In Broad Daylight: Fuller Information and Higher-Order Punishment Opportunities Can Promote...

In Broad Daylight: Fuller Information and Higher-Order Punishment

Opportunities Can Promote Cooperation

Kenju Kamei – Bowling Green State University

Louis Putterman – Brown University

• In laboratory experiments with many subject pools, voluntary contributions to a group activity (public good) can be stabilized by opportunities to assign costly punishment (informal sanctions [IS]).

• But some second-generation contribution-and-punishment experiments have suggested that an overly sanguine impression about IS arises from artificial suppression of counter-punishment and vendettas.

• We investigate experimentally whether providing subjects with full information on initial punishments and allowing unrestricted higher-order punishment reduces the benefits of IS in a VCM setting.

• We reconfirm that counter-punishment is efficiency-reducing in an information-poor environment like that of Nikiforakis (2008), but we find that generalized higher-order punishment opportunities in a fuller-information environment are associated with higher, not lower, cooperation and earnings.

Background• A large literature (Ledyard, 1995; Zelmer, 2003;

Gӓchter and Herrmann, 2008) shows that in the finitely repeated VCM with n ≥ 2 and 0 < mpcr < 1, contributions decline with repetition (absent punishment, communication, etc.).

• Fehr and Gӓchter (2000) and numerous subsequent studies showed that adding a second stage to each period, in which subjects can engage in costly IS, reverses or retards the decline.

A figure from Fehr and Gӓchter (2000).

• To prevent vendettas, FG randomly scrambled subject IDs in their partner groups; even so, there was some punishment of high contributors, which Cinyabuguma, Page and Putterman (2006) and Herrmann, Thöni and Gӓchter (2008) argue may mainly be attempts to counter-punish. (Herrmann et al. find that in subject pools of countries in southeast and eastern Europe and the middle east, “anti-social punishment” is so common that availability of IS doesn’t aid cooperation.)

• Nikiforakis (2008) suggested that identification of one’s punisher and the possibility to retaliate is more realistic in many situations.

• He replicated FG (2000)’s results in one treatment but in another added a third stage in which subjects could counter-punish.

• In Nikiforakis’s counter-punishment treatment, a subject i learns only who punished i by how much and can only counter-punish those individuals (in a dedicated 3rd stage).

• After the 3rd stage, a new period begins with scrambled identities.

Nikiforakis (2008) partner treatment results.

• Similar results obtained by Hopfensitz and Reuben (2009) and Engel, Kube & Kurschilgen (2011).

• Denant-Boemont, Masclet and Noussair (2007) replicated Nikiforakis’s counter-punishment results, also introduced a “fuller-information” treatment.

• In it, each period has 3 stages as in Nikiforakis (2008) but subjects are informed of all stage 2 bi-lateral punishments and anyone can engage in stage 3 punishment.

• In principle, both counter-punishment and “punishment enforcement” are possible.

• “Punishment enforcement” can include - Punishing individuals who fail to punish low contributors to the group account+

- Punishing individuals who punish anti-socially* or perversely** ++

● DB-et al.’s fuller information treatment produced cooperation levels less harmed by availability of the 3rd stage (2nd punishment opportunity) than the counter-punishment only treatment, but no improvement in cooperation or efficiency relative to FG (2000).+ PEO punishment enforcement for omission ++PEC punishment enforcement for commission




* Anti-social punishment: i punishes j, where Ci < Cj.** Perverse punishment: a contributor of more than the group average for the period is punished.Most cases of anti-social punishment are also cases of perverse punishment, but this isn’t necessary.Consider: contributions 2, 4, 6, 8. Contributor of 2 punishes contributor of 4. This punishment is anti-social but not perverse.




* Perverse punishment: a contributor of more than (or equal to) the group average for the period is punished.** Anti-social punishment: i punishes j, where Ci < Cj.Most cases of anti-social punishment are also cases of perverse punishment, but this isn’t necessary.I’ll call punishment that is not “perverse”: “normal.”

• Cinyabuguma et al. (2006) studied “higher-order punishment” (punishment conditioned on others’ 1st order punishing) in a more constrained setting and found efficiency to be just as high with such punishment avialable as in a standard FG type cooperation-and-punishment experiment.

• Recent experiments on feuding allow the number of punishment stages in a period to be determined endogenously. These include Nikiforakis and Engelmann (2011), Nicklisch and Wolff (2011), and Nikiforakis, Noussair and Wilkening (forthcoming).

Motivation of Our Experiment• We conjecture that fuller information about

who punished whom may improve cooperation both (a) by hastening norm emergence, and (b) by making possible “punishment enforcement” (especially Punishment Enforcement for Commission [PEC] rather than Punishment Enforcement for Omission [PEO]).

Motivation (cont.)• We suspect that dedicated higher-order punishment

stages can have an “experimenter demand effect”—if subjects have no other decisions to make except to punish again, they are more likely to punish again.

• We therefore limit the number of stages available for nothing other than punishing, instead letting punishment of high order occur by maintaining identity information across periods.

• Punishment opportunities and the (1st order) social dilemma itself (how much to contribute) are thus “inter-leaved” in terms of action stages.

Experimental Design• Standard VCM structure with n = 4, mpcr =

0.4, E = 20, Ci must be integer.• Standard punishment technology in which it

costs an individual 1 point to reduce the earnings of the targeted individual by 3 points (1:3 cost ratio), as in FG (2002), Nikiforakis-Normann (2008), etc.

Period t earnings of subject i are , where pp means higher-order pun.

min

Design (cont.)• Subjects play for 15 periods in partner groups.• There are two Reference treatments without

possibility of (informed) higher-order punishment, six treatments with h-o pun.

• 3 EGO treatments: Subject IDs change each period, subjects only learn who punished them, subjects can only counter-punish.

• 3 FULL treatments: Subject IDs fixed for all 15 periods, subjects learn all bilateral punishments, subjects can engage in higher-order punishment of any group member(s).

Design (cont.)• In each category (EGO, FULL) there is a 2-stage treatment,

a 3-stage treatment without additional history information, and a 3-stage treatment with additional history information:

EGO2, EGO3, EGO3histFULL2, FULL3, FULL3hist

● The purpose of 2-stage treatments is to reduce “experimenter demand,” but at least last period’s punishment must be shown at this period’s punishment stage, to permit counter-punishment.● We have “3hist” treatments to have both “history display” (as in 2-stage treatments) and the extra punishment stage (as in EGO3 and FULL3).

Design (cont.)• For comparison, each set of treatments has its

Reference treatment: EGO2, EGO3, EGO3hist, Reference (random ID) FULL2, FULL3, FULL3hist, Reference (fixed ID)

Reference treatments have 2 stages per period and no possibility of informed higher-order punishment (similar to FG2000, etc.).

Table 1. Summary of treatments, contributions and earnings

Treatment Information Structure1

The number of stages in each period

History2 higher order punishment

opportunities

Total number

of sessions

Total number of

groups3

Average contributions

Average Earnings

(a) Treatments with Full Information and Fixed ID Reference

Reference (Fixed ID) N 2 NO NO 2 10 14.0 25.5

FULL2 F 2 YES YES 2 10 16.7 28.3

FULL3 F 3 NO YES 2 10 14.9 26.4

FULL3hist F 3 YES YES 2 9 18.3 29.5

(b) Treatments with Ego-centered Information and Random ID

Reference

Reference (Random ID) N 2 NO NO 2 10 14.5 26.6

EGO2 E 2 YES YES 2 10 16.5 28.0

EGO3 E 3 NO YES 2 10 10.3 23.5

EGO3hist E 3 YES YES 3 12 13.7 26.6

Experiment as a whole 17 81

Notes: 1N = no information on who punished whom, E = “Ego-centered information,” F = “Full information.” 2 YES indicates that history of all past periods’ contributions and punishments are displayed, except in treatment EGO2, where history information is available for the most recent period only. In EGO2 and EGO3hist, only history information concerning subjects who have punished the decision-maker is displayed. 3 Each group has 4 subjects.

Results: contributions

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Reference (fixed ID)

FULL2

FULL3

FULL3hist

Period

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Reference (random ID)

EGO2

EGO3

EGO3hist

Period

Contributions are significantly higher in FULL3 and in FULL3hist than in Ref (fixed)

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


FULL2

FULL3

FULL3hist

Period

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


EGO2

EGO3

EGO3hist

Period

Contributions are significantly lower in EGO3 than in Ref (random) and EGO2.

Results: earnings

15

17

19

21

23

25

27

29

31

33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


FULL2

FULL3

FULL3hist

Period

15

17

19

21

23

25

27

29

31

33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


EGO2

EGO3

EGO3hist

Period

Earnings are significantly higher in FULL3hist than in Ref (fixed).

15

17

19

21

23

25

27

29

31

33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


FULL2

FULL3

FULL3hist

Period

15

17

19

21

23

25

27

29

31

33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


EGO2

EGO3

EGO3hist

Period

Earnings are significantly lower in EGO3 than in Ref (random), higher in EGO3hist than in EGO3, and higher in EGO2 than in EGO3.

• The one treatment that performs significantly worse than others is EGO3, which closely parallels the Nikiforakis (2008) counter-punishment treatment.

• Either eliminating a 3rd stage dedicated to punishment or carrying over history from period to period suffice to reduce inefficiency relative to the Reference treatments. (Both not needed.)

• The treatment that performs best is FULL3hist, with fullest information and higher-order punishment opportunities.

Table 1. Summary of treatments, contributions and earnings

Treatment Information Structure1

The number of stages in each period

History2 higher order punishment

opportunities

Total number

of sessions

Total number of

groups3

Average contributions

Average Earnings

(a) Treatments with Full Information and Fixed ID Reference

Reference (Fixed ID) N 2 NO NO 2 10 14.0 25.5

FULL2 F 2 YES YES 2 10 16.7 28.3

FULL3 F 3 NO YES 2 10 14.9 26.4

FULL3hist F 3 YES YES 2 9 18.3 29.5

(b) Treatments with Ego-centered Information and Random ID

Reference

Reference (Random ID) N 2 NO NO 2 10 14.5 26.6

EGO2 E 2 YES YES 2 10 16.5 28.0

EGO3 E 3 NO YES 2 10 10.3 23.5

EGO3hist E 3 YES YES 3 12 13.7 26.6

Experiment as a whole 17 81

Notes: 1N = no information on who punished whom, E = “Ego-centered information,” F = “Full information.” 2 YES indicates that history of all past periods’ contributions and punishments are displayed, except in treatment EGO2, where history information is available for the most recent period only. In EGO2 and EGO3hist, only history information concerning subjects who have punished the decision-maker is displayed. 3 Each group has 4 subjects.

There is more cost from punishment in the Reference treatments than in corresponding treatments with higher-order punishment opportunities, except for the EGO3 vs. Reference (random) comparison.

(a) Treatments with

Full Information (b) Treatments with

Eco-centered Information

Reference (Fixed ID)

FULL2 FULL3 FULL3hist Reference

(Random ID) EGO2 EGO3 EGO3hist

Total 2nd stage punishment cost (per subject, per period)

2.91 1.72 0.74 1.03 2.09 1.84 2.17 1.34

Total 3rd stage punishment cost (per subject, per period)

---- ---- 1.87 0.50 ---- ---- 0.51 0.23

Total punishment cost (per subject, per period)

2.91 1.72 2.61 1.53 2.09 1.84 2.68 1.57

Note: average total cost of punishment per period per subject calculated as cost to punisher plus cost to punishment recipient.

Expenditure on, and loss of earnings to, punishment

• Feuding experiments such as Nikiforakis and Engelmann (where presence of higher order punishment opportunities is less damaging to contributions and earnings than in Nikiforakis [2008] but definitely not helpful) provide equally full information and opportunities to engage in higher-order punishment of anyone, as in our FULL treatments.

• The difference is that in N&E’11 punishing continues in each period until a stage is reached at which no one wants to punish or no one can punish or can be punished (due to budget depletion).

• In our treatments, there’s a maximum of two punishment stages before the next period brings a new contribution stage.

• Which approach (limited vs. endogenous punishment stages) is more realistic may depend on what environment is being modeled.

• We think our approach makes sense for understanding an ongoing collective activity, e.g. a work team.

∞∞∞

What explains poor performance in EGO treatments, especially EGO3, vs. good performance in FULL treatments, especially FULL3hist?

• We find little evidence for “punishment enforcement” of either type (PEO, PEC) in the FULL treatments.

• But we find different patterns of counter-punishment in EGO vs. FULL treatments.

• Perverse and normal 1st order punishers are about equally likely to be counter-punished, and receive similar amounts of counter-punishment, in the EGO treatments, especially EGO3, whereas

• Perverse 1st order punishers receive significantly more counter-punishment than normal 1st order punishers in the FULL treatments, suggesting more agreement there on what (1st order) punishments are justified.

Fig.3. 3rd Stage counter-punishment as proportion of 2nd stage punishment events

Notes: We call the punishment “non-perverse” if it is directed to those who contributed less than the average contribution in their group. The punishment is “perverse” if it is directed at those who contributed more than or equal to the average contribution in their group.

0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0%

EGO3

FULL3

EGO3hist

FULL3hist

The percentage of events in which the second stage perverse punishers received counter-punishment in Stage 3 out of the total number of perverse punishment events in Stage 2

The percentage of events in which the second stage non-perverse punishers received counter-punishment in Stage 3 out of the total number of non-perverse punishment events in Stage 2

• Regressions to predict 3rd stage (2nd order) punishment as a function of contributions and 2nd stage (1st order) punishments in the same period show:

- significant correlations between 1st order punishment and 2nd order counter-punishment amounts in the FULL but not EGO treatments- significantly more counter-punishment of perverse than of normal 1st order punishers per unit of 1st order punishment in the FULL treatments

(3) Regression 2: Tobit Reg. with standard errors clustered by subjectid, no constant

EGO3 EGO3hist FULL3 FULL3hist Independent variable (5) (6) (7) (8)

Average contribution in period t 0.092** -0.078 -0.32*** -0.44*** (0.043) (0.047) (0.065) (0.066)

(i) Absolute negative deviation of subject j’s contribution from i’s contribution in period t

-0.21 (0.17)

-0.068 (0.055)

0.19*** (0.046)

0.13*** (0.038)

(ii) Positive deviation of j’s contribution from i’s contribution in period t

-0.22*** (0.084)

-0.14** (0.053)

-0.19 (0.11)

-0.23*** (0.082)

(iii) The amount of 2nd stage punishment i received from j if j contributed more than i; 0 otherwise

0.19 (0.23)

0.24 (0.26)

2.19*** (0.71)

1.63*** (0.23)

(iv) The amount of 2nd stage punishment i received from j if j contributed less than or equal to i; 0 otherwise

0.088 (0.15)

0.074 (0.074)

4.07*** (0.99)

4.12*** (0.43)

(v) The amount of 2nd stage Punishment j gave to subjects who contributed less than or equal to i (except i)

---- ---- -1.24** (0.56)

-0.40** (0.18)

(vi) The amount of 2nd stage punishment j gave to subjects who contributed more than i (except i)

---- ---- -0.22

(0.056) -1.00 (0.75)

Period -0.19 0.045 -0.21*** 0.15*** (0.12) (0.037) (0.056) (0.057)

# of Observations 143 120 1800 1620 Log Pseudo likelihood -138.26 -95.41 -717.29 -192.21

F 4.23 3.71 19.96 39.96 Prob > F .0006 .0021 .000 .000

F Test on (iii) = (iv)

F 0.15 0.52 4.39 29.00 p-value (2-sided) .6979 .4720 .0362** .0000***

Notes: The right-censoring limit is not specified. In columns (1) and (2), only observations in which subject j gave a positive amount of Stage 2 punishment to at least one subject in his or her group are used, since no 3rd stage punishment opportunities are available otherwise. The numbers of left-censored(right-censored) observations are 107(0) in column (5), 91(0) in column (6), 1662(3) in columns (7), and 1578(0) in column (8). *, ** and *** indicate significance at the 0.10 level, at the 0.05 level and at the .01 level, respectively. (3b) Tests for the equality of coefficients on variable (iii)

Dep. Var.:3rd stage (2nd order) pun. igave to j (We control for

determinants of 1st stage pun.)

Main expecteddeterminants of 2nd stage pun.

(3) Regression 2: Tobit Reg. with standard errors clustered by subjectid, no constant

EGO3 EGO3hist FULL3 FULL3hist Independent variable (5) (6) (7) (8)

Average contribution in period t 0.092** -0.078 -0.32*** -0.44*** (0.043) (0.047) (0.065) (0.066)

(i) Absolute negative deviation of subject j’s contribution from i’s contribution in period t

-0.21 (0.17)

-0.068 (0.055)

0.19*** (0.046)

0.13*** (0.038)

(ii) Positive deviation of j’s contribution from i’s contribution in period t

-0.22*** (0.084)

-0.14** (0.053)

-0.19 (0.11)

-0.23*** (0.082)

(iii) The amount of 2nd stage punishment i received from j if j contributed more than i; 0 otherwise

0.19 (0.23)

0.24 (0.26)

2.19*** (0.71)

1.63*** (0.23)

(iv) The amount of 2nd stage punishment i received from j if j contributed less than or equal to i; 0 otherwise

0.088 (0.15)

0.074 (0.074)

4.07*** (0.99)

4.12*** (0.43)

(v) The amount of 2nd stage Punishment j gave to subjects who contributed less than or equal to i (except i)

---- ---- -1.24** (0.56)

-0.40** (0.18)


---- ---- -0.22

(0.056) -1.00 (0.75)

Period -0.19 0.045 -0.21*** 0.15*** (0.12) (0.037) (0.056) (0.057)

# of Observations 143 120 1800 1620 Log Pseudo likelihood -138.26 -95.41 -717.29 -192.21

F 4.23 3.71 19.96 39.96 Prob > F .0006 .0021 .000 .000


F 0.15 0.52 4.39 29.00 p-value (2-sided) .6979 .4720 .0362** .0000***

Notes: The right-censoring limit is not specified. In columns (1) and (2), only observations in which subject j gave a positive amount of Stage 2 punishment to at least one subject in his or her group are used, since no 3rd stage punishment opportunities are available otherwise. The numbers of left-censored(right-censored) observations are 107(0) in column (5), 91(0) in column (6), 1662(3) in columns (7), and 1578(0) in column (8). *, ** and *** indicate significance at the 0.10 level, at the 0.05 level and at the .01 level, respectively. (3b) Tests for the equality of coefficients on variable (iii)

We see the take-away message being that in the FULL treatments, especially FULL3hist, there’s more concerted counter-punishment of perverse punishers, which perhaps helps drive higher contributions and efficiency in those treatments.

• In both 2 stage treatments (EGO2, FULL2), regressions suggest significant counter-punishment of 1st order punishments of the previous period, with greater counter-punishment of perverse than of normal 1st order punishment in both treatments.

(Note that ‘teasing apart’ punishing for contribution choice from punishing for past punishment choice is not an exact process.)

(2) Regression Result

Dependent variable: punishment received by subject j from subject i in Stage 2 in Period t

Linear Reg. w/o constant Tobit Reg. w/o constant Independent Variable EGO2 FULL2 EGO2 FULL2

[1] [2] [3] [4]

Average contribution in period t

0.0060*** (0.0016)

0.0044 (0.0028)

-0.13*** (0.027)

-0.16*** (0.032)

Absolute negative deviation in period t 0.065*** (0.019)

0.082*** (0.023)

0.24*** (0.043)

0.28*** (0.036)

Positive deviation in period t 0.011*** 0.013*** -0.0042 0.038 (0.0036) (0.0050) (0.036) (0.046)

[Last Period’s Punishment Behavior:]

(i) Absolute negative deviation of subject j’s contribution from i’s contribution in period t-1 ----

-0.0034 (0.0050)

---- -0.015 (0.038)

(ii) Positive deviation of j’s contribution from i’s contribution in period t-1

---- -0.012** (0.0055)

---- -0.18*** (0.053)

(iii) The amount of 2nd stage punishment i received from j in period t-1 if j contributed more than i in period t-1; 0 otherwise

0.098** (0.045)

0.076** (0.035)

0.65*** (0.23)

1.10*** (0.26)

(iv) The amount of 2nd stage punishment i received from j in period t-1 if j contributed less than or equal to i in period t-1; 0 otherwise

0.34** (0.14)

0.18 (0.12)

1.02*** (0.41)

1.81*** (0.47)

(v) The amount of 2nd stage punishment j gave to subjects who contributed less than or equal to i (except i) in period t-1

---- -0.018* (0.0088)

---- -0.64*** (0.24)


---- 0.022 (0.078)

---- 0.078 (0.49)

Period -0.010*** -0.0067 -0.24*** -0.21 (0.0035) (0.0055) (0.034) (0.053)

# of Observations 1680 1680 1680 1680 Log likelihood ---- ---- -625.0 -556.4

F 18.61 28.45 22.59 20.19 Prob > F .000 .000 .000 .000

R-Squared .2785 .2958 ---- ----


F 3.05 0.77 0.62 2.58

p-value .0884* 0.3852 0.4311 0.1087

Notes: Standard errors are clustered by subjectid in each specification. Our specification as a whole allows Stage 2 punishment in period t > 1 to be conditioned on both Stage 1 contribution in t and Stage 2 punishment in t – 1. Observations referencing punishment received in period 1 are omitted due to absence

Counter-punishment of normal punishers

Counter-punishment of

perverse punishers.

• In both 2 stage treatments (EGO2, FULL2), regressions suggest significant counter-punishment of 1st order punishments of the previous period, with greater counter-punishment of perverse than of normal 1st order punishment in both treatments.

• Thus, reducing separation of punishment and counter-punishment opportunities doesn’t eliminate counter-punishment, but the observed counter-punishment doesn’t interfere with and may actually reinforce the ability of punishment to help sustain cooperation.

• We also estimated regressions with treatment dummy variables to see how our four treatment parameters affect contributions and earnings respectively. The parameters are:

I – Identities remain fixed across periodsT – Third StageH – History from previous periods shownF – Full information shown on all

punishments and opportunities to punish any subject.

Results show- Having fixed identifiers per se makes no significant difference to

contributions or earnings- Having a 3rd stage significantly reduces both contributions and

earnings. - However, having full information along with 3rd stage significantly

increases contributions and earnings. On net, contributions are slightly increased by having both T and F, earnings are slightly reduced by having both T & F.

- Having history information per se increases earnings by a smaller amount than the effects of 3rd stage or T & F, and with less statistical significance.

These results should be treated as suggestive only because they use individual level observations (averaged for an individual over all 15 period) without clustering errors by group. When errors are clustered or when group level observations are used in the regressions, there are no statistically significant results.

Conclusion• Our data suggest that the danger that one will be

counter-punished if punishment recipients learn who punished them and how much doesn’t necessarily undermine the ability of IS to promote cooperation.

• In several treatments, the availability of the information and opportunities for higher-order punishment are associated with higher contributions than in treatments with opportunities for 1st order punishment only.

• In one case, the difference is statistically significant.

• We find little evidence of (3rd party) punishment enforcement.

• Instead, treatments with fuller information and more general opportunities for higher-order punishment are marked by more pro-social bias in the pattern of counter-punishment: those who 1st order punish perversely receive more counter-punishment relative to non-perverse 1st order punishers in these FULL treatments.

• We conjecture that more complete information about the pattern of punishment in the group favors the emergence of norms supportive of cooperation (when the subject pool is one in which such norms are likely to be supported).

• This result is consistent with the typical presence of more cooperatively-inclined than anti-socially inclined individuals in the subject pool.

• Seeing that low contributors are punished more than high ones are and that punishers of high contributors tend to be heavily punished may lead more subjects to cooperate more in the contribution stage and to punish pro-socially if at all.

• The idea that voluntary cooperation or decentralized collective action can be aided by punishment opportunities may accordingly survive the availability of counter-punishment.

• But the danger of feuds appears to discourage initial punishment and even rare feuds deplete resources in the design of Nikiforakis and Engelmann (2011).

• Conclusions may therefore turn on which experimental setting is more relevant to which real world problems of interest.

Thank you.

In Broad Daylight: Fuller Information and Higher-Order Punishment Opportunities Can Promote...

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