Raising Revenue With Raffles: Evidence from a Laboratory Experiment

1. Raising Revenue With Raffles:Evidence from a Laboratory Experiment Wooyoung Lim, University of Pittsburgh Alexander Matros, University of Pittsburgh Theodore Turocy, Texas A&M University

2. Lotteries • As of 2008, 43 States have State Lotteries • 33% - 50% of USA population participates

3. Lotteries A lottery is a salutary instrument and a tax...laid on the willing only, that is to say, on those who can risk the price of a ticket without sensible injury, for the possibility of a higher prize. Thomas Jefferson

4. Lotteries Too many players buy too many tickets Why?

5. Literature • (A) Buy Hope? Clotfelter and Cook (1989, 1990, 1993)

6. Literature • (A) Buy Hope? Clotfelter and Cook (1989, 1990, 1993) • (B) Charity/Fund raising? Morgan (2000), Morgan and Sefton (2000)

7. Literature • (A) Buy Hope? Clotfelter and Cook (1989, 1990, 1993) • (B) Charity/Fund raising? Morgan (2000), Morgan and Sefton (2000) • What if no (A) and no (B)?

8. Plan • Theory • Experiments • Data • Behavioral Models • Results • Conclusion

9. Theory n risk neutral players V – prize value W – endowment xi 0 player i’s expenditure

10. Players’ maximization problem Player i solves the following problem

11. Rationalizable choices

12. Rationalizable choices

13. Nash equilibrium • Absolute performance • Unique Nash equilibrium!

14. Evolutionary Stable Strategies • Relative performance (spiteful behavior)

15. Experimental Design V = 1,000 tokens (= $10) W = 1,200 tokens (= $12) Quizzes Expected payoff tables N = 2, 3, 4, 5, 9 3 sessions for each N Pittsburgh Experimental Economics Laboratory October 2007 – March 2008

16. Experimental Design Quiz 1 • Assume that your contribution is 100 tokens and your opponent’s contribution is 900 tokens. What is your chance to win the lottery? • 100 / 900 • 100 / 1,000 • 100 / 800 • 800 / 900 • 900 / 1,000 • Assume that your contribution is 900 tokens and your opponent’s contribution is 100 tokens. What is your chance to win the lottery? • 100 / 900 • 100 / 1,000 • 800 / 900 • 900 / 1,000 • 900 / 900

17. Experimental Design Quiz 2 • Assume that your contribution is 100 tokens and your opponent’s contribution is 900 tokens. What is your expected payoff? • -100 • 0 • 100 • 900 • 1,000 • Assume that your contribution is 900 tokens and your opponent’s contribution is 100 tokens. What is your expected payoff? • - 900 • - 100 • 0 • 100 • 900

18. Experimental Design

19. Summary 1

20. N = 2

21. N = 3

22. N = 2, 3: Nash and ESS

23. N = 4

24. N = 5, 9

28. Data • Integer multiples of 100 in 78.1% • Integer multiples of 50 in 87.7% (+9.6%)

30. Behavioral Predictions • Quantal Response Equilibrium • Level – k reasoning • Learning Direction Theory

31. Quantal Response Equilibrium • McKelvey and Palfrey (1995) • Noisy optimization process •  - the best parameter (from the data) •  = 0 – all choices are random •  =  – no noise (QRE  Nash)

32. QRE

33. QRE

34. Level – k reasoning • Stahl and Wilson (1994, 1995) • Level – 0: random • Level – 1: best reply to Level – 0 • Level – 2: best reply to Level – 1

35. N = 2

36. N = 3

37. N = 4

38. N = 5

39. N = 9

40. Level – k reasoning • Ho, Camerer and Weigelt (1998) • Level – 0: uniform on [0, V] – density B0 • Level – 1: simulate N-1 draws from B0 compute best reply • Level – 2:

42. Level - k

43. Level – k reasoning • Level – 0 in N • Level – 1 in N • Costa-Gomes and Crawford (2004) classify subjects: at least 6 out of 10 96% can be classified! • Iterated elimination of dominated strategies: No

44. Learning Direction Theory • Selten and Buchta (1994) • “Subjects are more likely to change their past actions in the directions of a best response to the others’ previous period actions.”

45. Learning Direction Theory

46. Learning Direction Theory • If you lose, you change “Small lotteries” Yes Other lotteries No • If you win: you overpaid; if you lose: you underpaid “Small lotteries” Yes Other lotteries No • Adjust in the best reply direction “Small lotteries” Yes Other lotteries No

47. Conclusion Subjects’ behavior in lotteries w/t (A) and (B) a) Nash equilibrium b) ESS c) QRE d) Level – k reasoning e) Leaning direction theory

48. Conclusion Data a) “Almost” do not change to change in N b) Overspending even for N = 4, 5, 9

49. Conclusion Data: N = 2 a) Nash c) QRE (the least noise) d) Level – k reasoning (Level – 1) e) Leaning direction theory (BR changes)

50. Conclusion Data: N = 3 b) SSE c) QRE (noise) d) Level – k reasoning (Level – 1) e) Leaning direction theory (some BR changes)