1. Exploitation and the Perversion of Social Capital in Exchange Networks: Two Social-Psychological Models and a Proposed Experiment Phillip Bonacich, U.C.L.A. July 8, 2010
As a student of social networks I am best known for developing measures of centrality in networks, but I am also a social psychologist. Today I will present a model of power that I’m working on and intend, eventually, to test with laboratory experiments

2. Exploitation
The inequality in power that tens to emerge when two individuals differ in their dependency on one another.
Exploitation is a network phenomena because dependency refers to the availability of alternative relations

3. Exploitation can be benevolent

4. Exploitation can be malevolent

5. Or exploitation can be inadvertent

6. Some Principles of Exchange
The Golden Rule: Do unto others as you would have them do unto you.
Reciprocity: Return favors
Exploitation: Exploit others who are dependent on you.

7. Reciprocity is a strong principle
There is much research on the strength of the principle of reciprocity in human affairs. Natural selection may have operated to make us cooperate with those who cooperate with us.

8. Reciprocity can be perverted, according to Peter Blau
“The principle of reciprocity operates on the basis of equality between all those linked by the cycle of reciprocity. Its malfunction leads to inequality, but that is an abnormal situation.”
“To surpass a rival in generosity, to crush him if possible under future obligation, which is hoped he cannot meet, thus taking from him privileges, titles, rank, authority and prestige.”

9. The power-dependence approach
PAB = DBA The power of A over B equals the dependence of B upon A. B is dependent A to the degree to which he receives valuable rewards unavailable elsewhere.
Blau is discussing sociopathic misuses of resources to put others in situations of submission. The power-dependence approach, developed by the sociologists Peter Blau, George Homans, and Richard Emerson, sees some amount of exploitation of dependence as a normal and unavoidable feature of social life. It has been used, for example, to explain differences in power in marriage between working and non-working spouses, where the former have greater economic and social opportunities outside the relationship. Revolutionary Road. Kate Winslet (April Wheeler) and Leonardo DiCaprio (Frank Wheeler)

10. Linda Molm’s Experiment
Linda Molm, a sociologist as the University of Arizona, has done extensive research on exchange and has created an experiment that can be used to study power and dependence. I am not modeling exploitation in general but her experiment in particular – to suggest a set of predictions if I were to run a variant of her experiment, which I plan to do, NSF be willing. Social psychology advances if everyone uses the same tools

11. Conditions
At each trial subjects chose one of their contacts to reward.
The reward was costless to the giver.
There were a large number of trials.
Subjects were not aware of the shape of the network or, naturally, their position within it.
Subjects knew how much of their limited resources they gave others but not how much their gifts were worth to others.
Some pairs could reward each other with many more (four times as many) points than could other pairs. Dotted lines

12. Molm’s results
The guiding principle was reciprocity: subjects in advantaged positions did not exploit their more dependent partners.
A and B exchanged equally and fully, as did C and D.
How can exploitation occur if actors were not aware of the dependence of others?

13. Model For Reciprocity

14. Implications Of Reciprocity

15. This was the result.

16. Exploitation vs. Reciprocity

17. What if B behaves rationally while others reciprocate
What if B behaves rationally while others reciprocate? Earnings of all positions as a function of how frequently B rewards A.
However, I’s clear that A and D are at a disadvantage. B’s rewards to A are so much greater than D’s. B can get A to reciprocate easily and use his other opportunities to encourage C to reciprocate. This chart is from simulations. All actors except B are assumed to behave according to the principle of reciprocity. The X axis shows the relative frequency with which B rewards A.

18. Frequency with which A and C reward B as a function of how frequently B rewards A
Again, the X axis is the frequency with which B rewards A. B doers not have to reward A very much to get his undivided loyalty while still encouraging frequent rewards from C.

19. The A and X matrices for the Box Network
C changed into A and P changed into X, as I thought of the allocation as a proportion of ones resources rather thab as a probability.

20. Reciprocity and Dependence
Fitting the Molm experimental design, the dependence of j on i (and the power of i over j) is the proportion of j’s rewards he receives from i. This should also equal how much of his resources j gives I, under reciprocity.

21. I Model T(ransitional): Actors want to reciprocate
The pattern of results is insensitive to the choice of alpha.

22. II Actors initiate reciprocity in others

23. Maximizing rewards
Assume this maximization occurs with respect to every i and j.

24. Maximizing Behavior in Four-person Box NetworkC D x
.94
,06
.21
.79 X
.06
reward
.90
6.92
power
2.23
5.55
Power is total dependence, weighted by value of tie: power i = a ji D ji So far, in every network I’ve looked at, the results are in a “Nash equilibrium”: no one has a unilateral incebtive to change.

25. Reciprocity versus exploitation
Rewards represented by size of disk.

26. Tee Network
These networks will seem odd. They are chosen because they have been experimented on. Everyone has alternative relations.

27. Maximizing Behavior in Tee networkC D E x
.82
.18
.19 X
.62
.54
.46
.07
.86
reward
.83
6.72
5.92
2.20
power
1.59
9.03
4.29
2.49

28. Reciprocity versus exploitation
Add tee with another A position

29. Un-analyzable

30. Un-analyzable

31. Model A(ltered)

32. New A and X matrices

33. 4-line giving using Model AB C D
.003
.997
.064
1.104
.832

34. Giving in Star Network Using Model AB C D
1.873
.376
.818
.184

35. New experiment: full information