Outline

1. The Emergence of Cultural Signatures and Persistence of Internal Diversity:A Model of Conformity and ConsistencyJenna BednarAaron BramsonAndrea Jones-RooyScott E Page

2. Outline • Background • Culture • Institutions and Mechanism Design • Ensembles of Institutions • Broad Forces: Coordination & Consistency • Coordination Consistency Model • Coordination Model • Our Model • Analytic Results ( and 2) • Computational Results (the rest)

3. Culture? Behavior Beliefs Semiotics Preferences Norms

4. Survey Approach Hoftstede: Power Distance Individualism Masculinity Uncertainty Avoidance

5. US Power Distance 32 Individualism 90 Masculinity 60 Uncertainty Avoidance 40

6. France Power Distance 61 Individualism 63 Masculinity 32 Uncertainty Avoidance 80

7. El Salvador vs Korea El Sal Korea Power Distance 62 56 Individualism 12 11 Masculinity 41 33 Uncertainty Avoid 80 80

8. Institutions and Behavioral Repertoires

9. Larger Project Behavioral Repertoire Institutions Bednar and Page (2007) “Can Game(s) Theory Explain Culture? The Emergence of Cultural Behavior Within Multiple Game” Rationality and Society

10. Larger Project Behavioral Repertoire Institutions Bednar and Page (2007) “Can Game(s) Theory Explain Culture? The Emergence of Cultural Behavior Within Multiple Game” Rationality and Society

11. Mount-Reiter Diagram Social Objective Environment Outcome Behavioral Rule Outcome Function Actions (Message Space)

12. Equilibrium requires COORDINATED behavior: - tit for tat - costly signaling - alternation - driving on the left

13. Multiple Institutions E O E O M M E O E O M M Bednar (2008), Bednar and Page (2007)

14. Empirical evidence suggests that people avoid cognitive dissonance, that they used cased based decision rules, and that they transfer routines from one setting to another. We call this consistency.

15. Coordination Consistency Model

16. Pure Coordination Game Player 2 A B A B Player 1

17. Hard and Soft Externalities An externality is hard (economic) f it’s easily measured An externality is soft (psychological) if it’s not.

18. No Bright Line Some decisions involve both hard and soft coordination externalities. Suppose I’m buying a bike. The more people that buy mountain bikes, the more trails that get created (hard). Buying a mountain bike might also make me hip (soft).

19. Two empirical regularities explained and two inconvenient truths that lie outside the model.

20. Coordination

21. Exception Proves Rule

23. Dagen H At 4:45 am on September 3, 1967, all cars on the road in Sweden came to a stop. They switched sides (from the left to the right) and at 5 am, the cars began moving again.

24. ICT1: Diversity within Cultures

25. ICT2: Cultural Signatures

26. Elevator Version Describe a model in which agents attempt to coordinate with others and to be internally consistent that produces intra cultural heterogeneity, inter cultural heterogeneity, and cultural signatures.

27. A List of Questions Ketchup in the fridge? Do people wear shoes inside your house? Do you cross the street when the don’t walk sign is flashing? Read the newspaper at the breakfast table? Do you hug your friends when you see them? Paper napkins?

28. YNYYY Nation Ketchup in the fridge? Yes Do people wear shoes inside your house? No Do you cross the street when the don’t walk sign is flashing? Yes Read the newspaper at the breakfast table? Yes Do you hug your friends when you see them? Yes Paper Napkins? Yes

29. How Many Cultures? Six questions Two answers each 2 x 2 x 2 x 2 x 2 x 2 = 64

30. The Set of The Possible Dead People: bury or burn Foods you eat? Dress? Music you play Stories you tell 8 x 19 x 40 x 6 x 11 x 23 x 2 x 43 .. = HUGE

31. Four Assumptions Coordination: incentive to choose an equilibrium action Consistency: incentive to be consistent across games Dynamics: people learn Errors: people make mistakes

32. Model Agent: (H,C,C,H,H,C,C,C) Coordination rule: match actions of others in common games Consistency rule: match actions of self on different games

33. Coordination Rule Pick two players at random and a game at random. Set the action of the first player equal to the action in the second player. (H,C,C,H,H,C,C,C) meets (C,H,C,C,H,C,C,H) (C,C,C,H,H,C,C,C)

34. Coordination Equilibrium All agents should coordinate in each game but the choices of actions should be arbitrary. Distinct cultures but no signatures. (C,C,C,H,H,C,C,C)

35. Consistency Rule Pick two games at random. Set the action in the first equal to the action in the second. (H,C,C,H,H,C,C,C) (C,C,C,H,H,C,C,C)

36. Consistency Equilibrium Each agent should be consistent but no two agents need be consistent in the same way. Consistent people but no coordination. (C,C,C,C,C,C,C,C) (H,H,H,H,H,H,H,H)

37. Coordination & Consistency With probability p an agent applies the coordination rule, and with probability (1-p) an agent applies the consistency rule.

38. Equilibrium Societies converge to either (C,C,C,C,C,C,C,C) or (H,H,H,H,H,H,H,H)

39. Two Considerations The Second Law The Trembling Hand

40. The Second Law The second law of thermodynamics suggests a unique stable equilibrium--- but it’s not of much predictive value.

41. Simplest Model Two agents Two games Two actions

42. States of the World Coordinated and Consistent Off by One Consistent not Coordinated Coordinated not Consistent Neither (Total Mess)

43. Consistency Dynamic 1 2 1 2 2 1

44. Consistency Transition Map 1/2 1 1/4 1/4 1

45. Coordination Transition Map 1/2 1 1/4 1 1/4

46. Coordination & Consistency Transition Map 1/2 1/2 1 1/4 1/8 1/2 1/8 1/2 1/2

47. Time To Convergence p = probability of coordination

48. Limiting Case With N agents and M dimensions time to equilibrium scales as follows: T ~  N2M2 for p near 1/2 T ~  N2M/p for p near 0 T ~  M2N/(1-p) for p near 1 Scott E Page, Leonard M. Sander, and Casey Schneider - Mizell ``Conformity and Dissonance in Generalized Voter Models” Journal of Statistical Physics, 2007.

49. The Trembling Hand Agents make mistakes with probability epsilon.

50. Markov Process 1-  0 0 0 1/4 (1- )/2 . ..