Monetary Stakes and Socioeconomic Characteristics in Ultimatum Games: An Experiment with Nation-Wide Representative Subjects

Tsu-Tan FuCenter for Survey Research and Institute of Economics, Academia Sinica, Nankang, Taipei 115, TaiwanWei-Hsin KongInstitute of Industrial Economics, National Central UniversityC.C. YangInstitute of Economics, Academia Sinica, Nankang, Taipei 115, TaiwanDepartment of Public Finance, National Chengchi University, Wenshan, Taipei 116, Taiwan

• 1. Introduction

• Roth et al. (1991)

• Ultimatum game • Stahl (1972) and Rubinstein (1982)

• Stakes?

• 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

• 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

• 2. Experimental design

• Subjects

• Procedures

• 3. Results• Characteristics of the sample

Table1. Descriptive statistics of the sample

　 Definition Mean Standard Deviation.

GenderDummy;1 for male0 for female

0.512 0.500

ParentDummy;1 for Yes0 for No

0.636 0.481

StudentDummy;1 for Yes0 for No

0.074 0.263

Income NT dollars/ month 28574.3 29906.2Age Years of age 40.882 12.670 Age distribution

20-40 49.18%

40-60 43.49%

60~ 7.33%

100.00%Education Years of schooling 12.242 3.565 Education distribution

Elementary & below 11.90%

Junior high school 12.03%

Senior high school 34.18%

Junior college 18.48%

College & above 23.42%

100.00%

• Offer and (conditional) acceptance pattern

Table 2. Summary of offers and (conditional) acceptances

Stake=200 Stake=1000

OfferChoice Offer Acceptance Odder Acceptance

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%)

Total 197 (100.00%) 175 (88.83%) 200 (100.00%) 188 (94.00%)

0%

20%

40%

60%

80%

100%

120%

1 2 3 4 5 6

P200:Proposer at stake=200 R200:Responder at stake=200P1000:Proposer at stake=1000 R1000:Responder at stake=1000

P200P1000

Choices

R1000

0R200

Percentage

Figure 1. Frequencies of offers and acceptances by stakes

• 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).

• 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

Table3 Frequencies of offers and acceptances by students and non-students

Offers Acceptances

Choices Student (%)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%)

5 26 (81.30%) 250 (68.50%) 19 (100.00%)

243 (95.70%)

6 0 (0.00%) 22 (6.00%) 2 (100.00%)

16 (80.00%)

Total 32 (100.00%) 365 (100.00%) 27(100.00%)

336 (91.60%)

▲

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

1 2 3 4 5 6

Student proposerStudent responder

Non-student proposerNon-student responder

Percentage

Choices

Figure 2. Frequencies of offers and acceptances by students and non-students

• Factors affecting responders’ behavior • Experiments with children indicate that fairness tastes

are not innate, but learned through socialization

• 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.

Proposers Responders

Age Education Income Age Education Income

Age 1 1

Education -0.5506 1 -0.4773 1

Income 0.1503 0.246 1 0.069 0.3143 1

Table 4. Correlations between Age, Education, and Income

Table 5. Probit estimates of responder behavior (dependent variable y=1 if accept, y=0 otherwise)

Full sample Full sample Full sample 200-sample 1000-sample

(1) (2) (3)

Stake 0.434 0.3913 0.394

(0.204)*** (0.2146)* (0.214)*

0.0302 0.0228 0.0231 Offer 2.815 2.8311 2.792 1.558 4.219

(0.675)*** (0.7053)*** (0.701)*** (1.083) (1.080)***

0.1701 0.1432 0.1425 0.0995 0.1035

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

Age2 0.0013 0.001 0.003 0.0003

(0.0009) (0.001) (0.001)*** (0.001)

0.2810 0.292 0.7613 0.0367

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

Education 0.0096 0.012 -0.005 0.032

(0.0371) (0.035) (0.050) (0.055)

0.0130 0.017 -0.008 0.0218

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

InD 0.3894

(0.5516)

0.0021 Constant 0.036 1.8941 1.931 4.917 0.747

(0.321) (1.5670) (1.494) (2.335)** (2.691)Observation 394 394 394 194 200LR χ2 19.12*** 32.45*** 31.78*** 15.76*** 24.39***Pseudo R2 0.088 0.1459 0.1464 0.1268 0.2686

• 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.

• 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

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 Full sample Full sample 200-sample 1000-sample

(1) (2) (3)

Stake -0.3589 -0.3592 -0.3597

(0.1187)*** (0.1194)*** (0.1193)***

Age 0.0576 0.0512 0.1212 -0.033

(0.0410) (0.0390) (0.0532)*** (0.0589)

Age2 -0.0006 -0.0005 -0.0014 0.0004

(0.0005) (0.0005) (0.0006)*** (0.0007)

Gender 0.0009 -0.0061 -0.0671 0.0462

(0.1232) (0.1191) (0.1694) (0.1713)

Education 0.03214 0.0327 -0.0158 0.076

(0.0224) (0.0213) (0.0321) (0.0295)***

Parent -0.0804 -0.0426 -0.3544 0.2825

(0.1928) (0.1928) (0.2686) (0.2831)

Income -0.0013

(0.030)

InD -0.2176

(0.2856)

λ1-1.8211 -0.2717 -0.3757 0.1154 -0.9322

(0.1254) (0.8011) (0.7490) (1.0253) (1.1148)

λ2-1.5189 0.0360 -0.0685 0.3366 -0.5577

(0.1104) (0.8009) (0.7474) (1.0226) (1.1126)

λ3-1.1317 0.4286 0.323 0.9147 -0.2769

(0.0988) (0.8010) (0.7463) (1.0199) (1.1112)

λ4-0.8678 0.6952 0.5893 1.1503 0.0213

(0.0945) (0.8010) (0.7460) (1.0200) (1.1102)

λ51.4442 3.0292 2.9194 3.3153 2.6872

(0.1142) (0.8139)*** (0.7610)*** (1.0434)*** (1.1367)***

Observation 397 397 397 197 200LRχ2 9.25*** 15.49*** 14.96*** 5.33 7.55Pseudo R2 0.0106 0.0178 0.0172 0.0127 0.0175

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

1 2 3 4 5 6

Predict-200 Predict-1000 CDF-200 CDF-1000

Choices

Probability

Figure3. Predicted offer probability and its cumulative distribution by stakes

• 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.

• 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.

• 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.

• 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.