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Impact of Tag Recognition in Economic Decisions

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

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  1. Impact of Tag Recognitionin Economic Decisions David J. Poza ECESIS Valladolid, February 2010

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. The Model • What portion to choose? 30% (low) 50% (medium) 70% (high) • Payoff matrix:

  8. 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

  9. 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

  10. The Model • Representation of the agents according to their memory status The simplex:

  11. 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

  12. The model with one agent type memory memory The agents are indistinguishable from one another (no tags)

  13. 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:

  14. 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

  15. 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)

  16. 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

  17. INTRATYPE MEMORY INTRATYPE MEMORY The model with two agent types • Three results in the case of intratype matches:

  18. INTERTYPE MEMORY INTERTYPE MEMORY The model with two agent types • Two results in the case of intertype matches:

  19. 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

  20. 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

  21. Model extensions Equitable equilibrium Fractious state Two points of attraction:

  22. 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:

  23. 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:

  24. Model extensions • When we introduced the fast & frugal decision rule, segregation appeared much more frequently • In intratype matches • In intertype matches Two agent types:

  25. 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

  26. The model with one agent type Introduction of new payoff matrices:

  27. The model with one agent type Sensitivity analysis:

  28. 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)

  29. 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

  30. 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!

  31. Regular Spatial Structures 1st scenario: Random distribution of the tags

  32. Regular Spatial Structures - intratype games - equitable equilibrium fractious state segregation 1st scenario: Random distribution of the tags

  33. Regular Spatial Structures - intertype games - equitable equilibrium segregation 1st scenario: Random distribution of the tags

  34. Regular Spatial Structures 2nd scenario: Tags distributed in four squares

  35. Regular Spatial Structures - intratype games - equitable equilibrium fractious state segregation 2nd scenario: Tags distributed in four squares

  36. Regular Spatial Structures - intertype games - equitable equilibrium segregation 2nd scenario: Tags distributed in four squares

  37. Regular Spatial Structures 3rd scenario: Tags distributed in two stripes

  38. Regular Spatial Structures - intratype games - equitable equilibrium fractious state segregation 3rd scenario: Tags distributed in two stripes

  39. Regular Spatial Structures - intertype games - segregation segregation equitable equilibrium 3rd scenario: Tags distributed in two stripes

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

  41. Conclusions Applet available at: http://sites.google.com/site/classesgrid/

  42. Thank you for your attention David J. Poza ECESIS Valladolid, February 2010

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