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is simpler to analyze and it also seems more appropriate for a model of social behavior. However, special assumptions are needed to rationalized non-strategic behavior. In the Sslm, for example, an agent is assumed to make a once-in-a-lifetime decision. Because his payoff is independent of other agents'actions, it is rational for him to behave myopically and ig nore the affect of his action on the agents who follow him. In the sNm. an agent's payoff is independent of other agents'actions but, unlike the SSLM agents make repeated decisions. In order to eliminate strategic behavior, we assume that the economy comprises a large number of individually in- significant agents and that agents only observe the distribution of actions t each date. Since a single agent cannot affect the distribution of actions he cannot influence the future play of the game. This allows us to "strategic"considerations and focus on the pure Bayesian-learning of the model The agents Formally, we assume there is a finite set of locations indexed by i=1,.,n At each location, there is a non-atomic continuum of identical agents. In he sequel, the continuum of agents at location i is replaced by a single representative agent i who maximizes his short-run payoff in each period Uncertainty is represented by a probability measure space( Q, F,P) where s is a compact metric space, F is a a-field, and P a probability measure. Time is represented by a countable set of dates indexed by t 1.2 Let ACR be a finite set of actions and let U:AxQ-R be the common payoff function, where U(a, )is a bounded, measurable function for every action a. Each(representative)agent i receives a private signal Ji(w) at date 1, where ;: Q2-+R is a random variable The network A social network is represented by a family of sets N;: i=l,.,n), where N≤{1,…,-1,i+1,…,n} For each agent i, Ni denotes the set of agents j# i who can be observed by agent i. We can think of Ni as representing is"neighborhood". The sets IN: 1=1, , n define a directed graph with nodes N=(1,.,ny and edges E= U(i,): J N. The social network determines the information How in the economy. agent i can observe the action of agent j if and only if j E Ni. Agents have perfect recall so their information set at each date includes the actions they have observed at every previous date For any nodes i and j, a path from i to j is a finite sequence il, . iK such that i1=i, iK =3 and ik+1 E Nik for k= 1,.K-1. A node connected to j if there is a path from i to j. The network INil is connected if every pair of nodes i and j is connected. Connectedness is essential for uniformity of behavior. but not for other resultsis simpler to analyze and it also seems more appropriate for a model of social behavior. However, special assumptions are needed to rationalized non-strategic behavior. In the SSLM, for example, an agent is assumed to make a once-in-a-lifetime decision. Because his payoff is independent of other agents’ actions, it is rational for him to behave myopically and ig￾nore the affect of his action on the agents who follow him. In the SNM, an agent’s payoff is independent of other agents’ actions but, unlike the SSLM, agents make repeated decisions. In order to eliminate strategic behavior, we assume that the economy comprises a large number of individually in￾significant agents and that agents only observe the distribution of actions at each date. Since a single agent cannot affect the distribution of actions, he cannot influence the future play of the game. This allows us to ignore “strategic” considerations and focus on the pure Bayesian-learning aspect of the model. The agents Formally, we assume there is a finite set of locations indexed by i = 1, ..., n. At each location, there is a non-atomic continuum of identical agents. In the sequel, the continuum of agents at location i is replaced by a single representative agent i who maximizes his short-run payoff in each period. Uncertainty is represented by a probability measure space (Ω, F, P), where Ω is a compact metric space, F is a σ-field, and P a probability measure. Time is represented by a countable set of dates indexed by t = 1, 2, .... Let A ⊂ R be a finite set of actions and let U : A × Ω → R be the common payoff function, where U(a, ·) is a bounded, measurable function for every action a. Each (representative) agent i receives a private signal σi(ω) at date 1, where σi : Ω → R is a random variable. The network A social network is represented by a family of sets {Ni : i = 1, ..., n}, where Ni ⊆ {1, ..., i − 1, i + 1, ..., n}. For each agent i, Ni denotes the set of agents j 6= i who can be observed by agent i. We can think of Ni as representing i’s “neighborhood”. The sets {Ni :1=1, ..., n} define a directed graph with nodes N = {1, ..., n} and edges E = ∪n i=1{(i, j) : j ∈ Ni}. The social network determines the information flow in the economy. Agent i can observe the action of agent j if and only if j ∈ Ni. Agents have perfect recall so their information set at each date includes the actions they have observed at every previous date. For any nodes i and j, a path from i to j is a finite sequence i1, ..., iK such that i1 = i, iK = j and ik+1 ∈ Nik for k = 1, ..., K − 1. A node i is connected to j if there is a path from i to j. The network {Ni} is connected if every pair of nodes i and j is connected. Connectedness is essential for uniformity of behavior, but not for other results. 5
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