Experimental Evidence on Trading Favors in Networks Markus Mobius and Tanya Rosenblat November 2004

What Do We Mean by Social Capital? Social Capital is the value of social obligations or contacts formed through a social network. Relationships are useful. But maintaining relationships is costly.

What Do We Mean by Social Capital? Example: May 17 Deep Thought - [ESA Meetings in Amsterdam in June – still need Hotel! Hotels were sold out in March…] Scenario 1: Have a friend in Amsterdam. Ask if I can stay at her house. Scenario 2: Have a friend in Brussels. He has a friend in Amsterdam. He asks if I can stay at her house.

Scenario 1: Tanya Sabine

Scenario 1: Tanya Sabine Request for a favor

Scenario 1: Tanya Sabine TanyaSabine

Scenario 1: Tanya Sabine TanyaSabine Favor Granted

Why did Sabine do it?  She hopes she can stay in Boston in the future.  She thinks I’ll help her out with something else.  I’ve done many favors for her in the past.  She is just very nice. Imagine I don’t know Sabine, but just find her name in the phonebook. Will she let me stay at her place?

Scenario 2: Tanya Alain Sabine

Scenario 2: Tanya Alain Sabine Request for a favorRequest relayed

Scenario 2: Tanya Alain Sabine Tanya Alain Sabine Favor given to Alain

Scenario 2: Tanya Alain Sabine Tanya Alain Sabine Favor done for AlainFavor done for Tanya

Why did Alain do it?  He knows that I won’t destroy Sabine’s apartment.  He thinks I’ll help him out with something else.  I’ve done many favors for him in the past.  He is just very nice. Why did Sabine do it?  She thinks Alain will help her out with something else.  Alain has done many favors for her in the past.  She is just very nice.

Social Capital (Putnam’s Definition) Social capital refers to the collective value of all “social networks” [who people know] and the inclinations that arise from these networks to do things for each other [“norms of reciprocity”]

Social Capital (Putnam’s Definition) Social capital works through multiple channels: information flows (e.g. learning about jobs) norms of reciprocity (mutual aid)  Bonding networks that connect folks who are similar sustain particularized (in-group) reciprocity.  Bridging networks that connect individuals who are diverse sustain generalized reciprocity.

Motivation non-market interactions are important (Prendergast and Stole 1999; Granovetter 1973) how are favors paid? what ‘currency’? long-term bilateral relationships; reciprocity

Motivation often no double coincidence of wants across time: frequent within-group interaction but infrequent interaction with any particular agent (Granovetter’s weak links) group information (institutions; gossip) networks as monitoring mechanisms

Main Questions Are there cooperative “network” equilibria? (YES) Do agents actually choose to play these cooperative equilibria? => Experimental Framework

Theoretical Intuition Large number of agents, continuous time Alarm clocks go off independently at rate 1 and then an agent needs a good (e.g., information about jobs) Share p of agents can provide the good (every agent other than the one with the need can provide with probability p) Ex: p=5%; 1000 agents; 50 people can do it. Helping costs c but gives benefit b>c => there are benefits from trade

Theoretical Intuition Similar to Prisoner’s Dilemma I help you now in a repeated game environment because you will help me in the future => bilateral networks based on reciprocity. However, if we interact infrequently cooperation is hard to sustain. Kandori (1992)  low frequency interaction through random matching (can “help” each other only infrequently)  cooperation can be sustained through contagious punishment  cooperation breaks down as N becomes large  Group punishments help.

Theoretical Intuition Need information aggregation for group punishment Global Image Scores as a Particular Aggregation Mechanism Sigmund and Nowak (1998)  image scores allow group punishments  global image scores are memory intensive as N becomes large Money as a Particular Image Score Kocherlakota (1998): money as memory

Theoretical Intuition – Network Mechanism to Sustain Cooperation Networks with weak links Local Image Scores – I only have information about behavior of my circle of friends. Can only punish my friends. Ex. Everyone has 4 friends but no friends in common.

13542 Weak Link Network with 4 friends – everyone has 4 friends but no friends in common

13542 If Agent 2 owes a favor to Agent 1, we say 1 has an open link to 2.

Theoretical Intuition – Network Mechanism to Sustain Cooperation Every link is either open or closed with probability ½ at the beginning of time. How much is an open link worth to me? Out of my 3 friends 1 ½ owe me favors. If I ask you for a favor, 1½ of your friends owe you a favor. => The number of owed favors increases exponentially => eventually somebody can grant my request for sure.

13542 Agent 1 needs help. Agents 2 and 5 owe Agent 1 favors. 6 owes to 5; 7 owes to 6; 8 owes to 7; 8 can do it Can do it

asks 5; 5 asks 6; 6 asks 7; 7 asks 8; 8 does it Can do it

13542 Note that 1 doesn’t know 8! Why does 8 do it? – He values his relationship with Can do it

Theoretical Intuition – Network Mechanism to Sustain Cooperation Why wouldn’t I invest in infinitely many links? Ex. If I have 100 friends who owe favors to me, I won’t have any need to reciprocate favors – I’ll spend all the time consuming the links. So nobody wants to be friends with me in the first place.

Theoretical Intuition – Network Mechanism to Sustain Cooperation Can show that there is a network equilibrium with relaying requests for help in which cooperation can be sustained. Next Step: Design an experiment to see if agents choose to play this equilibrium.

Related Experimental Work We know that there is a lot of cooperation in the lab when theory suggests there should be none Examples of direct reciprocity include  Prisoner’s Dilemma (Andreoni and Miller,1993; Cooper, DeJong, Forsythe, and Ross (1996))  centipede game (McKelvey and Palfrey,1992)  public goods game (Croson, 1998)  investment game (Berg, Dickhaut and McCabe, 1995)  employer/ employee relationships (Fehr, Gachter and Kirchsteiger, 1997; Fehr and Gachter, 1998)

Related Experimental Work Experimental Results on Indirect Reciprocity = “How should I treat you if I know how you treated somebody else?”  In one shot games: investment game (Dufwenberg, Gneezy, Guth and van Damme, 2000; Buchan, Croson, and Dawes, 2001)  In repeated interactions - helping games with global image scores  Wedekind and Milinksi (2000),  Seinen and Schram (2000) and Bolton, Ockenfels, Katok and Huck (2001): vary amount of image score information available to donors

Related Experimental Work Main results:  some baseline altruism  strategic indirect reciprocity - evidence that agents can learn to cooperate using global image scores Design an experiment with networks and local image scores.

Experiment helping game where subjects choose whom to ask agents are not always able to help => no small cliques only local information (cannot observe others’ interactions) two treatments: direct and indirect games

Direct Game: 10 players who can send (direct) messages to each other. No referrals allowed.

Indirect Game: Weak link network that connects you to all other players. Can send direct messages and forward messages received.

Indirect Game: Weak link network that connects you to all other players. Can send direct messages and forward messages received.

Conducted in Argentina from August 2002 to April 2003 Instructions in Spanish (reverse translations) Mediated in points with exchange rate 100 points = 0.40 Pesos Flat participation fee of 12 pesos Experiment lasted 1 – 1 ½ hours Average hourly wage for college students at the time 6-10 Pesos/hr Each subject participated in 2 sessions of several rounds in length. Experiment

a probabilistic ending time for every round – resulting average length 14 rounds initial account: 1500 Points message cost: 2 Points benefit of getting the good: 300 Points cost of giving the good: 200 Points Experiment

Messages are costly to avoid meaningless messaging and to put a limit on messaging because new round starts only after all messages have been dealt with. 50 goods; each player can give 5 out of 50 goods When good is not given a player cannot tell whether this is because the other player could not give or chose not to give. In the indirect treatment, when the good is granted, the player never finds out about who along the chain granted it. Parameters are set such that theoretically cooperation cannot be sustained in direct game; there is a network equilibrium for indirect game

Timing – Direct Game In each round: Subjects choose the recipient(s) of messages and send messages. Receivers of messages send responses. If they can give the good, they have to choose either to give or to ignore request. The round is over when there are no outstanding messages Subjects learn about the one good they need and the five goods they can produce.

Timing – Direct Game In each round: Subjects learn about the one good they need and the five goods they can produce. Subjects choose the recipient(s) of messages and send messages. Receivers of messages send responses. If they can give the good, they have to choose either to give or to ignore request. The round is over when there are no outstanding messages The need and production abilities change every round.

Timing – Direct Game In each round: Subjects learn about the one good they need and the five goods they can produce. Subjects choose the recipient(s) of messages and send messages. Receivers of messages send responses. If they can give the good, they have to choose either to give or to ignore request. The round is over when there are no outstanding messages The need and production abilities change every round. Sending a message costs 2 points.

Timing – Direct Game In each round: Subjects learn about the one good they need and the five goods they can produce. Subjects choose the recipient(s) of messages and send messages. Receivers of messages send responses. If they can give the good, they have to choose either to give or to ignore request. The round is over when there are no outstanding messages The need and production abilities change every round. Sending a message costs 2 points. Recipients of goods never find out why they did not get the good.

Timing – Direct Game In each round: Subjects learn about the one good they need and the five goods they can produce. Subjects choose the recipient(s) of messages and send messages. Receivers of messages send responses. If they can give the good, they have to choose either to give or to ignore request. The round is over when there are no outstanding messages The need and production abilities change every round. Sending a message costs 2 points. Recipients of goods never find out why they did not get the good. Agents can send as many messages as they want if they have points to pay for them.

Timing – Indirect Game In each round: Subjects choose the recipient(s) of messages and send messages. Receivers of messages send responses. They always have an option to refer request to someone else. If they can give the good, they have to choose either to give, to ignore request or to refer request. The round is over when there are no outstanding messages Subjects learn about the one good they need and the five goods they can produce.

Subjects 89 subjects from University of Tucuman variety of majors 4 direct and 5 indirect games of 2 sessions each

Subjects 89 subjects from University of Tucuman variety of majors 4 direct and 5 indirect games of 2 sessions each Income Proxy

Hypotheses: H1: The probability that a needed good is provided in the indirect treatment is larger than the probability that a needed good is provided in the direct treatment. Therefore, average earnings should be higher in the indirect treatment.

Hypotheses: H2: The probability that a givable request is granted is greater in the indirect treatment. Note that H2 is not a consequence of H1, because in indirect game messaging is less efficient: agent might not relay a message in which case it doesn’t reach a player who could have provided the good. So possible that more givable requests are granted in the indirect game but earnings are lower nevertheless.

Hypotheses: H3: The probability of granting a givable request increases between sessions in the indirect game and decreases between sessions in the direct game. H4: In the indirect game agents who receive many favors should be also the agents who grant a lot of favors. In the direct game there is no relation between receiving favors and granting them.

Results H1: 30 percent of favors get fulfilled in direct game versus 52 percent in indirect earnings are higher in indirect game

Results: H2: The probability that a givable request is granted is greater in the indirect treatment. H3: The probability of granting a givable request increases between sessions in the indirect game and decreases between sessions in the direct game.

Data Analysis: Extract all messages in which receiver had requested good in his production possibility set. Plot the time at which messages were sent on the x-axis and a moving average of the propensity to grant a givable request averaged over the last 20 messages on the y-axis.

First Sessions: Direct Game Black Indirect Game Red

Second Sessions: Direct Game Black Indirect Game Red

Direct Game: First Session Black Second Session Red

Direct Game: First Session Black Second Session Red The probability of granting a givable request declines between treatments!

Indirect Game: First Session Black Second Session Red

Indirect Game: First Session Black Second Session Red The probability of granting a givable request does not decline between treatments!

Results: H4: In the indirect game agents who receive many favors are likely to be the agents who grant a lot of favors. In the direct game there is no relation between receiving favors and granting them. For each subject, count the number of received and sent favors for both sessions of a treatment. 39 data points for direct and 50 for indirect. Plot the number of total favors received on x-axis and the number of total favors granted on y-axis.

Direct Game: No relationship!!!

Indirect Game: Positive Relationship

Network Formation Even though available communication network is exogenous, agents still have to choose recipients of messages. In the direct game, messages are unfocused and so is reciprocation of favors. In the indirect game, (in part by construction) focus on few friends but achieve much more efficient outcomes.

Concluding Remarks We’ve chosen an environment in which cooperation was hard to sustain because agents could be helpful to each other only infrequently. Current data suggests that there is more cooperation and less free-riding when subjects can satisfy their needs through referrals. Building social capital pays off in this setting.

To Do: More data with current parameters. Treatments without visual image score information Treatments with relaying and 10 players Limiting the number of relayed messages in treatment with 3 friend weak link network.