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Unformatted text preview: 6.207/14.15: Networks Lectures 17 and 18: Network Effects Daron Acemoglu and Asu Ozdaglar MIT November 16 and 18, 2009 1 Networks: Lectures 17 and 18 Introduction Outline Network effects Strategic complements Equilibria with network effects Dynamics of network effects Network effects with local interactions Network effects in residential choices Network effects in the labor market Supermodular games Contagion in networks and graphical games Public Reading: EK, Chapter 17 Jackson, Chapter 9.6 2 Networks: Lectures 17 and 18 Introduction Network Effects We say that there are network effects when the desired behavior of an individual depends on some average of the actions of others. Network effects with local interactions when these effects work through the behavior of “neighbors”. At this level of generality, several games we have already studied exhibit network effects. However, network effects become more interesting in the context of markets, particularly, when we study product, residential or technology choices. In what follows, we will first illustrate network effects, then provide several different frameworks for studying them. 3 Networks: Lectures 17 and 18 Introduction Example without Network Effects Consider a society consisting of a large number of individuals (for example i ∈ ℐ ≡ [0 , 1], though i = 1 , ..., I for I large would also be fine). Each individual chooses between two products denoted by s i ∈ { , 1 } . First suppose that each individual has preferences given by u ( s i , x i ) = [ x i − c ] s i , where x i ∈ ℝ + could be thought of as the type of the individual, representing his utility from taking action s i = 1, and c is the cost of this action. Suppose that x i has a distribution given by G in the population (with continuous density g ). 4 Networks: Lectures 17 and 18 Introduction Example without Network Effects (continued) It is straightforward that all individuals with x i > c will take action s i = 1 , and those with x i < c will take action s i = 0. Focus on Nash equilibria. Then the following is immediate: Proposition In the unique equilibrium, a fraction S = 1 − G ( c ) of the individuals will choose s i = 1 . So far there are no network effects. 5 Networks: Lectures 17 and 18 Introduction Network Effects in Product Choice Now imagine that s i = 1 corresponds to choosing a new product, such as BluRay vs. HD DVD, or signing up to a new website, such as MySpace or Facebook; ℐ is a set of potential friends (“network”). The utility of signing up is higher when a greater fraction of one’s friends have signed up. This is an example of a network effect . In the context of the environment described above, we can capture this by modifying each agent’s utility function to: u ( s i , x i , S ) = [ x i h ( S ) − c ] s i , where S is the fraction of the population choosing s i = 1 and h : [0 , 1] ℝ is an increasing function capturing this network effect. → This is an aggregative game, in the sense...
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 Fall '09
 Acemoglu
 Dynamics, Game Theory, network effects, response dynamics, Supermodular Games, Residential Choices

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