Asymmetry of Control in the Prisoner’s Dilemma Game:

Dependence and Responsibility

Adam Stivers D. Michael Kuhlman

Presented at the 16th International Conference on Social Dilemmas, Hong Kong June 24th, 2015

Social Interdependence(Kelley & Thibaut, 1978)

What makes a situation socially interdependent:

1) Social: deals with interactions involving 2 or more Decision Makers (DMs): people, groups, teams, corporations, countries, etc. (participant and unknown “other” for today)

2) Interdependent: For each DM there are outcomes with different utilities that depend, to some extent, on the decisions of the other DM (true for the “given matrix” in all PDG’s)

• For this talk today, it matters to me whether I gain validation from peers. For this, I depend (at least to some extent) on you.

• You are here with an interest in learning about social dilemmas (or at least staying awake). But, this depends (at least to some extent) on whether I can tell you anything informative. For this, you are depending on me.

• In this relationship, we are socially interdependent, because we both depend on the other to achieve outcomes that are meaningful for self, but…

• Fortunately, in this socially interdependent situation, there is not much conflict of interest (I hope)

Okay, but why does this matter?

How did we get here?

The ability to form and maintain interdep relationships was imperative for the survival of our evolutionary ancestors (e.g., Bowles & Gintis 2011; de Waal, 2008), and…

The Big Questions???

How do we stay here?

Developing cooperation in socially interdependent situations is critical to negotiating modern day problems such as resource depletion, nuclear proliferation, and democratic participation (for a review; Van Lange et al., 2013)

Components of Social Interdependence (Kelley & Thibaut, 1978)

Kelley, H. H. & Thibaut, J. W. (1978). Interpersonal relations: A theory of interdependence. New York: Wiley.

In Social Interdependence Theory there are 4 important components and the first 2 are Necessary:

• Dependence: each DM’s outcomes are influenced to some degree by the choices of partner: Other DM’s Fate Control (Partner Control) over you.

• Responsibility: each DM has, to some degree, influence over the other DM’s outcomes: Your Fate (Actor) Control over the other DM

• Behavioral or Joint Control: in some cases the choices of 1 DM effect the utility of the other DM’s choices. A PDG may or may not have Joint Control. -Today: Behavioral Control = 0

• Grand Mean: This is the average of all possible outcomes for a given player. -This can very across PDG’s: higher or lower overall outcomes

-This can asymmetrically vary across DM’s in the SAME game (Future Study) -Today GM = 50

Important for the content of this talk, all of these components can systematically vary across situations (games). In particular:

The DM1 can be more/less DEPENDENT on the choices of the other DM2 The DM1 can be more/less RESPONSIBLE for the outcomes of the other DM2

Furthermore, Kelley and Thibaut (1978) provide a way to quantify these components…

Quantifying Dependence(Kelley et al., 2003)

C' NC'

C 90 100

90 0

NC 0 10

100 10

Let’s focus on the Row Players outcomes, Dependence is all about who has control of the Row Player’s outcomes:

When the Column Player chooses C’, the Mean for the Row Player is 95

When the Column Player chooses NC’, the Mean for the Row Player is 5

The difference between these 2 columns is 90, this is Partner Control (PC)

When the Row Player chooses C, the Mean for the Row Player is 45

When the Row Player chooses C, the Mean for the Row Player is 55

The difference between these 2 rows is 10, this is Actor Control (AC)

C' NC'

C

90 0

NC

100 10

M = 95 M = 5

Dependence = PC2 + JC2

AC2 + PC2 + JC2

Dependence = 8100 + 0 100 + 8100 + 0

Dependence = 0.99

M = 45

M = 55

C' NC'

C 90 100

90 0

NC 0 10

100 10

C' NC'

C 90 100

NC 0 10

Quantifying Responsibility(Kelley et al., 2003)

Now, let’s focus on the Column Players outcomes, the Responsibility of the Row Player is the proportion of control he/she has over the other person:

The difference between the 2 rows is 90, this is the Actor Control (AC) the row player has over the outcomes of the other DM

The difference between the 2 columns is 10, this is Partner Control (PC) the column player has over their own outcomes

M = 45 M = 55

Responsibility = AC2 + JC2

AC2 + PC2 + JC2

Responsibility = 8100 + 0 100 + 8100 + 0

Responsibility = 0.99

M = 95

M = 5

The Prisoner’s Dilemma Game (PDG)(Flood & Drescher; reviewed by Poundstone, 1992)

The classic Prisoner’s Dilemma Game is a one-shot interaction between 2 players who are each given a binary choice (confession or silence):

Choice A

Choice A Choice B

Choice B

Player 1

Player 2• Player 1 Dominant Strategy: Choose B for best personal outcome

• Player 2 Conflict of Interest: Better off personally if Player 1 chooses A

• Collective Disaster: Mutual Choice B yields worse outcome than Mutual Choice A• For each player (70 > 30)• For the collective (140 > 60)

70 0

100 30

70 100

0 30

70 100

70 0

0 30

100 30

Social Dilemma:• Individually, each player is better off choosing B. But this is Non-cooperative

(NC), because…• Collectively, the pair is better off if each Cooperatively (C) chooses A • But, not all PDG’s are created equal, some have more (or less) conflict of

interest…

C' NC'

C 90 100

90 0

NC 0 10

100 10

Social Interdependence in the PDG(Rapoport & Chammah, 1965)

Some PDG’s have high interdep:• Dependence = 0.99• Responsibility = 0.99• K index = 0.8

• The game on the right has a higher temptation for non-cooperation, and• The game on the right a higher risk of exploitation (“sucker effect”; Kerr, 1983)• Dependence = Responsibility, this is ALWAYS true in SYMMETRIC GAMES• The difference in social interdependence between these 2 games has been

quantified by Rapoport & Chammah’s (1965) “K index”• A higher “K index” is functionally related to higher Dependence and Responsibility• In symmetric games, it is impossible to distinguish the effects of Dependence and

Responsibility because they are ALWAYS identical.

C' NC'

C 60 100

60 0

NC 0 40

100 40

Some PDG’s are less interdep:• Dependence = 0.69• Responsibility = 0.69• K index = 0.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

SVO Moderates Effect of K

K Index

% C

oope

ratio

n

• Cooperators: oriented to maximize Joint Gain (+ self, + other) or to promote Equality

• Individualists oriented to maximize Own Gain (+ self, 0 other)

• Competitors oriented to maximize Relative Gain (+ self, - other)

• Decades of research have yielded a robust finding that when games are more socially interdependent (high K index) more people will choose to cooperate

• In a study done by Camac (1988) This was particularly true for people with a Cooperative SVO

• It was also true for Individualists, who are more non-cooperative overall

• But this was not true for Competitors who are non-cooperative regardless of the K index But why does this happen?

Social Value Orientation (SVO), the K index, and Cooperation(Camac, 1988)

.

In the PDG, Row Player’s outcomes are (to some degree) dependent on Column’s choices. From here on, we’ll use “Dependence “ as this component of a relationship.

Hypothesis 1: People are more cooperative when their outcomes are more dependent on the choices of others

And, Column Player’s outcomes are (to some degree) dependent on Row’s choices. That is, Row is (to some degree) responsible for Column’s well being. From here on, we’ll use “Responsibility” as this component of a relationship.

Hypothesis 2: People are more cooperative when they have more responsibility for the outcomes of others

Or, maybe both:Hypothesis 3: People are more cooperative when they have more dependence on the choices of other and more responsibility for the outcomes of others

Finally, we will test whether SVO moderates the (potential) effects of Dependence and Responsibility.

Hypothesis 4: Cooperators will cooperate more when they are more Responsible, based on moral concerns (Van Lange & Kuhlman, 1994)

Hypothesis 5: Individualists will cooperate more when they are more Dependent based on strength concerns (Van Lange, Liebrand, & Kuhlman, 1990)

To test the hypotheses, we used 3 sets of games:

Set 1: Symmetric games (9 games) K index: [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8]In all games Dependence and Responsibility were equal.

Game Two Dependence Responsibility

Low Dep/Rsp .60 .60

Game Nine Dependence Responsibility

High Dep/Rsp .99 .99

Set 2: Dependence Manipulation (9 games)Dependence varied from .60 to .99 Responsibility held constant at .84

Game Two Dependence Responsibility

Low Dep .60 .84

Game Nine Dependence Responsibility

High Dep .99 .84

Set 3: Responsibility Manipulation (9 games)Dependence held constant at .84Responsibility varied from .60 to .99

Game Two Dependence Responsibility

Low Rsp .84 .60

Game Nine Dependence Responsibility

High Rsp .84 .99

Procedures

1) SVO: assessed with the Delaware adaptation of Liebrand’s Ring Measure prior to “playing” the Prisoner’s Dilemma games.

2) All Ps viewed 27 matrix games, then all games were presented a 2nd time and P’s indicated a choice of A or B on the 27 games. Game order was randomized with restrictions in the Spring Semester and counter-balanced in the Fall Semester

3) Other player in the game is hypothetical: no deception

MethodParticipants1) 409 U Delaware undergrads participated in 4 roughly equal sessions in the

Spring 2014 (2 sessions) and Fall 2014 semesters (2 sessions).

2) Exclusions: 31 Ps failed quiz on instructions, 22 P’s had Unclassified SVO, 11 P’s had unusual SVO’s (Aggressor/Altruist). 345 P’s remained

Coop Indv Comp TOTALMale 73 57 23 153Female 106 61 25 192TOTAL 179 118 48 345

Prelim Analyses1) No effects or interactions for Semester or Session (no order effects)

2) No effects or interactions for Gender

Both variables not included in subsequent analyses

Design

Repeated Measures ANOVA: 3(SVO) X 3 (Set) X 2 (Block)

SVO: Cooperator / Individualist / Competitor (between subjects)

Set: Symmetric / Dependence / Responsibility (within subjects)

Block Game 1,2,3,4 / Game 6,7,8,9 (within subjects)

Results: Design & Main Effects

Main effect for SVO: • Prosocials > Proselves (p < .001)• Individualists vs Competitors (p = .13)

Main effect for Block: Social Interdependence in general increases cooperation

F(2,333) = 62.47, p < .001, η2 = 26.7% F(2,333) = 40.6, p < .001, η2 = 10.6%

NO Main effect for Set: p > 0.3

Results: 2-Way Interactions

• There was an effect for Dependence, in fact, it was not different from the Symmetric Set (p > .15)

• Responsibility had NO EFFECT on cooperation, and the slope was less than the other 2 sets: F(2, 333) = 47.28, p < .001, η2 = 12.1%

• Prosocials were more responsive to interdependence than proselves (F(1,333) = 22.57937, p <0.0001)

• Individualists vs Competitors ns

F(2,333) = 30.59, p < .001, η2 = 8.2% F(2,333) = 11.32, p < .001, η2 = 6.2%

Gm1 Gm2 Gm3 Gm4 Gm5 Gm6 Gm7 Gm8 Gm90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Sets1 and 2 Combined

%Co

op

F(1,333)=4.302, p = 0.0388.

• Again, changes in Dependence are driving cooperation, and• This change in cooperation is strongest in Prosocials, but…• Only in the Dep/Sym games, responsiveness in Set 3 (RESP) is

reduced in Coops, and if anything it goes in the opposite direction. • Take Home Message: Dependence, (not Responsibility) makes

Prosocials (but not Proselves) more cooperative. This is what drives the famous “K index” effect.

Gm1 Gm2 Gm3 Gm4 Gm5 Gm6 Gm7 Gm8 Gm90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Set 3: Dep Constant, Resp Varies

CoopsIndosComps

Results: 3-Way Interactions

Discussion of Results

Hypothesis 1: People are more cooperative when their outcomes are more dependent on the choices of others YES, STRONG EFFECTHypothesis 2: People are more cooperative when they have more responsibility for the outcomes of others NO, Opposite TrendHypothesis 3: People are more cooperative when they have more dependence on the choices of other and more responsibility for the outcomes of others NO, only DependenceHypothesis 4: Cooperators will cooperate more when they are more Responsible, based on moral concerns (Van Lange & Kuhlman, 1994) NO, only DependenceHypothesis 5: Individualists will cooperate more when they are more Dependent based on strength concerns (Van Lange, Liebrand, & Kuhlman, 1990) NO, Prosocials show this effect

The Asymmetric Matrix Game: while the use of symmetric games have proliferated over the past 50 years, asymmetric games have seldom been used and only to manipulate the Grand Mean. 2 Good Reasons to change this:

1) Theoretical: the asymmetric game allows us to address fundamentally interesting questions about how people behave when they are in a position of more/less control or dependence than others (Kelley & Thibaut, 1978)

2) Practical: Outside the laboratory, we are seldom given independent choices with equal utilities. Even inside the laboratory, there is substantial evidence that the “given” matrix is transformed into an “effective” matrix based on personal preferences and situational pressures (Au & Kwong, 2004; Bogaert, Boone, & Declerck, 2008; Messick & McClintock, 1968; Murphy & Ackermann, 2014; Van Lange & Kuhlman, 1994)

Future Directions:

More asymmetric games! Manipulation of the Grand Mean and Behavioral Control:

70 100

120 50

0 30

150 80

C NC

C

NC

70 100

70 30

0 30

100 0

C NC

C

NC

Discussion: Asymmetry

Special Thanks!

Bowles, S., & Gintis, H. (2011). A cooperative species: Human reciprocity and its evolution. Princeton University Press, Princeton, NJ. Retrieved from http://search.proquest.com/docview/885700457?accountid=10457

Camac, C. R. (1988) The Importance of Fear, Greed and Social Orientation in Determining Behavior in Social Dilemmas. Unpublished doctoral dissertation, Department of Psychology, University of Delaware

De Waal, Frans B. M. (2008). How selfish an animal? the case of primate cooperation. Moral markets: The critical role of values in the economy. (pp. 63-76) Princeton University Press, Princeton, NJ. Retrieved from http://search.proquest.com/docview/62

Kelley, H. H., Holmes, J. G., Kerr, N. L., Reis, H. T., Rusbult, C. E., & Van Lange, Paul A. M. (2003). An atlas of interpersonal situations Cambridge University Press, New York, NY. doi:http://dx.doi.org/10.1017/CBO9780511499845

Kelley, H. H. & Thibaut, J. W. (1978). Interpersonal relations: A theory of interdependence. New York: Wiley.Kerr, N. L. (1983). Motivation losses in small groups: A social dilemma analysis. Journal of Personality and Social Psychology, 45, 819-828.

doi: 10.1037/0022-3514.45.4.819.Liebrand, W. B., Jansen, R. W., Rijken, V. M., & Suhre, C. J. (1986). Might over morality: Social values and the perception of other players

in experimental games. Journal of Experimental Social Psychology, 22(3), 203-215. Retrieved from http://search.proquest.com/docview/617308496?accountid=10457

Messick, D. M., & McClintock, C. G. (1968). Motivational bases of choice in experimental games. Journal of Experimental Psychology, 4, 1-25.

Murphy, R. O., & Ackermann, K. A. (2014). Social value orientation: Theoretical and measurement issues in the study of social preferences. Personality and Social Psychology Review, 18(1), 13-41. doi:http://dx.doi.org/10.1177/1088868313501745

Poundstone, W. (1992). Prisoner’s dilemma: Jon von Neumann, game theory, and the puzzle of the bomb. New York, NY: Random House, Inc.

Rapoport, A., & Chammah, A. M. (1965). Prisoner’s dilemma. Ann Arbor, MI: University of Michigan Press.Van Lange, P. A. M., Balliet, D., Parks, C. D., & Van Vugt, M. (2013). Social dilemmas: Understanding human cooperation. New York, New

York: Oxford University Press.Van Lange, P.A.M., & Kuhlman, D. M. (1994). Social value orientations and impressions of partner’s honesty and intelligence: A test of

the might versus morality effect. Journal of Personality and Social Psychology, 67, 126-141.Van Lange, P. A. M., Liebrand, W. B. G., & Kuhlman, D. M. (1990). Causal attribution of choice behavior in three N-person Prisoner’s

Dilemmas. Journal of Experimental Social Psychology, 26, 34-48.

The Prisoner’s Dilemma Game (PDG) and the K index

The “K index” gives us the ability to quantify the extent to which a PDG has a Conflict of Interest

The outcomes of the game are identified as:

Temptation to exploit partner

Reward for mutual cooperation

Penalty for mutual defection

Sucker payoff for trusting non-cooperator

For PDG, ALWAYS T > R > P > S

To the extent that R > P, there is a Less Conflict of Interest

Scaled by the total range of outcomes, this yields the equation:

K = (R – P) / (T – S)

In PDG, 0 < K < 1

C NC

C R' T'

R S

NC S' P'

T P

Delaware adaptation of Liebrand (1986) Ring Measure of SVO

Set 1 Symmetric Games

Set 2 Dependence Varies, Responsibility Constant

Set 3 Responsibility Varies, Dependence Constant