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Clubs, Beliefs, and Entrapment Scott Duke Kominers Harvard University AMS Session on Behavioral Sciences Joint Mathematics Meetings January 7, 2009 Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 1 / 6 Overview

  1. Clubs, Beliefs, and Entrapment Scott Duke Kominers Harvard University AMS Session on Behavioral Sciences Joint Mathematics Meetings January 7, 2009 Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 1 / 6

  2. Overview Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 2 / 6

  3. Overview Question Why do people join clubs? Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 2 / 6

  4. Overview Question Why do people join clubs they would rather not be in? Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 2 / 6

  5. Overview Question Why do people join clubs they would rather not be in? Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 2 / 6

  6. Overview Question Why do people join clubs they would rather not be in? Classical Answer Because they have to. Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 2 / 6

  7. Overview Question Why do people join clubs they would rather not be in? Subtle Answer Because they have to. Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 2 / 6

  8. Overview Question Why do people join clubs they would rather not be in? Subtle Answer Because they think they have to. Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 2 / 6

  9. Overview Question Why do people join clubs they would rather not be in? Subtle Answer Because they think they have to. Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 2 / 6

  10. Examples Question Why do people join clubs they would rather not be in? Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  11. Examples Question Why do we tip in restaurants? Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  12. Examples Question Why do we tip in restaurants? Answer Because we have to. Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  13. Examples Question Why do we tip in restaurants? Answer Because we have to. But the first tippers . . . Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  14. Examples Question Why do we tip in restaurants? Answer Because we have to. But the first tippers wanted to. Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  15. Examples Question Why do we tip in restaurants? Answer Because we have to. But the first tippers wanted to. Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  16. Examples Question Why do we tip in restaurants? Answer Because we have to. But the first tippers wanted to. Positive utility from early adoption Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  17. Examples Question Why do we tip in restaurants? Answer Because we have to. But the first tippers wanted to. Positive utility from early adoption + network effect Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  18. Examples Question Why do we tip in restaurants? Answer Because we have to. But the first tippers wanted to. Positive utility from early adoption + network effect = entrapment! Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  19. Examples Question Answer Positive utility from early adoption + network effect = entrapment! Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  20. Examples Question Why do we use VHS tapes, instead of Betamax? Answer Positive utility from early adoption + network effect = entrapment! Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  21. Examples Question Why do we use VHS tapes, instead of Betamax? Answer Because we have to. Positive utility from early adoption + network effect = entrapment! Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  22. Examples Question Why do we use VHS tapes, instead of Betamax? Answer Because we have to. But the first VHS users . . . Positive utility from early adoption + network effect = entrapment! Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  23. Examples Question Why do we use VHS tapes, instead of Betamax? Answer Because we have to. But the first VHS users had to hope that VHS would catch on. Positive utility from early adoption + network effect = entrapment! Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  24. Examples Question Why do we use VHS tapes, instead of Betamax? Answer Because we have to. But the first VHS users had to hope that VHS would catch on. Positive utility from early adoption + network effect = entrapment! Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  25. Examples Question Why do we use VHS tapes, instead of Betamax? Answer Because we have to. But the first VHS users had to hope that VHS would catch on since Betamax was “better”. Positive utility from early adoption + network effect = entrapment! Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  26. Examples Question Why do we use VHS tapes, instead of Betamax? Answer Because we have to. But the first VHS users had to hope that VHS would catch on since Betamax was “better”. Positive utility from early adoption + network effect = entrapment! Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  27. Examples Question Why do we use VHS tapes, instead of Betamax? Answer Because we have to. But the first VHS users had to hope that VHS would catch on since Betamax was “better”. Positive utility from early adoption + network effect = entrapment! Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 3 / 6

  28. Math Model Notation Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 4 / 6

  29. Math Model Notation Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 4 / 6

  30. Math Model Notation N > 1 players, indexed i = 1 , 2 , . . . , N Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 4 / 6

  31. Math Model Notation N > 1 players, indexed i = 1 , 2 , . . . , N Must (simultaneously) choose Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 4 / 6

  32. Math Model Notation N > 1 players, indexed i = 1 , 2 , . . . , N Must (simultaneously) choose Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 4 / 6

  33. Math Model Notation N > 1 players, indexed i = 1 , 2 , . . . , N Must (simultaneously) choose Join Status Quo Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 4 / 6

  34. Math Model Notation N > 1 players, indexed i = 1 , 2 , . . . , N Must (simultaneously) choose Join Status Quo J ( i , n ) S ( i , n ) Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 4 / 6

  35. Math Model Notation N > 1 players, indexed i = 1 , 2 , . . . , N Must (simultaneously) choose Join Status Quo J ( i , n ) S ( i , n ) where n = number of others choosing Join Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 4 / 6

  36. Math Model Notation N > 1 players i = 1 , 2 , . . . , N Join Status Quo J ( i , n ) S ( i , n ) Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 5 / 6

  37. Math Model Our Assumptions Notation N > 1 players i = 1 , 2 , . . . , N Join Status Quo J ( i , n ) S ( i , n ) Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 5 / 6

  38. Math Model Our Assumptions Notation N > 1 players i = 1 , 2 , . . . , N Players sorted in order of enthusiasm for Join : Join Status Quo J ( i , n ) S ( i , n ) ∂ A ∂ S ∂ i < 0 , ∂ i > 0 Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 5 / 6

  39. Math Model Our Assumptions Notation N > 1 players i = 1 , 2 , . . . , N Players sorted in order of enthusiasm for Join : Join Status Quo J ( i , n ) S ( i , n ) ∂ A ∂ S ∂ i < 0 , ∂ i > 0 Positive network effect: ∂ A ∂ S ∂ n > 0 , ∂ n < 0 Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 5 / 6

  40. Math Model Our Assumptions Notation N > 1 players i = 1 , 2 , . . . , N Functional forms (following Dixit (2003)): Join Status Quo J ( i , n ) S ( i , n ) Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 5 / 6

  41. Math Model Our Assumptions Notation N > 1 players i = 1 , 2 , . . . , N Functional forms (following Dixit (2003)): Join Status Quo J ( i , n ) S ( i , n ) J ( i , n ) = β + γ n − δ i S ( i , n ) = σ i − τ n Scott Duke Kominers (Harvard) Clubs, Beliefs, and Entrapment January 7, 2009 5 / 6

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