1. Why Do People Under-Search? —The Effects of Payment Dominance on Individual Search Decisions And Learning Gong, Binglin Shanghai JiaoTong University Ramachandran, Vandana University of Maryland June 2007 @ ESA Rome

2. Outline Research Questions Literature Review Theoretical Background Discussion of Payoff Functions Experimental Design Experimental Results Conclusions

3. Research Question Why do people under-search, as observed in previous sequential search experiments? Does payment dominance play a role here? If so, how and how much?

4. Literature: Theory of Search Optimal search—reservation value strategy Keep searching if the expected gain from search is higher than the search cost, and stop otherwise. --Stigler (1961) If the distribution is known, and search costs are constant, the optimal search strategy is to use a reservation value, and recall should not matter (should never be used).

5. Literature: Experiments on Search Schotter and Braunstein (1981): optimal search— reservation value strategy Kohn and Shavell (1974): With increased search costs, players become less selective Sonnemans (1996), (1997): subjects write down strategies instead of realized points Cox and Oaxaca (1989), (1996), (2000): finite horizon, unknown distribution Hey (1981), (1987): individual behavior, rules of thumb They found that search is highly efficient (in terms of earnings) and there is some tendency to recall. Lower reservation values than risk neutral predictions were observed.

6. Why Do People on Average Search Less Than Predicted? Risk Posture –All the above predictions are based on risk neutrality. If people are risk averse, then accepting current value is safer than searching –Risk posture may not be a sufficient explanation (Rabin 2000 - all experiments offer very low monetary prizes, over which one may assume that subjects are locally risk neutral. Cox and Oaxaca get different “risk preferences” estimates for the same subjects in different treatments.) Extra cost for search –Other than the costs assigned in the experiment, people need to take time and effort to search and figure out best strategy. Flat payoff –Stopping rules that give rise to too little search perform rather well in most cases (Sonnemans 1998)

7. Literature: Payment Dominance Glenn Harrison (1989) Comments by Friedman, Kagel and Roth, Cox, Smith, and Walker, Merlo and A. Schotter (1992 ) Reply by Glenn Harrison (1992 ) When an economic problem is complicated but people can learn from the history, a flat payoff function can limit the information people get from experience and lead to noisier behavior. Economists should look at not only the “message space”, but also the “payoff space”. Experimenters should design experiments carefully to avoid the payment dominance problem.

8. Example of A Sequential Search Problem (Known Distribution, with Recall) In each period, one can randomly draw one award from the uniform distribution between 0 and 2, after paying the search cost s=0.2. These are known to the searcher. After each draw, one can decide whether to stop or to keep searching. If one stops after n draws, her total payoff is the highest draw minus the total search cost, s*n.

9. Theoretical Predictions for Risk Neutral Individuals Using optimal search strategy, when distribution is known, the reservation value r should satisfy: The expected number of draws n will be The expected earning in each round is If optimal strategy is used, the expected earning should be equal to reservation value.

10. Estimate The Reservation Value 0 r/2 r 1+r/2 2 Award~U[0,2] Reservation Value r E(accepted draw)=1+r/2 E(rejected draw)=r/2 Estimator of reservation value: 2*average(accepted-1, rejected) We get an estimated reservation value for each subject in each round.

11. What We Learn About Payoff The bigger the award (price, wage, etc.) dispersion is, the steeper the payoff function is. The smaller the search cost is, the steeper the payoff function is.

14. Reservation value E(earning) Search cost

15. Experimental Test of Payoff Dominance Use plat payoff and steep payoff as treatments, look at the difference of deviation from optimal strategy. Treatment123 DistributionU[0,2] U[0,10] Search Cost0.050.500.05 Slope of E(Payoff) (left, right) 0.3, -200.1, -0.10.45, -30 Diff. in Payoff in the relatively flat area 0.60.0864 Predicted Reservation Value big variance serious under- search very big variance under-search r*, maxE(payoff)1.5530.5869

16. Alternate Order of Treatments Subject IDTreatment Order 1-4123 5-8132 9-12213 13-16231 17-20312 21-24321

17. Strategy Method And Real Search We use a mix of s trategy method and real search in this experiment 1.Reading instructions (reveal distribution of awards) 2.Subjects choose strategy (reservation value +) 3.Subjects make decisions in real sequential search (repeat for 10 rounds) 4.Subjects revise strategy (reservation value +) 5.All decisions are paid.

18. Why? By using s trategy method - real searches - s trategy method, we can measure the effect of learning from real search experiences. When we use s trategy method and pay subjects the expected payoffs, we can eliminate risk aversion as a reason for under- search.

20. Basic Statistics on Stated And Estimated Reservation Values

21. Note: devr1b = r1b –r1*, … Deviation from Optimal Reservation Value

22. Note: pdevr1e=devr1e/1.553*100, pdevr2e=devr2e/0.586*100, pdevr3e=devr3e/9*100. Percentage Deviation from Optimal Reservation Value

23. Deviation from Optimal Reservation Value As Percentage of The Upper Bound of Award Distribution Note: phdevr1e=devr1e/2*100, phdevr2e=devr2e/2*100 phdevr3e=devr3e/10*100

24. Learning from Real Search Note: learn1=abs(devr1b)-abs(devr1a) learn2=abs(devr2b)-abs(devr2a) learn3=abs(devr3b)-abs(devr3a)

25. Treatment Effects Results of Wilcoxon Sign-Rank Tests Individual Treatment Level

26. Learning Effects Results of Wilcoxon Sign-Rank Tests Individual Treatment Level

28. Conclusions Asymmetric expected payoff function can partly explain under-searching. Over-searching can happen when payoff function is flat on both sides. Flat payoff function leads to noisier behavior in individual search decisions. People learn more from real searches when payoff function is steeper. People sometimes make bigger mistakes in strategy method than in real searches.

29. Future Study Bigger sample size  More power Add a risk posture test in the experiment Variance of payoff Other distributions of awards

30. Thank you!