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Impact of Tag Recognition in Economic Decisions. David J. Poza. ECESIS Valladolid, February 2010. Objectives. Replication of the Classes Model Robert Axtell, Joshua M. Epstein, H. Peyton Young: The emergence of economic classes in an agent-based bargaining model (2004) Model analysis

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impact of tag recognition in economic decisions

Impact of Tag Recognitionin Economic Decisions

David J. Poza

ECESIS

Valladolid, February 2010

objectives
Objectives
  • Replication of the Classes Model
    • Robert Axtell, Joshua M. Epstein, H. Peyton Young: The emergence of economic classes in an agent-based bargaining model (2004)
  • Model analysis
    • Decision rule
    • Payoff matrix
index
Index

PART I

  • Replication of the Classes Model

1.1. The model

1.2 The model with one agent type

1.3 The model with two agent types

  • Model extensions

2.1. Changing the decision rule

2.2. Changing the payoff matrix

  • Results
index1
Index

PART I

  • Replication of the Classes Model

1.1. The model

1.2 The model with one agent type

1.3 The model with two agent types

  • Model extensions

2.1. Changing the decision rule

2.2. Changing the payoff matrix

  • Results
the model
The Model
  • Model overview:
    • Two agents demand some portion of a ‘pie’
  • The portion of the pie they get depends on their opponent’s demand:
    • If the sum of the two demands is less or equal than 100% of the pie, each player gets what he demanded
  • Otherwise, both get nothing
  • Decisions based on their experience about previous matches

pie

the model1
The Model
  • Bargaining process flow chart:
      • Create a population of n agents with an m-size memory (at first, m random values)
      • For each iteration:

2.1. Put the agents into pairs (at random)

2.2. For each pair of agents:

          • They choose randomly with probability ɛ
          • They use the information stored in their memory to demand the portion that maximizes their benefit with probability 1-ɛ

2.3. They store the decision taken by their opponent in their memories

2.4. Go to step 2.2. until all the agents have played

3. Go to step 2 and start a new iteration

the model2
The Model
  • What portion to choose?

30% (low) 50% (medium) 70% (high)

  • Payoff matrix:
the model3
The Model

2

P(L)=

7

Check

memory

m = 7

30

50

70

50

50

50

30

4

1

P(M)=

P(H)=

7

7

  • Decision rule:

Demand the option that maximizes the expected benefit

the model4
The Model

2

P(30)=

7

Check

memory

Compute the

mean benefit

Maximize

benefit

7

Benefit I get if I demand low (30)

B(30)= 30 · P(30) + 30 · P(50) + 30 · P(70)

= 30

Demand medium

Benefit I get if I demand medium (50)

B(50)= 50 · P(30) + 50 · P(50) + 0 · P(70)

= 42.9

Benefit I get if I demand high (70)

1

4

B(70)= 70 · P(30) + 0 · P(50) + 0 · P(70)

= 20

P(50)=

P(70)=

7

7

  • Decision rule:

Demand the option that maximizes the expected benefit

the model5
The Model
  • Representation of the agents according to their memory status

The simplex:

index2
Index

PART I

  • Replication of the Classes Model

1.1. The model

1.2 The model with one agent type

1.3 The model with two agent types

  • Model extensions

2.1. Changing the decision rule

2.2. Changing the payoff matrix

  • Results
the model with one agent type
The model with one agent type

memory

memory

The agents are indistinguishable from one another (no tags)

the model with one agent type1
The model with one agent type

Equitable equilibrium

Fractious state

all the agents have at least (1-ɛ)·m instances of M in their memories

all the agents have at most ɛ·m instances of M in their memories

Two points of attraction:

index3
Index

PART I

  • Replication of the Classes Model

1.1. The model

1.2 The model with one agent type

1.3 The model with two agent types

  • Model extensions

2.1. Changing the decision rule

2.2. Changing the payoff matrix

  • Results
the model with two agent types
The model with two agent types
  • They are able to identify their opponent’s tag
  • There are two types of matches
    • INTRATYPE MATCHES: Among players with the same tag
  • INTERTYPE MATCHES: Among players with different tag
  • Each agent has a distinguishable tag (colour)
the model with two agent types1
The model with two agent types
  • One for intratype matches
  • Another for intertype matches

INTRATYPE MEMORY

INTERTYPE MEMORY

INTRATYPE MEMORY

INTERTYPE MEMORY

  • Two memory sets  two simplexes
  • The agents have two memory sets
slide17

INTRATYPE MEMORY

INTRATYPE MEMORY

The model with two agent types

  • Three results in the case of intratype matches:
slide18

INTERTYPE MEMORY

INTERTYPE MEMORY

The model with two agent types

  • Two results in the case of intertype matches:
index4
Index

PART I

  • Replication of the Classes Model

1.1. The model

1.2 The model with one agent type

1.3 The model with two agent types

  • Model extensions

2.1. Changing the decision rule

2.2. Changing the payoff matrix

  • Results
model extensions
Model extensions

1

4

P(M)=

P(H)=

7

7

2

P(L)=

m = 7

7

Check

memory

Choose the

best reply

Choose the

best reply

Check

memory

7

probability that my opponent demands low

probability that my opponent demands medium

probability that my opponent demands high

30

30

50

70

50

50

50

My opponent is likely to choose medium

  • Fast & frugal decision rule:

Demand the best reply againts the opponent’s most frequent demand

model extensions1
Model extensions

Equitable equilibrium

Fractious state

Two points of attraction:

model extensions2
Model extensions

Mean-based decision rule

Mean-based decision rule

Mean-based decision rule

Mean-based decision rule

Mode-based decision rule

  • Comparison of the two decision rules:
    • Percentage of runs that reached an equitable equilibrium:
the model with one agent type2
The model with one agent type

Mode-based decision rule

Mode-based decision rule

  • Comparison of the two decision rules:
    • Percentage of runs that reached an equitable equilibrium:
model extensions3
Model extensions
  • When we introduced the fast & frugal decision rule, segregation appeared much more frequently
    • In intratype matches
    • In intertype matches

Two agent types:

index5
Index

PART I

  • Replication of the Classes Model

1.1. The model

1.2 The model with one agent type

1.3 The model with two agent types

  • Model extensions

2.1. Changing the decision rule

2.2. Changing the payoff matrix

  • Results
the model with one agent type3
The model with one agent type

Introduction of new payoff matrices:

the model with one agent type4
The model with one agent type

Sensitivity analysis:

conclusions
Conclusions
  • Model extensions
    • New decision rule
      • Same points of attraction
      • Points of attraction visited with different rates
      • Segregation occurs more frequently
    • New payoff matrix
      • Each matrix has a different convergence time
  • Replication of the Classes Model
    • Build the program & simulations
    • Same results (1-agent type and tag model)
slide29

Conclusions

Applets available at:

  • Model with one agent type:

http://www.insisoc.org/bargaining_model_no_tags.html

  • Model with two agents types:

http://www.insisoc.org/bargaining_model_tag_model.html

index6
Index

PART II

  • Agents distributed on a regular spatial structure

1.1. Random distribution of the tags

1.2. Tags distributed in four squares

1.3. Tags distributed in two stripes

  • Results

3. Time to play with the application!

regular spatial structures
Regular Spatial Structures

1st scenario: Random distribution of the tags

regular spatial structures1
Regular Spatial Structures

- intratype games -

equitable equilibrium

fractious state

segregation

1st scenario: Random distribution of the tags

regular spatial structures2
Regular Spatial Structures

- intertype games -

equitable equilibrium

segregation

1st scenario: Random distribution of the tags

regular spatial structures3
Regular Spatial Structures

2nd scenario: Tags distributed in four squares

regular spatial structures4
Regular Spatial Structures

- intratype games -

equitable equilibrium

fractious state

segregation

2nd scenario: Tags distributed in four squares

regular spatial structures5
Regular Spatial Structures

- intertype games -

equitable equilibrium

segregation

2nd scenario: Tags distributed in four squares

regular spatial structures6
Regular Spatial Structures

3rd scenario: Tags distributed in two stripes

regular spatial structures7
Regular Spatial Structures

- intratype games -

equitable equilibrium

fractious state

segregation

3rd scenario: Tags distributed in two stripes

regular spatial structures8
Regular Spatial Structures

- intertype games -

segregation

segregation

equitable equilibrium

3rd scenario: Tags distributed in two stripes

conclusions1
Conclusions
  • New points of attraction:
    • Borders medium-medium
  • New cases of segregation
    • Different decisions depending on the border within agents with the same tag
slide41

Conclusions

Applet available at:

http://sites.google.com/site/classesgrid/

thank you for your attention

Thank you for your attention

David J. Poza

ECESIS

Valladolid, February 2010