1. Monetary Stakes and Socioeconomic Characteristics in Ultimatum Games: An Experiment with Nation-Wide Representative Subjects Tsu-Tan Fu Center for Survey Research and Institute of Economics, Academia Sinica, Nankang, Taipei 115, Taiwan Wei-Hsin Kong Institute of Industrial Economics, National Central University C.C. Yang Institute of Economics, Academia Sinica, Nankang, Taipei 115, Taiwan Department of Public Finance, National Chengchi University, Wenshan, Taipei 116, Taiwan

2. 1. Introduction Roth et al. (1991) Ultimatum game Stahl (1972) and Rubinstein (1982) Stakes?

3. Camerer (2003, Section 2.2.2) Taken together, these studies show that very large changes in stakes (up to several months’ wages) have only a modest effect on rejections. Raising stakes also has little effect on Proposers’ offers, presumably because aversion to costly rejection leads subjects to offer closer to 50 percent when stakes go up. (p. 61) Pure self-interest preferences or game theory? Rabin (1993), Fehr and Schmidt (1999) and Bolton and Ockenfels (2000) Other-regarding or social preferences

4. The Rabin-Fehr-Schmidt-Bolton-Ockenfels approach attempts to account for experimental data by theoretically building an extended model in which both wealth and non-wealth factors in players’ preferences are counted in. In contrast, we attempt to account for experimental data by empirically separating wealth factors from non-wealth factors in players’ preferences, and isolating the pure effect of wealth factors from the overall effects observed in the experimental data. Non-wealth factors in players’ preferences are typically unobserved. The gist of our approach is to use players’ observable socioeconomic characteristics as proxies for these unobservables. Experimental subjects are rather homogeneous in socioeconomic attributes. The constrained subject pool and the selectivity of the subject pool Representative subjects

5. 2. Experimental design Subjects Procedures

6. 3. Results Characteristics of the sample

7. Table1. Descriptive statistics of the sample DefinitionMeanStandard Deviation. Gender Dummy; 1 for male 0 for female 0.5120.500 Parent Dummy; 1 for Yes 0 for No 0.6360.481 Student Dummy; 1 for Yes 0 for No 0.0740.263 IncomeNT dollars/ month28574.329906.2 AgeYears of age40.88212.670 Age distribution 20-4049.18% 40-6043.49% 60~7.33% 100.00% EducationYears of schooling12.2423.565 Education distribution Elementary & below11.90% Junior high school12.03% Senior high school34.18% Junior college18.48% College & above23.42% 100.00%

8. Offer and (conditional) acceptance pattern Table 2. Summary of offers and (conditional) acceptances Stake=200 Stake=1000 Offer Choice OfferAcceptanceOdderAcceptance N(%)N N N 1(90/10)7(3.55%)4(57.14%)14(7.00%)11(78.57%) 2(80/20)4(2.03%)3(75.00%)12(6.00%)7(58.33%) 3(70/30)19(9.64%)18(94.74%)13(6.50%)12(92.31%) 4(60/40)12(6.09%)10(83.33%)18(9.00%)18(100%) 5(50/50)137(69.54%)126(94.03%)139(69.50%)136(97.84%) 6(40/60)18(9.14%)14(77.78%)4(2.00%)4(100.00%) Total197(100.00%)175(88.83%)200(100.00%)188(94.00%)

9. P200 P1000 Choices R1000 0 R200 Percentage Figure 1. Frequencies of offers and acceptances by stakes

10. Smith and Walker (1993) survey 31 experimental studies which report data on the effect of increased monetary rewards. They conclude: “in virtually all cases rewards reduce the variance of the data around the predicted outcome” (p. 245).

11. Camerer and Hogarth (1999) review 74 experiments with different degrees of performance-based financial incentives. One of their main findings is that “Incentives often reduce variance by reducing the number of extreme outliners, probably caused by thoughtless, unmotivated subjects” (p. 31). Student versus non-student sample

12. Table3 Frequencies of offers and acceptances by students and non-students OffersAcceptances ChoicesStudent(%) Non- Students (%)Student(%) Non- Students (%) 1 1 (3.10%) 20 (5.50%) 1(100.00%) 14(70.00%) 2 0 (0.00%) 16 (4.40%) 0 (0.00%) 10(62.50%) 3 1 (3.10%) 31 (8.50%) 3(100.00%) 27(93.10%) 4 4(12.50%) 26 (7.10%) 2(100.00%) 26(92.90%) 526(81.30%)250(68.50%) 19(100.00%)243(95.70%) 6 0 (0.00%) 22 (6.00%) 2(100.00%) 16(80.00%) Total32(100.00%)365(100.00%) 27(100.00%)336(91.60%)

13. ▲ 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00% 123456 Student proposer Student responder Non-student proposer Non-student responder Percentage Choices Figure 2. Frequencies of offers and acceptances by students and non-students

14. Factors affecting responders’ behavior Experiments with children indicate that fairness tastes are not innate, but learned through socialization

15. Evidence from social and behavioral science tends to support the hypothesis that men are more individually-oriented (selfish) while women are more socially-oriented (selfless). Fairness norms may be learned through experience, but they may also be embodied through formal education. Indeed, education is perhaps the most important instrument of embodying fairness norms into people’s preferences for most societies. A person’s years of schooling or education attainment, defined as Education, may thus reflect her degree of the embodiment of fairness norms.

16. ProposersResponders AgeEducationIncomeAgeEducationIncome Age11 Education-0.55061-0.47731 Income0.15030.24610.0690.31431 Table 4. Correlations between Age, Education, and Income

17. Table 5. Probit estimates of responder behavior (dependent variable y=1 if accept, y=0 otherwise) Full sample 200-sample1000-sample (1) (2) (3) Stake0.4340.39130.394 (0.204)***(0.2146)*(0.214)* 0.03020.02280.0231 Offer2.8152.83112.7921.5584.219 (0.675)***(0.7053)***(0.701)***(1.083)(1.080)*** 0.17010.14320.14250.09950.1035 Age-0.0901-0.093-0.221-0.016 (0.0762)(0.074)(0.117)*(0.139) -0.4274-0.4435-1.2505-0.0398 Age20.00130.0010.0030.0003 (0.0009)(0.001)(0.001)***(0.001) 0.28100.2920.76130.0367 Gender-0.3762-0.394-0.537-0.357 (0.2197)*(0.212)*(0.287)*(0.357) -0.0219-0.0232-0.0398-0.001 Education0.00960.012-0.0050.032 (0.0371)(0.035)(0.050)(0.055) 0.01300.017-0.0080.0218 Parent-0.5659-0.572-0.359-1.099 (0.3412)*(0.340)*(0.400)(0.828) -0.0373-0.038-0.298-0.0332 Income-0.0042 (0.0355) -0.0014 InD0.3894 (0.5516) 0.0021 Constant0.0361.89411.9314.9170.747 (0.321)(1.5670)(1.494)(2.335)**(2.691) Observation394 194200 LR χ 2 19.12***32.45***31.78***15.76***24.39*** Pseudo R 2 0.0880.14590.14640.12680.2686

18. The model fitting statistics for the 2nd regression show an increase in significance of LR chi-square test and in value of Pseudo R-square from 0,088 to 0.1464, which means a 70% increase in model explaining power with the inclusion of socioeconomic variables. Eckel and Grossman (2001) ;Solnick(2001) In the low stake sample, the economic variable Offer is no longer significant, while those socioeconomic variables including Age and Gender become significant. In the high stake sample, by contrast, none of socioeconomic variables is significant while the economic factor Offer is the dominant and only significant varaible.

19. Rabin (1993) “fairness equilibrium” Stigler (1981), p. 176) claims: “[When] self-interest and ethical values with wide verbal allegiance are in conflict, much of the time, most the time in fact, self-interest theory … will win.” Factors affecting proposers’ behavior

20. Table 6. Ordered Probit estimates of proposer behavior (dependent variable y=1 if offer=90/10, y=2 if offer=80/20, …, y=6 if offer=40/60) Full sample 200-sample1000-sample (1)(2) (3) Stake -0.3589 -0.3592-0.3597 (0.1187)*** (0.1194)***(0.1193)*** Age0.05760.05120.1212-0.033 (0.0410)(0.0390)(0.0532)***(0.0589) Age2-0.0006-0.0005-0.00140.0004 (0.0005) (0.0006)***(0.0007) Gender0.0009-0.0061-0.06710.0462 (0.1232)(0.1191)(0.1694)(0.1713) Education0.032140.0327-0.01580.076 (0.0224)(0.0213)(0.0321)(0.0295)*** Parent-0.0804-0.0426-0.35440.2825 (0.1928) (0.2686)(0.2831) Income-0.0013 (0.030) InD-0.2176 (0.2856) λ1λ1 -1.8211-0.2717-0.37570.1154-0.9322 (0.1254)(0.8011)(0.7490)(1.0253)(1.1148) λ2λ2 -1.51890.0360-0.06850.3366-0.5577 (0.1104)(0.8009)(0.7474)(1.0226)(1.1126) λ3λ3 -1.13170.42860.3230.9147-0.2769 (0.0988)(0.8010)(0.7463)(1.0199)(1.1112) λ4λ4 -0.86780.69520.58931.15030.0213 (0.0945)(0.8010)(0.7460)(1.0200)(1.1102) λ5λ5 1.44423.02922.91943.31532.6872 (0.1142)(0.8139)***(0.7610)***(1.0434)***(1.1367)*** Observation397 197200 LRχ 2 9.25***15.49***14.96***5.337.55 Pseudo R 2 0.01060.01780.01720.01270.0175

21. Choices Probability Figure3. Predicted offer probability and its cumulative distribution by stakes

22. Since the curve representing the CDF in the low stake strictly lies below that in the high stake, it is apparent that the CDF in the low stake first-degree stochastically dominates the CDF in the high stake.

23. Age is the only socioeconomic variable that features significantly when stakes are low, while Education is the only socioeconomic variable that features significantly when stakes are high. It thus seems that experience (Age) is important for determining offers when stakes are low, while embodiment of fairness norms (Education) becomes important when stakes are high. those who are young and old offer less and reject less often than those who are in the middle age. This implies that those who are young and old behave closer toward the subgame- perfection prediction of the standard theory than those who are in the middle age. It thus seems that experience teaches people to move away from the prediction of the economic model in the earlier stage of their life, but return toward it in the later stage. The turning points are around 39 and 43 years of old, respectively, for responders and proposers.

24. It should be emphasized that this lifecycle pattern holds only if stakes are low. When stakes are high, monetary incentives dominate responders’ behavior and Education is the only socioeconomic variable that features significantly in explaining players’ offer behavior.

25. Conclusion We find that: (i) raising stakes substantially reduce the number of “outliners” on both offers and rejections; (ii) higher stakes exert a significant impact on players’ offer and rejection behavior as the standard economic theory predicts even for inexperienced or one-shot play; and (iii) socioeconomic characteristics dominate responders’ behavior when stakes are low, whereas monetary stakes dominates responders’ behavior when stakes are high. Smith and Walker (1993) [Increased] financial reward shifts the central tendency of the data toward the predictions of rational models, …[and] rewards reduce the variance of the data around the predicted outcomes.