Networks: Lecture 16IntroductionSocial NetworksModels of Social NormsSmall Groups and Local InteractionsCohesivenessTrust in Networks6.207/14.15: Networks Lecture 16: Cooperation and Trust in Networks Daron Acemoglu and Asu Ozdaglar MIT November 4, 2009 1Networks: Lecture 16 Introduction Outline The role of networks in cooperation A model of social norms Cohesion of groups and social norms Trust in networks Reading: Osborne, Chapters 14 and 15. 2Networks: Lecture 16 Introduction The Role of Social Networks Recall the importance of “social contacts” in finding jobs. Especially of “weak ties” (e.g., Granovetter (1973) “The Strength of Weak Ties”: most people find jobs through acquaintances not close friends. The idea is that recommendations from people you know are more trusted. Similarly, social networks important in starting businesses? Recall that in many developing economies (but also even in societies with very strong institutions), networks of “acquaintances and contacts” shape business behavior. (e.g., Munshi (2009) “Strength in Numbers: A Network-Based Solution to Occupational Traps”). The Indian diamond industry is dominated by a few small subcasts, the Marwaris, the Palanpuris, the Kathiawaris—in the same way that Antwerp and New York diamond trade used to be dominated by ultra-Orthodox Jews. 3Networks: Lecture 16 Introduction Trust in Networks The rise of the Kathiawaris most likely related to their close-knit network. When the Marwaris and the Palanpuris institutionalized their relationship with Antwerp (often opening branches of their firms there). Moreover, over time, lower intermarriage rates for these groups. Network relationships seem to matter less. The Kathiawaris initially a lower, agricultural subcast, some of them working as cutters for the Marwaris and the Palanpuris. Strong network ties, intermarriage rates etc. After the increase in the world supply of rough diamonds in the 1970s (following the opening the Australia’s Argyle Mines), the Kathiawaris slowly dominate the business. Mutual support, referrals, long-term relationships based on networks. Recall that Munshi’s argument was that network connections helped the Kathiawaris pull ahead of the richer and more established Marwaris and Palanpuris. 4Networks: Lecture 16 Introduction Trust in Networks (continued) Perhaps trust is more difficult when the network is larger. The Marwari and the Palanpuri businessmen were sufficiently more established, so they did not depend on their subcast links, so implicitly reneging on their long-term relationships within their cast would have carried relatively limited costs for them. But if so, then there would be little “trust” in the network of the Marwaris and the Palanpuris. In contrast, the Kathiawaris strongly depended on their network, so any reneging (or appearance of reneging) would lead to their exclusion from the business community supporting them forever—and this support is very valuable to the Kathiawaris. Thus in this example, after a certain level, fewer links may be better—to make one more dependent on his network and thus more trustworthy. 5Networks: Lecture 16 Introduction Social Norms Even in broader social groupings, some types of implicit understanding on expected behavior important. We sometimes refer to these as social norms: how to dress, how to interact with others, limits on socially costly selfish behavior, etc. How are they supported? This lecture: using repeated games to understand social norms and trust in social networks. 6Networks: Lecture 16 Models of Social Norms Modeling Social Norms We will think of social norms as the convention—expected play—in the game. The key question is whether a particular social norm is sustainable as the equilibrium in society. Consider a society consisting of N players playing an infinitely-repeated symmetric two-player strategic form game G = ⟨ℐ, A, u⟩. Throughout N is a large number. Here A denotes the set of actions at each stage, and thus ui : A × A ℝ. () → titj)is played at stage t between players i and j tjThat is, u is the state payoff to player i when action profile a , a (We will think of a social norm simply as an action a∗ ∈ A that all t ti= i.∕a = a , a players are expected to play. 7Networks: Lecture 16 Models of Social Norms Modeling Social Norms (continued) Suppose, to start with, that players are matched randomly at each date (you may wish to think that N is even). Let ai be the sequence of plays for player i , i.e., {( )}t t ∞ai = ai , aj(i,t), where j (i, t) denotes the player matched to i t=0 at time t. The payoff of player i is then ∑∞U(ai ) = �t u(ait , ajt (i,t)) t=0 where � ∈ [0, 1) is again the discount factor. 8Networks: Lecture 16 Models of Social Norms Full Monitoring Full monitoring applies when players observe the entire history of past actions. For example, they observe the entire history of play in each random match. With full monitoring, the following personalized trigger strategies are possible. If individual i deviates from the social norm a∗ at time t, everybody observes this, and will play some punishment action a ∈ A against i (they can still cooperate with other players). Then the arguments from standard repeated games (in particular the folk theorems) immediately imply the following theorem. 9Networks: Lecture 16 Models of Social Norms Full Monitoring Theorem Theorem Let aNE be a static equilibrium of the stage game. With full monitoring, for any a ∈ A with u (a, a) > u (aNE , aNE ), there exists some � < 1 such that for all � >�, there exists an equilibrium supporting social norm a. Proof (essentially identical to the proof of the folks theorems): Deviation has some benefit ¯u now and thus overall return ( )NE NEu a , au¯ + � ,1 − � since all other players will punish the deviator (e.g., playing the NE). u(a,a)Cooperation has return 1−� . Therefore, ¯(aNE , aNE ) � ≥ � ≡ u − uu − u (a, a) ∈ (0, 1) ¯guarantees that the social norm of cooperation is sustainable. 10Networks: Lecture 16 Models of Social Norms Application Recall the prisoners’ dilemma: Cooperate Defect Cooperate 1, 1 −1, 2 Defect 2, −1 0, 0 In this game, (C , C ), that is “cooperation,” can be supported as the social norm in society when � ≥ 1/2. 11Networks: Lecture 16 Models of Social Norms Problems with Full Monitoring