For a seller, this is the lowest token value it
  currently owns.

15
The DA Market Environment

• On each day, each agent receives 4 new tokens
  with the following values

16
The Supply and Demand Curves
17
The DA Market Simulation

• Each simulation lasts 300 GP generations, where
  each generation is 2pop_size days long.
• On each day, 4 new token values are assigned to
  each of the 8 traders.
• Each day ends when all 16 tokens are successfully
  traded or 25 auction rounds are completed.

18
The DA Market Simulation - Continue

• For a GP buyer, one strategy is randomly selected
  each day from its population to conduct the
  auction series for that day.
• After 2pop_size days, each strategy in the
  population is likely to be selected at least once
  to conduct auction.
• The fitness of a GP strategy is the accumulated
  profit earned by that strategy at the end of the
  2pop_size day.

19
GP Buyer Biding Strategies

• Three types of information are provided for GP to
  evolve bidding strategies
• Past Experiences
• Time information
• Private information
• They are connected using the following operators
• ,, , /, min, max, if-then-else, gt, log etc.

20
GP Terminal Set
OTPD stands for on the previous day' PAR
stands for previous auction round''
21
GP Experimental Setup
22
Results Macro Market Efficiency
23
Market Realized Surplus Distribution Under
Different GP Population Size
24
Market Realized Surplus Distribution Under
Different Number of GP Buyers
25
Statistical Tests

• We conducted statistical tests on the simulation
  data using the following regression equation
• Y is the market efficiency
• X1 is the population size
• X2 is the the number of GP buyers in the market
• ?0 99
• ?1 0.028 the associated t value is 3.43
• ?2 -1.224 the associated t value is -11.56

26
Summary of Macro Market Behavior

• In general, the market efficiency increases as
  the population size of the GP buyers increases
• More intelligent GP buyers produced strategies
  that generated more profit without sacrificing
  the profit of the naive truth-telling sellers.
• As a result, the overall market efficiency is
  increased.

27
Summary of Macro Market Behavior - Continue

• The market efficiency decreases as the number of
  GP buyers in the market increases.
• The competition of multiple GP buyers in the
  market produced strategies that steal the profit
  from the naive truth-telling sellers.
• The total increase of GP buyers profit is lower
  than the decrease of the total profit of the
  naïve truth-telling sellers, hence the overall
  market efficiency is decreased.

28
How to Analysis Individual GP Agent Strategies

• We used the strategies evolved by GP with
  population size 10 and 50 at the last 10
  generations of every simulation run to conduct
  analysis, as they are more mature hence represent
  the GP buyers trading patterns.
• Population size 10
• 20 days ? 10 gens ? 90 runs 18,000 strategies
• Population size 50
• 100 days ? 10 gens ? 90 runs 90,000 strategies

29
One GP Buyer in the Market Population Size 10

• The 2 most frequently used strategies (93 of the
  18,000 strategies) are
• PMinBid bid the lowest bidding price on the
  previous day
• Profit 21 used in 40 of all analyzed strategies
  
• Profit 10.5 used in 31 of all analyzed
  strategies
• HTV bid the highest token value (truth-telling)
• Profit 14.5 used in 21 of all analyzed
  strategies
• The GP buyer is a risk-taker, who used less
  stable PMinBid more often to earn more profit
  than being a safe truth-teller (HTV).

30
One GP Buyer in the Market Population Size 50

• Learned more sophisticated strategies (P-22)
• If_Bigger_Then_Else PMinBid HTV HTV PMinBid
• Min PMinBid HTV bid the lower of PMinBid and HTV
• Profit 22 24 of all analyzed strategies
• Other Strategies
• PMinBid bid the lowest bidding price on the
  previous day
• Profit 21 33 of all analyzed strategies
• Profit 10.5 12 of all analyzed strategies
• HTV bid the highest token value (truth-telling)
• Profit 14.5 8 of all analyzed strategies

31
One GP Buyer in the Market Intelligent Behaviors

• The smarter GP buyer is able to fine-tune
  existing strategies to produce more profitable
  strategies (P-22).
• The smarter GP buyer used PMinBid more wisely
• the percentage of its usage that generated a
  profit of 21 has increased (4031 Vs. 3312).

32
One GP Buyer in the Market Intelligent Behaviors
- Cont

• The smarter GP buyer has learned that the
  co-existence of these 3 groups of strategies
  (PMinBid, HTV and P-22) are mutually beneficial
  therefore maintained the diversity in the
  population to make profitable bidding decisions.
• PMinBid utilizes historical auction information
  and relies on P-22 strategies being in the
  population to make more profit.
• The P-22 strategies rely on the presence of
  PMinBid and HTV in the population to compose the
  strategies.

33
Two GP Buyers in the Market Population Size 10

• The two most used bidding strategies groups by GP
  buyer 1
• P-17 strategies that generate profit 17
• P-24 strategies that generate profit 24
• The two most used bidding strategies groups by GP
  buyer 2
• P-35 strategies that generate profit 35
• P-37 strategies that generate profit 37

34
GP Buyer 1 P-17 Vs. GP Buyer 2 P-35

• P-17 HTV (truth-telling)
• P-35 PMax (bid the highest transaction price on
  the previous day)
• But if GP buyer 1 used PMinBid to against PMax of
  GP buyer 2, it would earn more profit (20.5) and
  causes GP buyer 2 to make less profit (29.5).
• Why GP buyer 1 did not learn using PMinBid?
• 300 generations are not long enough for GP buyer
  1 to leaned the PMinBid strategy when there is
  another GP buyer in the market.

35
GP Buyer 1 P-24 Vs. GP Buyer 2 P-37

• They have learned 4 bidding patterns
• (Min PMax HTV) Vs. PMax
• (Min PMinBid HTV) Vs. PMax
• (Min PMax HTV) Vs. PMinBid
• (Min PMinBid HTV) Vs. PMinBid
• GP buyer 1 has combined two strategies to form
  new bidding strategy.
• This co-evolution dynamics of 2 GP buyers with
  population size 10 promoted the emergence of
  similar type of bidding strategies which were
  only learned when the GP buyer has population
  size 50.

36
Two GP Buyers Population 10 Intelligent Behaviors

• GP buyer 1 switched from PMinBid to the less
  profitable HTV (truth-telling) strategy (-)
• GP buyer 1 was able to learn more sophisticated
  and profitable strategy Min PMinBid HTV ()
• The aggregated result of the two changes has
  increased the overall profit of GP buyer 1.

37
Two GP Buyer in the Market Population Size 50

• They have learned the same 4 bidding patterns
• (Min PMax HTV) Vs. PMax
• (Min PMinBid HTV) Vs. PMax
• (Min PMax HTV) Vs. PMinBid
• (Min PMinBid HTV) Vs. PMinBid
• However, the number of P-17 Vs. P-35 cases has
  decreased while the number of P-24 Vs. P-37 has
  increased.
• The co-evolution dynamic of 2 GP buyers with
  population 50 has created an win-win result as
  both GP buyers learned to use more profitable
  strategies more frequently to conduct the auction.

38
Two GP Buyers Population Size 50 Intelligent
Behaviors

• Both GP buyers learned to use a more profitable
  strategy more frequently to conduct the auction
  ().
• The profits of both buyers have increased.

39
Summary DA Macro Market Performance

• Using GP with different population size to model
  agents with heterogeneous intelligence, the DA
  market simulations show
• Market efficiency increases when the individual
  buyers intelligence increases more intelligent
  buyers developed strategies to collect extra
  profits that did not conflict with sellers
  profits.
• Market efficiency decreases when the number of
  intelligent buyers increases market becomes more
  competitive and the intelligent buyers developed
  aggressive strategies that damaged the naïve
  truth-telling sellers profits. The total market
  profit has declined.

40
Summary Individual GP Strategies (One GP Buyer)

• The more intelligent buyer has shown the
  following intelligent behaviors
• The smarter GP buyer is able to fine-tune
  existing strategies to produce more profitable
  strategies.
• The smarter GP buyer used more profitable
  strategy more frequently.
• The smarter GP buyer has learned to maintain
  diversity in the strategy population to make
  profitable bidding decisions.

41
Summary Individual GP Strategies (Two GP Buyers)

• The co-evolution of the two intelligent buyers
  strategies generated both positive and negative
  impacts on the two buyers.
• One GP buyer leaned more sophisticated strategies
  in this dynamic environment, which it did not
  learn under the stable environment.
• The other GP buyer applied strategies that
  prevented the GP buyer from learning more
  profitable strategies to protect its own profit.
• Both GP buyers have learned to use more
  profitable strategy more frequently to conduct
  the auction.

42
Concluding Remarks

• The GP buyer agents demonstrated human like
  learning ability.
• In the market we studied, the intelligence of an
  agent has impact on both macro and micro market
  behaviors.
• Using GP with different population size to design
  economic agents with heterogeneous intelligence
  is a possible way to investigate the emergent
  complexities in agent-based computational
  economics.

43
Future Work

• We will replace the naïve truth-telling sellers
  by GP agents with different population sizes to
  analyze more complex trading behaviors.
• We will conduct human subjects experiments to
  compare and contrast the trading strategies
  devised by human and by GP traders.

44
Reference

• S-H Chen, R-J Zeng and T. Yu, Co-evolving
  Trading Strategies to Analyze Bounded Rationality
  in Double Auction Markets, Genetic Programming,
  Theory and Practice VI, R. Riolo, T. Soule and B.
  Worzel (editors), pages 195-215, Springer, 2009