The weak side of informal social control Paper prepared for Conference Game Theory and Society. ETH Zürich, July 27-30, PDF Free Download

The weak side of informal social control Paper prepared for Conference Game Theory and Society. ETH Zürich, July 27-30, 2011 Andreas Flache Department of Sociology ICS University of Groningen

Collective action and informal social control The free rider problem in collective good production Contribution is costly, but free riders are hard to exclude groups may fall far short of optimal provision One of the solutions is informal social control Reward contributors and / or punish free riders Shunning, approval, ostracism Nagging second order free rider problem Provision of social control imposes in itself a collective action problem. 2

Endogenous solutions Altruistic punishment (Fehr & Gächter 2003) free riding causes strong negative emotions most people expect these emotions emotions trigger punishment Network closure and low cost selective reward (Coleman, 1990) "An expression of encouragement or gratitude for anothers' action may cost the actor very little but provide a great reward for the other Emotional dependence on cohesive group (Homans 1974) Group members reward one another with expressions of approval. Ostracism is the penalty for failing to conform. The more cohesive the group, the stronger the pressure. 3

and a new problem? Most groups exist over longer time periods What happens when informal social control is only one part of a network of ongoing exchange relations between group members? not only free riders depend on punishing group members for obtaining social approval, but also vice versa. retaliation of punishment or unconditional reciprocation of social rewards becomes possible 4

How social control fails in cohesive groups: student group assignments Quotes from Groningen students about group assignments: It seemed so nice and cosy with four friends in a work group. But in the end, you are more inclined to take it easy. You expect that your friends will shoulder the burden for you It is much easier in a group of friends to come with some poor excuse if you did not show up once more In assignment groups, students criticize each other practically never for lack of activity, because students who are also friends just will not let each other down. (quote from a teacher) University newspaper September 2001 (translation by AF) 5

And at the workplace Langfred (2004) posits reluctance among members of a self-managing team to implement and enforce monitoring, due to the fear of sanction or punishment, and concern for the feelings of fellow team members Source: Langfred, C.W. (2004). Academy of Management Journal, 47, 385-399. 6

A game theoretical model of weakness of strong ties (Flache, Macy & Raub 2000; Flache 2002, J Math Soc) Repeated game: each round probability τ of continuation. Others actions of previous rounds are known. All individuals take independently and simultaneously N decisions: Contribute C to the collective good or not (c i = 1 or c i = 0) Give R to Alter 1 or not, Give R to Alter 2 or not, (r ij = 1 or r ij = 0) Individual preferences: the utility function: Total number of contributions by the group (+) Number of reward units received (+) Own contribution ( ) Number of reward units given ( ) N N N α u = c + β r kc k' r i j ji i ij N j= 1 i j i j Two linked PD s: α < k N β < k α: value of collective good, β: unit value of reward, k: cost of contribution, N: group size, k : unit cost of giving reward 7

Possible competing reciprocity strategies: Task cooperation (TC): I give C iff enough others give C. Performance: Contribution Collective good C alt C ego C alt C ego Full cooperation (FC): I give C and R to everyone iff enough others give C and give R to me. Cohesion: Rewards ) Ego R alt R ego Alter Relational cooperation (RC): I give R to Alter iff Alter gives R to me. 8

Possible competing reciprocity strategies: Performance: Contribution Collective good Task cooperation (TC): I give C iff enough others give C. C alt C ego C alt C ego Full cooperation (FC): I give C and R to everyone iff enough others give C and give R to me. Cohesion: Rewards ) Ego R alt R ego Alter Relational cooperation (RC): I give R to Alter iff Alter gives R to me. 10

Does rational behavior in this game imply a weakness of strong ties? Does the possibility of relational cooperation make conditions for task- or full cooperation more restrictive? Task cooperation: I give C iff enough others give C. Full cooperation: I give C and R to everyone iff enough others give C and R to me. Relational cooperation: I give R to Alter iff Alter gives R to me. Performance: Contribution Cohesion: Rewards ) Collective good C alt C ego C alt C ego Ego R alt R ego Alter 11

Possible competing reciprocity strategies: Task cooperation (TC): I give C iff enough others give C. Full cooperation (FC): I give C and R to everyone iff enough others give C and give R to me. Relational cooperation (RC): I give R to Alter iff Alter gives R to me. All three reciprocity strategies are modelled in terms of trigger strategies. Hence, adhering to the norm is individually rational iff the shadow of the future τ is sufficiently large: τ > τ T = T R P T: payoff from unilateral deviation R: payoff from universal co-operation P: payoff from universal defection S: payoff from suffering exploitation 12

Which reciprocity strategy is the solution (if any )? (cf. Flache, Macy & Raub 2000, Flache 2002, J Math Soc) For given parameter α,β,k,n,k and given shadow of the future, τ : Only symmetric trigger strategy combinations that constitute a payoff dominant subgame perfect equilibrium (spe) can be solution. Of those: We focus on those with maximal punishment (necessary condition for individual rationality). The group selects the payoff dominant spe. Given other parameters, this yields a unique solution for every level of τ Assuming uniform distribution of τ For every parameter vector α,β,k,n,k we obtain expected level of performance (p) and of cohesion (p ).

Model predictions Possibility of relational cooperation does not distract from task- or full cooperation (1) If relational cooperation is spe then either no other, or FC is spe If full cooperation is individually rational, it yields always the highest utility it is the solution. 1 0 τ full cooperation, dominates TC and RC full cooperation, dominates RC only relational no cooperation cost / benefit relational relatively favorable

Model predictions (2) Possibility of relational cooperation does not distract from full cooperation (2) If relational cooperation is spe then either no other, or FC is spe If full cooperation is individually rational, it yields always the highest utility it is the solution. 1 0 τ full cooperation, dominates TC and RC full cooperation, dominates TC only task cost / benefit task no cooperation relatively favorable

Model predictions (3) Effects of possibility relational cooperation (Conditions used for lab experiment) 1 0.8 0.6 0.4 0.2 0 No RC RC performance cohesion Performance = fraction of τ-unit interval in which solution is full or task cooperation. N: group size = 5 α: value of collective good = 0.3 β: unit value of reward = 0.1 k: cost of contribution = 0.2 k : unit cost of giving reward = 0.03 Cohesion = fraction of τ-unit interval in which solution is full- or relational cooperation. 16

One mechanism for a weakness of strong ties : low rationality Flache & Macy (1996, J Math Soc) proposed for this game a reinforcement learning model. Prediction: relational control can distract from performance. Satisficing: agents can lock in on outcome of mutual social reward, despite zero performance Random coordination: mutual cooperation is easier to coordinate in bilateral reward game than in multilateral contribution game. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 No RC RC performance cohesion 17

But there is also a high rationality mechanism: noise and uncertainty (Flache 2002, J Math Soc) Task uncertainty: small chance ε that i s contribution is not effective. Imperfect information: others only see result of a contribution. Reciprocity strategies involving task contribution need to be restrictive enough to deter deviation, but entail unnecessary mutual punishment efficiency losses. Extension of the solution theory: group adopts the optimal individually rational strategy profile: some amount of task-defection is tolerated (cutoff level), whole group cooperates again after fixed punishment time (cf. Green & Porter 1984, Bendor and Mookherjee 1987, Kreps 1990). spe with highest expected payoff is selected from optimal FC,TC and RC profiles. 18

Results of model with uncertainty and noise: Possibility of relational cooperation can distract from full cooperation (1) When both full cooperation and relational cooperation are individually rational, relational cooperation can be more efficient. Reason: full cooperation requires occasional punishments if to much contribution error occurs efficiency losses. 1 0 τ full cooperation, dominates TC & FC relational cooperation dominates FC only relational no cooperation cost / benefit relational relatively favorable

Model predictions model with task uncertainty Effects of possibility relational cooperation (Conditions used for lab experiment) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 No RC RC performance cohesion error probability ε = 0.1 Performance = fraction of τ-unit interval in which solution is full- or task cooperation. N: group size = 5 α: value of collective good = 0.3 β: unit value of reward = 0.1 k: cost of contribution = 0.2 k : unit cost of giving reward = 0.03 Cohesion = fraction of τ-unit interval in which solution is full- or relational cooperation. 20

Model predictions model with task uncertainty Effects of possibility relational cooperation (Conditions used for lab experiment) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 No RC RC performance cohesion error probability ε = 0.15 Performance = fraction of τ-unit interval in which solution is full- or task cooperation. N: group size = 5 α: value of collective good = 0.3 β: unit value of reward = 0.1 k: cost of contribution = 0.2 k : unit cost of giving reward = 0.03 Cohesion = fraction of τ-unit interval in which solution is full- or relational cooperation. 21

Key predictions Possibility of relational cooperation decreases performance Possibility of relational cooperation increases cohesion assuming uncertainty, relatively severe collective good dilemma and relatively favorable cost/benefit ratio for reward exchange. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 No RC RC performance cohesion 22

Experiment: game Per round 5 decisions per player: Today I work hard (yes / no) I give approval to colleague 1 (yes / no) I give approval to colleague 2 (yes / no) I give approval to colleague 3 (yes / no) I give approval to colleague 4 (yes / no) work outcome: Overall score = Work + relational outcome, accumulated over 30 rounds (indefinite end) The higher the score, the higher the chances to win 20. relational outcome: Number others who work 0 1 2 3 4 I do not work 0 6 12 18 24 I work -14-8 -2 4 10 Two linked PD s: α < k N β < k Number of colleagues you approve of: Number of colleagues who approve of you: 0 1 2 3 4 0 0 10 20 30 40 1-3 7 17 27 37 2-6 4 14 24 34 3-9 1 11 21 31 4-12 -2 8 18 28 25

Experiment: manipulation Relational cooperation condition 26

Experiment: manipulation No relational cooperation condition Same payoff structure but no information given on received rewards 27

Note: There is no error in contribution and no uncertainty about others true contribution levels in the experiment. That is: objective error probability ε = 0. 28

Experiment: results (1) Effect of possibility of relational cooperation on performance 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 N=70 subjects (35/35) 7 groups per condition no rel coop rel coop Change average contribution level by condition Multilevel linear regression logit c it main effect condition: negative (p<.01) condition x time: negative (p<.01) N = 70 subjects x 30 rounds = 2100 29

Experiment: results (2) Effect of possibility of relational control on cohesion 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 N=70 subjects (35/35) 7 groups per condition no rel coop rel coop Change average reward level by condition Multilevel regression average r i+,t main effect condition: positive condition x time: no effect (p<.01) 30

Experiment: results (3) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 No RC RC performance cohesion Averages by condition (0..1) (round 3..27) N=70 subjects (35/35) Multilevel regression average c i main effect condition: negative (p<.1) 7 groups per condition Multilevel regression average r i+ main effect condition: positive (p<.01) 31

Effects on determinants of popularity Popularity = average incoming reward r ij Without possibility of relational control: Main determinant of popularity is contribution With possibility of relational control: Main determinant of popularity is rewarding others But contribution still has a small positive effect 32

So far The possibility of bilateral reward exchange ( relational cooperation ) can undermine social control in collective action Effects of relational cooperation are best predicted by a model assuming error and uncertainty (or by reinforcement learning) although there was no error in our experiment. Uncertainty assumption may capture perceived risks of bilateral reward exchange vs. multilateral contribution exchange Inclusion of risk dominance in repeated game model appears to be better way to model this. Future research. 33

Another future direction: network structure Noise and observation of group output + network ties with perfect observation New trigger strategies Always defect forever if you see a defection via your network (c.f. e.g. Raub & Weesie 1990, Buskens 1998,2002 ) (stop task contribution and reward of defector) Otherwise follow trigger strategy (cutoff, length) 34

D D D D D D D D D D D D D Network adapted from field study of Wittek (1997) D D D New implications: 1) More density, shorter average path length more performance Less chance of weakness of strong ties 2) Tolerating free riders can be rational and efficient if they are marginal in the network Less restrictive trigger profile less erroneous punishment more efficiency 35

Overall conclusions Informal social control may fail to sustain collective good production, giving way to relational cooperation particularly when there is repeated interaction in the group, the collective good dilemma is severe and dependence on peer rewards is high, networks of mutual observation are sparse, as opposed networks of mutual approval, and many actors are in the margin of the observation network But many questions remain Reward vs punishment? Perceived uncertainty or risk dominance or low rationality 36