1. Rie Mashima & Nobuyuki Takahashi (Hokkaido University)
Is the enemy’s friend an enemy?
An experimental study to examine strategies in indirect reciprocity settings
Rie Mashima & Nobuyuki Takahashi
(Hokkaido University)

2. Overview
Purpose:
to empirically examine people’s strategies in situations of indirect reciprocity
We introduce theoretical solutions (strategies) which make indirect reciprocity possible.
We show results of a laboratory experiment which was conducted to examine people’s actual strategies in situations of indirect reciprocity.

3. ◆How can altruism exist in society?
Kin selection (Hamilton, 1964)
←only among close kin.
Direct reciprocity (e. g., Tit for tat)
←only among two players.
Indirect reciprocity
Indirect reciprocity can make altruism possible among N-persons.
When one person who helps a second person is reciprocated not by the second person, but by a third person.
How can indirect reciprocity emerge?
(What kind of strategy can make indirect reciprocity possible?)

4. Framework of giving game
In each round, a donor is randomly chosen.
The donor decides whether to give his resource to the recipient with a cost of c　(recipient receives a benefit b: b>c) .
Each player has a reputation score which has two values: “Good” or “Bad”.
A donor gives if he thinks the recipient’s score is “Good”.
A donor doesn’t give if he thinks the recipient’s score is “Bad”.
Score
How to assign a score is regulated by a strategy.

5. 2nd-order information 1st-order information gave Good or or Bad
Strategy
A donor assigns a score to a recipient by using two types of information based on recipient’s previous behavior as a donor.
(1)Their previous behavior
(2)The reputation of their previous recipient
2nd-order information
1st-order information
(2)The reputation of the recipient’s previous recipient
(1) The recipient’s previous behavior
gave
Good or or
Bad
did not give
current recipient
current donor
current recipient’s previous recipient

6. Good Bad Gave Did not give Strategy
A donor assigns a score to a recipient by using two types of information based on recipient’s previous behavior as a donor.
(1)Their previous behavior
(2)The reputation of their previous recipient
Table 1. Four genes that assign the score to others
Current recipient’s
Good
Bad
Gave
Did not give
previous recipient’s reputation
previous behavior

7. What kind of strategy is the solution?
・4 genes determine how to assign a score to each type of other by using two types of information.
・Strategies are represented by the sets of 4 genes.
(e. g. GGGG→ALLC (unconditional cooperator)
BBBB→ALLD (unconditional defector)
…16 strategies are possible.)
Although every strategy gives to a good recipient, each strategy has a different pattern to assign a score.
Table 1. Four genes that assign the score to others
Current recipient’s
Good
Bad
Gave
① Good or Bad
② Good or Bad
Did not give
③ Good or Bad
④ Good or Bad
What kind of strategy is the solution?
← Previous theoretical studies have been conducted using
evolutionary computer simulations & mathematical analyses.
previous recipient’s reputation
previous behavior

8. Strategies proposed by previous theoretical studies
ALLD dominated in 20/20 replications.
ALLD dominated in 6/20 replications.
Instead, other two strategies could make
indirect reciprocity possible.
Critically examining these strategies, we found that neither Image scoring nor Standing can make indirect reciprocity possible (Takahashi & Mashima, in press).
GGBB: Image scoring strategy (Nowak & Sigmund, 1998)
Good
Bad
Gave
Did not give
GGBG: Standing strategy (L & H, 2001; P & B, 2003)
Good
Bad
Gave
Did not give

9. Theoretical solutions (Takahashi & Mashima, JTB, in press)
Our theoretical studies proposed two strategies.
Strict Discriminator (GBBB)
Extra Standing (GBBG)
Good
Bad
Gave
Good
Bad
Did not give
Bad
Bad
Good
Bad
Gave
Good
Bad
Did not give
Bad
Good

10. Theoretical solutions (Mashima & Takahashi, in press)
Three keys to make indirect reciprocity possible
Our theoretical studies proposed two strategies.
Only the strategies which regard “a person who gave to Bad” (←unconditional cooperator) as ‘Bad’ can make indirect reciprocity possible.
Our results of a series of computer simulations and mathematical analysis showed that…
Strict Discriminator (GBBB)
Extra Standing (GBBG)
Good
Bad
Gave
Good
Bad
Did not give
Bad
Bad
Good
Bad
Gave
Good
Bad
Did not give
Bad
Good

11. Theoretical solutions (Mashima & Takahashi, in press)
Three keys to make indirect reciprocity possible
To regard a person who didn’t give despite having had a chance to give to a Good person as “Bad” (i.e., to exclude a free rider)
Our theoretical studies proposed two strategies.
Only the strategies which regard “a person who gave to Bad” (←unconditional cooperator) as ‘Bad’ can make indirect reciprocity possible.
Our results of a series of computer simulations and mathematical analysis showed that…
Strict Discriminator (GBBB)
Extra Standing (GBBG)
Good
Bad
Gave
Good
Bad
Did not give
Bad
Bad
Good
Bad
Gave
Good
Bad
Did not give
Bad
Good

12. Theoretical solutions (Mashima & Takahashi, 2003; Takahashi & Mashima, 2003)
Three keys to make indirect reciprocity possible
To regard a person who didn’t give despite having had a chance to give to a Good person as “Bad” (i.e., to exclude a free rider)
(b) To regard a person who gave to a Good person as “Good” (i.e., to help a conditional giver)
These two characteristics are identical with those of previous solutions (IS, Standing). Moreover..
Our theoretical studies proposed two strategies.
Only the strategies which regard “a person who gave to Bad” (←unconditional cooperator) as ‘Bad’ can make indirect reciprocity possible.
Our results of a series of computer simulations and mathematical analysis showed that…
Strict Discriminator (GBBB)
Extra Standing (GBBG)
Good
Bad
Gave
Good
Bad
Did not give
Bad
Bad
Good
Bad
Gave
Good
Bad
Did not give
Bad
Good

13. Theoretical solutions (Mashima & Takahashi, 2003; Takahashi & Mashima, 2003)
Three keys to make indirect reciprocity possible
To regard a person who didn’t give despite having had a chance to give to a Good person as “Bad” (i.e., to exclude a free rider)
(b) To regard a person who gave to a Good person as “Good” (i.e., to help a conditional giver)
(c) To regard a person who gave to a Bad person as “Bad” (i.e., to exclude an unconditional giver).
Our theoretical studies proposed two strategies.
Only the strategies which regard “a person who gave to Bad” (←unconditional cooperator) as ‘Bad’ can make indirect reciprocity possible.
Our results of a series of computer simulations and mathematical analysis showed that…
The most important difference between our conclusion and that of previous studies.
Strict Discriminator (GBBB)
Extra Standing (GBBG)
Good
Bad
Gave
Good
Bad
Did not give
Bad
Bad
Good
Bad
Gave
Good
Bad
Did not give
Bad
Good

14. The most important key to make indirect reciprocity possible is to distinguish a person who gave to “Good” from a person who gave to “Bad” and regard a person who gave to “Bad” as “Bad” (i.e., to regard a friend of enemy as an enemy, too).
Theoretical solutions (Mashima & Takahashi, 2003; Takahashi & Mashima, 2003)
Do people actually regard others in such a way? (Do people really exclude such “saints” who helped Bad?)
Strict Discriminator (GBBB)
Extra Standing (GBBG)
Good
Bad
Gave
Good
Bad
Did not give
Bad
Bad
Good
Bad
Gave
Good
Bad
Did not give
Bad
Good

15. A vignette study (Mashima & Takahashi, in press)
We conducted a vignette study to examine people’s patterns of evaluation toward others in situations of indirect reciprocity.
Respondents read a scenario which described the behavior of the target person (1st and 2nd order Info). It described…
what the target person did (gave or didn’t give)
the reputation of a previous recipient of the target (a Good person who had given his/her resource to another person or a Bad person who hadn’t given to anyone)
Respondents answered their impressions about the target.

16. A vignette study (Mashima & Takahashi, in press)
Three keys to make indirect reciprocity possible
To regard a person who didn’t give as “Bad”
To regard a person who gave to a Good person as “Good”
To regard a person who gave to a Bad person as “Bad”
We conducted a vignette study which examined people’s patterns of evaluation toward others in situations of indirect reciprocity.
Respondents read a scenario which described the behavior of the target person (1st and 2nd order Info). It described…
what the target person did (gave or didn’t give)
the reputation of a previous recipient of the target (a Good person who had given his/her resource to another person or a Bad person who hadn’t given to anyone)
Respondents answered their impressions about the target.
Results were consistent with our theoretical conclusion.
Respondents…
a) NEGATIVELY evaluated a person who didn’t give.
b) POSITIVELY evaluated a person who gave to a Good person.
c) NEGATIVELY evaluated a person who gave to a Bad person.

17. A vignette study (Mashima & Takahashi, in press)
Three keys to make indirect reciprocity possible
To regard a person who didn’t give as “Bad”
To regard a person who gave to a Good person as “Good”
To regard a person who gave to a Bad person as “Bad”
We conducted a vignette study which examined people’s patterns of evaluation toward others in situations of indirect reciprocity.
Respondents read a scenario which described the behavior of the target person (1st and 2nd order Info). It described…
what the target person did (gave or didn’t give)
the reputation of a previous recipient of the target (a Good person who had given his/her resource to another person or a Bad person who hadn’t given to anyone)
Respondents answered their impressions about the target.
Results were consistent with our theoretical conclusion. (People actually regarded as “Bad” not only a person who didn’t give but also a person who gave to “Bad”)
Respondents…
a) NEGATIVELY evaluated a person who didn’t give.
b) POSITIVELY evaluated a person who gave to a Good person.
c) NEGATIVELY evaluated a person who gave to a Bad person.

18. A vignette study (Mashima & Takahashi, in press)
Three keys to make indirect reciprocity possible
To regard a person who didn’t give as “Bad”
To regard a person who gave to a Good person as “Good”
To regard a person who gave to a Bad person as “Bad”
We conducted a vignette study which examined people’s patterns of evaluation toward others in situations of indirect reciprocity.
Respondents read a scenario which described the behavior of the target person (1st and 2nd order Info). It described…
what the target person did (gave or didn’t give)
the reputation of a previous recipient of the target (a Good person who had given his/her resource to another person or a Bad person who hadn’t given to anyone)
Respondents answered their impressions about the target.
However, these results are nothing but self-reports...
Do people actually behave in such a manner when they are faced with a real exchange?
Consistent with our theoretical conclusion. (People actually regarded as “Bad” not only a person who didn’t give but also a person who gave to “Bad”)
Respondents…
a) NEGATIVELY evaluated a person who didn’t give.
b) POSITIVELY evaluated a person who gave to a Good person.
c) NEGATIVELY evaluated a person who gave to a Bad person.

19. Our purpose is…
to examine people’s actual behaviors when they faced with the situations of resource exchange with a cost.
We conducted a laboratory experiment of N-person giving game.

20. keep it for themselves (They received 50 yen).
Experimental method
Participants engaged in 17 rounds of a giving game in 8-person group through computers.
Giving game
On each round, participants were given 50 yen as an endowment and decided whether they
give it to one of the other participants (The endowment they gave were doubled and given to their recipients: recipients received 100 yen) or
keep it for themselves (They received 50 yen).
After each round, they received the feedback information (=how much they received in the round).
Participants: 39 undergraduate students in Hokkaido University

21. 2nd-order information about all members.
Experimental method
Participants engaged in 17 rounds of a giving game in 8-person group through computers.
Giving game
On each round, participants were given 50 yen as an endowment and decided whether they
give it to one of the other participants (The endowment they gave were doubled and given to their recipients: recipients received 100 yen) or
keep it for themselves (They received 50 yen).
After each round, they received the feedback information (=how much they received in the round).
When they made their decisions, they could see
1st-order information
2nd-order information about all members.
Participants: 39 undergraduate students in Hokkaido University

22. Displayed information
Two types of information about past behaviors of all 8 members were shown on the computer screen.
This person…
Gave in the last round
to the person who had not given two rounds before

23. Displayed information
Two types of information about past behaviors of all 8 members were shown on the computer screen.
This person…
1st-order information:
whether each target gave or didn’t give on the last round
Gave in the last round
to the person who had not given two rounds before

24. Displayed information
Two types of information about past behaviors of all 8 members were shown on the computer screen.
This person…
1st-order information:
whether each target gave or didn’t give on the last round
Gave in the last round
2) 2nd-order information:
(If 1st-order information was “gave”,) whether the person had given to a giver or had given to a non-giver on the last round
to the person who had not given two rounds before

25. Dependent variables: Preference for each type
What kind of person participants chose (or avoided) as recipients?
DV: giving rate toward each type of others
Didn’t give in the last round
3) Non-giver (NG)
Gave in the last round
toward a person who had given 2 rounds before
1) Giver to Giver (GtoG)
Gave in the last round
2) Giver to Non-giver (GtoNG)
toward a person who hadn’t given 2 rounds before
1st-order info
2nd-order info

26. Dependent variables: Preference for each type
Theoretically, The key to make indirect reciprocity is…
(a) To exclude a person who didn’t give to anyone
(b) To reward a person who gave to “Good” who had given in the past.
(c) To exclude a person who gave to “Bad” who hadn’t given.
What kind of person participants chose (or avoided) as recipients?
1) Giver to Giver (GtoG)
2) Giver to Non-giver (GtoNG)
3) Non-giver (NG)
1st-order info
Gave in the last round
Gave in the last round
Didn’t give in the last round ＞
2nd-order info
toward a person who had given 2 rounds before
toward a person who hadn’t given 2 rounds before
Predictions: participants...

27. Dependent variables: Preference for each type
Theoretically, The key to make indirect reciprocity is…
(a) To exclude a person who didn’t give to anyone
(b) To reward a person who gave to “Good” who had given in the past.
(c) To exclude a person who gave to “Bad” who hadn’t given.
What kind of person participants chose (or avoided) as recipients?
1) Giver to Giver (GtoG)
2) Giver to Non-giver (GtoNG)
3) Non-giver (NG)
1st-order info
Gave in the last round
Gave in the last round
Didn’t give in the last round ＞
Discrimination based on 1st-order info.
2nd-order info
toward a person who had given 2 rounds before
toward a person who hadn’t given 2 rounds before
Predictions: participants...
will not give to “Non-giver”.
DV: giving rate toward each type of others

28. Dependent variables: Preference for each type
Theoretically, The key to make indirect reciprocity is…
(a) To exclude a person who didn’t give to anyone
(b) To reward a person who gave to “Good” who had given in the past.
(c) To exclude a person who gave to “Bad” who hadn’t given.
What kind of person participants chose (or avoided) as recipients?
1) Giver to Giver (GtoG)
2) Giver to Non-giver (GtoNG)
3) Non-giver (NG)
1st-order info
Gave in the last round
Gave in the last round
Didn’t give in the last round ＞
Discrimination based on 1st-order info.
2nd-order info
toward a person who had given 2 rounds before
toward a person who hadn’t given 2 rounds before
Discrimination based on 2nd-order info.
Predictions: participants...
1. will not give to “Non-giver”.
2. will give more to “Giver to Giver” than to “Giver to Non-giver”.
DV: giving rate toward each type of others

29. Dependent variables: Preference for each type
Prediction: People discriminate their recipients based on not only 1st-order information, but also 2nd-order information.
Dependent variables: Preference for each type
Theoretically, The key to make indirect reciprocity is…
(a) to exclude a person who didn’t give to anyone
(b) to reward a person who gave to “Good” who had given in the past.
(c) to exclude a person who gave to “Bad” who hadn’t given.
What kind of person participants chose (or avoided) as recipients?
1) Giver to Giver (GtoG)
2) Giver to Non-giver (GtoNG)
3) Non-giver (NG)
1st-order info
Gave in the last round
Gave in the last round
Didn’t give in the last round ＞
Discrimination based on 1st-order info.
2nd-order info
toward a person who had given 2 rounds before
toward a person who hadn’t given 2 rounds before
Discrimination based on 2nd-order info.
Predictions: participants...
1. will not give to “Non-giver”.
2. will give more to “Giver to Giver” than to “Giver to Non-giver”.
DV: giving rate toward each type of others

30. Sample of the displayed screen
We used deception. Actually all the displayed information, including 1st-order, 2nd-order information and feedback information, was manipulated by the computer program in order to systematically examine people’s behavioral patterns, while controlling the number of each type of others. (In actuality, this was a standalone experiment.)

31. DV: Preference for each type
1) Giver to Giver
2) Giver to Non-giver
3) Non-giver
What types of target did participants choose as their recipients?

32. DV: Preference for each type
1) Giver to Giver
2) Giver to Non-giver
3) Non-giver
We calculated “the preference for each type*” as the measure of the tendency to give to (or avoid) the person of that type selectively rather than randomly for each round.
(*We will skip the details of the way for calculation here.)
If the value is zero: s/he chose the recipient randomly.
A positive value: gave to a person of that type selectively rather than randomly.
A negative value: avoided a person of that type rather than randomly.

33. Result: Average of preference for each type
Average of preference of each type (SD)
1) Giver to Giver
2) Giver to Non-giver
3) Non-giver
0.14 (0.23)
0.00 (0.18)
-0.14 (0.13)
Giver to Giver > Giver to Non-giver > Non-giver
The effect of type of target is statistically significant (F(2,62)=13.23, p<.0001).
The preference was the highest for ”Giver to Giver”, the second for “Giver to Non-Giver”, the lowest for “Non-giver”.
>
Results of a comparison between 3 types (ANOVA) showed that

34. Result: Average of preference for each type
Average of preference of each type (SD)
1) Giver to Giver
2) Giver to Non-giver
3) Non-giver
0.14 (0.23)
0.00 (0.18)
-0.14 (0.13)
>
>
Results of comparison between 3 types (ANOVA) showed that….
Participants used 1st-order information ←Supported prediction 1.
The effect of type of target is statistically significant (F(2,62)=13.23, p<.0001).
Giver to Giver > Giver to Non-giver > Non-giver
Participants didn’t give to “Non-giver”.

35. Result: Average of preference for each type
Average of preference of each type (SD)
1) Giver to Giver
2) Giver to Non-giver
3) Non-giver
0.14 (0.23)
0.00 (0.18)
-0.14 (0.13)
>
>
Results of comparison between 3 types (ANOVA) showed that….
Although “Giver to Giver” and “Giver to Non-giver” are both givers…
The effect of type of target is statistically significant (F(2,62)=13.23, p<.0001).
Giver to Giver > Giver to Non-giver > Non-giver
Participants didn’t give to “Non-giver”.

36. Result: Average of preference for each type
Average of preference of each type (SD)
1) Giver to Giver
2) Giver to Non-giver
3) Non-giver
0.14 (0.23)
0.00 (0.18)
-0.14 (0.13)
>
>
Results of comparison between 3 types (ANOVA) showed that….
Participants used not only 1st-order information but also 2nd-order information ←Supported prediction 2.
The effect of type of target is statistically significant (F(2,62)=13.23, p<.0001).
Giver to Giver > Giver to Non-giver > Non-giver
Participants didn’t give to “Non-giver”.
Participants gave more to “Giver to Giver” rather than to “Giver to Non-giver”.

37. Consistent with our predictions
Result: Average of preference for each type
Average of preference of each type (SD)
1) Giver to Giver
2) Giver to Non-giver
3) Non-giver
0.14 (0.23)
0.00 (0.18)
-0.14 (0.13)
>
>
Results of comparison between 3 types (ANOVA) showed that….
Consistent with our predictions
The effect of type of target is statistically significant (F(2,62)=13.23, p<.0001).
Giver to Giver > Giver to Non-giver > Non-giver
Participants didn’t give to “Non-giver”.
Participants gave more to “Giver to Giver” rather than to “Giver to Non-giver”.

38. Conclusion 1. not only exclude a non-giver,
Predictions: In situations of indirect reciprocity People…
1. not only exclude a non-giver,
2. but also exclude a person who gave toward a non-giver rather than a person who gave toward a giver.
What kind of person do people help and exclude in situations of indirect reciprocity?

39. ←consistent with prediction 1.
Conclusion
Predictions: In situations of indirect reciprocity People…
1. not only exclude a non-giver,
2. but also exclude a person who gave toward a non-giver rather than a person who gave toward a giver.
What kind of person do people help and exclude in situations of indirect reciprocity?
Participants didn’t give to “a previous non-giver” than to a previous giver.
Participants gave less to “a person who had given to a non-giver” than to “a person who had given to a giver”.
←consistent with prediction 1.
←consistent with prediction 2.

40. ←consistent with prediction 1.
Conclusion
Predictions: In situations of indirect reciprocity People…
1. not only exclude a non-giver,
2. but also exclude a person who gave toward a non-giver rather than a person who gave toward a giver.
People discriminate others based on not only 1st-order information but also 2nd-order information.
What kind of person do people help and exclude in situations of indirect reciprocity?
Participants didn’t give to “a previous non-giver” than to a previous giver.
Participants gave less to “a person who had given to a non-giver” than to “a person who had given to a giver”.
←consistent with prediction 1.
←consistent with prediction 2.

41. Conclusion
People discriminate others based on not only 1st-order information but also 2nd-order information.
People’s actual behavioral patterns are consistent with the theoretical conclusion that to exclude not only free riders but also unconditional cooperators who benefit free riders --- to regard enemy’s friend as an enemy, too --- is needed.

42. Thank you
for your attention!