Games on Social Networks

1. Games on Social Networks Stephen Leider Markus Mobius Tanya Rosenblat March 15, 2005 PLESS Workshop

2. Motivation • Andreoni and Miller (2002) and Fisman and Kariv (2005): considerable heterogeneity in altruistic preferences among economic agents. Some agents are purely selfish while others have various forms of altruistic preferences ranging from fair preferences (equal payoff to both agents) to preferences that aim to maximize total utility. • Mobius, Quoc-Anh and Rosenblat (2006) have shown that agents who are connected through a social network are aware of their neighbors’ types. This highlights one important function of social networks which is to provide information about others’ types. • That paper also shows that if interaction is non-anonymous previously selfish agents start to behave like altruists towards friends. This observation highlights a second important function of social networks which is to provide enforcement.

3. Motivation • The information and enforcement motives determine whom agents choose to play certain classes of games which are of everyday importance: • Asking for Help:Whom do we approach when we need help? There is an incentive to choose a person who is known to be altruistic because this person can be trusted to take one’s payoff into account. It will also help to choose a person with whom one interacts frequently because this person might help out of repeated game considerations. • Starting a business/Bargaining: Assume I can choose to start a business with another person whose surplus is to be divided. Assume that each of my friends at distance 1 and 2 has a certain profit opportunity. Whom would I approach to start a business? • Forming a Team:Assume I can choose to form a team with someone else and we both submit effort – whom would I like to be in a team with? How would this be affected if both players can observe each other’s effort/ cannot observe it?

4. Why are friends nice to us? • Social networks in two student dorms (N=569) • Preferences: use modified dictator games as in Andreoni-Miller (2002) to measure how altruistic we expect our friends to be and how altruistic they actually behave towards us (as compared to strangers). • Enforcment: Two within subject treatments to check for enforcement channel: (T1) recipient finds out and (T2) recipient does not find out.

5. Measuring Types • Use Andreoni-Miller (Econometrica, 2002) GARP framework to measure altruistic types • Modified dictator game in which the allocator divides tokens between herself and the recipient: tokens can have different values to the allocator and the recipient. • Subjects divide 50 tokens which are worth: • 1 token to the allocator and 3 to the recipient • 2 tokens to the allocator and 2 to the recipient • 3 tokens to the allocator and 1 to the recipient

6. Recipients Recipients are asked to make predictions in 7 situations (in random order): 1 direct friend; 1 indirect friend of social distance 2; 1 indirect friend of social distance 3; 1 person from the same staircase; 1 person from the same house; 2 pairs chosen among direct and indirect friends Share staircase Indirect Friend 2 links Indirect Friend 3 links Same house

7. Stage II: Recipients • Recipients make predictions about how much they will get from an allocator in a given situation and how much an allocator will give to another recipient that they know in a given situation. • One decision is payoff-relevant: • => The closer the estimate is to the actual number of tokens passed the higher are the earnings. Incentive Compatible Mechanism to make good predictions Get $15 if predict exactly the number of tokens that player 1 passed to player 2 For each mispredicted token $0.30 subtracted from $15. For example, if predict that player 1 passes 10 tokens and he actually passes 15 tokens then receive $15-5 x $0.30=$13.50.

8. Allocators For Allocator choose 5 Recipients (in random order): 1 direct friend; 1 indirect friend of social distance 2; 1 indirect friend of social distance 3; 1 person from the same staircase; 1 person from the same house. Share staircase Indirect Friend 2 links Indirect Friend 3 links Same house

9. Stage II: Allocators • We also ask allocator to allocate tokens to an anonymous recipient. • All together they make 6 times 3 allocation decisions in T1 treatment (recipient does not find out) and 6 times 3 allocation decisions in T2 treatment (recipient finds out).

10. Analysis (AM) • Selfish types take all tokens under all payrates. • Leontieff (fair) types divide the surplus equally under all payrates. • Social Maximizers keep everything if and only if a token is worth more to them.

11. Analysis (AM) • About 50% of agents have pure types, the rest have weak types. • Force weak types into selfish/fair/SM categories by looking at minimum Euclidean distance of actual decision vector from type’s decision.

13. Recipients think that friends are about 20% less selfish under both treatments.

15. Allocators are only weakly less selfish towards friends if the friends do NOT find out.

16. Allocators are 15% less selfish towards friends if friends can find out.

17. Methodology Measuring the Social Network (2005)

18. Facebook Network (2005) • Trivia game contest on Facebook.com • Pick 10 friends you know best • Asked a question about a random friend • Win prize if correct. • 2939 students participated (46%). • Social Network definition • If A lists B, or B lists A then there is a link. • Social Distance is the shortest path length between two people.

19. Measuring the Network • Rather than surveys, agents play in a trivia game • Leveraged popularity of www.thefacebook.com • Membership rate at Harvard College over 90% * • 95% weekly return rate * * Data provided by the founders of thefacebook.com

20. Markus • His Profile • (Ad Space) • His Friends

21. Trivia Game: Recruitment • On login, each Harvard undergraduate member of thefacebook.com saw an invitation to play in the trivia game. • Subjects agree to an informed consent form – now we can email them! • Subjects list 10 friends about whom they want to answer trivia questions. • This list of 10 people is what we’re interested in (not their performance in the trivia game)

23. Trivia Game: Trivia Questions • Subjects list 10 friends – this creates 10*N possible pairings. • Every night, new pairs are randomly selected by the computer • Example: Suppose Markus listed Tanya as one of his 10 friends, and that this pairing gets picked.

24. Trivia Game Example • Tanya (subject) gets an email asking her to log in and answer a question about herself • Tanya logs in and answers, “which of the following kinds of music do you prefer?”

26. Trivia Game Example (cont.) • Once Tanya has answered, Markus gets an email inviting him to log in and answer a question about one of his friends. • After logging in, Markus has 20 seconds to answer “which of the following kinds of music does Tanya prefer?”

28. Trivia Game Example (cont.) • If Markus’ answer is correct, he and Tanya are entered together into a nightly drawing to win a prize.

29. Trivia Game: Summary • Subjects have incentives to list the 10 people they are most likely to be able to answer trivia questions about • This is our (implicit) definition of a “friend” • This definition is suited for measuring social learning about products. • Answers to trivia questions are unimportant • ok if people game the answers as long as the people it’s easiest to game with are the same as those they know best. • Roommates were disallowed • 20 second time limit to answer • On average subjects got 50% of 4/5 answer multiple choice questions right – and many were easy

30. Recruitment • In addition to invitations on login, • Posters in all hallways • Workers in dining halls with laptops to step through signup • Personalized snail mail to all upper-class students • Article in The Crimson on first grand prize winner • Average acquisition cost per subject ~= $2.50

31. Participation • Consent: 2932 out of 6389 undergrads (46%), and 50% of upperclassmen • 10 friends: 2360 undergraduates (37%) • Participation by year of graduation:

32. Participation • By residential house (upperclassmen)

33. Network Data • 23,600 links from participants • 12,782 links between participants • 6,880 of these symmetric (3,440 coordinated friendships) • Similar to 2003 results • Construct the network using “or” link definition • 5576 out of 6389 undergraduates (87%) participated or were named • One giant cluster • Average path length between participants = 4.2 • Cluster coefficient for participants = 17% • Lower than 2003 results – because many named friends are in different houses

36. Pilot Design • 175 Harvard Seniors participated. • Subjects are explained each of 4 games. • For each game half of subjects are Choosers, see three pairs of Responders they could play with. 3 Treatments • Random: randomly assigned partner • Choice: Chose partner • Pay: Elicit willingness to pay for right to choose, otherwise randomly assigned. • If Chooser for first two games, was Responder for second two.

37. Pilot Design • Dictator Game (DG): Chooser allocates 100 points, each is worth $0.05 to Chooser and $0.10 to Responder • Reverse Dictator Game (RDG): Same as DG, but Responder allocates • Thief Game (TF): Chooser takes up to 100 tokens, each adds $0.05 to Chooser’s payoff and deducts $0.10 from Responder’s payoff • Trust Game (TG): Chooser and Responder given $4. Chooser sends $X, any sent is doubled. Responder returns up to $2X

38. Pilot Games • Modified Dictator Game (DG) Each point is worth $0.05 to Chooser and $0.10 to Responder Player 1 Chooser Player 2 Responder C allocates 100 points between himself and R C R1 R2 3 pairs

39. Pilot Games Each point is worth $0.05 to Chooser and $0.10 to Responder • Reverse Dictator Game (RDG) Player 1 Chooser Player 2 Responder R allocates 100 points between herself and C C R1 R2 3 pairs

40. Pilot Games Each point adds $0.05 to Chooser’s payoff and subtracts $0.10 from Responder • Thief Game (TF) Player 1 Chooser Player 2 Responder C takes up to 100 points from R C R1 R2 R2 3 pairs

41. Pilot Games • Trust Game (TG) C and R are given $4 Player 1 Chooser Player 2 Responder C sends x to R; R receives 2x C R2 R1 R sends up to 2x back to C 3 pairs

42. Does Distance Matter? For choices in the game, closer social distance corresponds with greater altruism (except for Trust Game Responders), especially at distance of one.

43. Does Distance Matter? For partner choice, Choosers exhibit a preference for partners of closer social distance, particularly in the Trust Game. Again, this is strongest for distance of one.

44. How does Partner Choice affect Game Decisions? • Choosing your partner has strong, but puzzling, effects on game decisions. • DG: Altruism higher • TF & TG: Altruism lower

45. Individual Heterogeneity • We can use the DG/RDG data to identify social preference “types”. • We’ll want to see how consistent this categorization is across games. • We can also look at a weaker “best fit” categorization of types.

46. Thief Game Decisions By Type

47. Trust Game SenderDecisions By Type

48. Trust Game ReturnDecisions By Type

49. Does Type affect Partner Choice? • More altruistic subjects place a higher premium on social closeness when choosing who to play with.

50. New Design • We know the social network of about 1600 potential subjects. • There are two main stages. In the first stage we measure subjects’ types using simple dictator games. In the second stage we match subjects (and already know types) to play • (i) a helping game • (ii) bargaining game • (iii) team game • In all second stage games we make some matches more desirable than others – everything else equal. This allows us to check to what extent considerations about other players’ types and enforcement power affect players choices.