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Implementing the Newton's Method Procedure in the Simulator
In the simulator, we use GeneralStateModel to update the Agent states. Each agent corresponds to a single firm, and its state is an array with three numeric components. Component 0 stores the current output of the firm, component 1 records what equilibrium mode the agent is in, as described on the previous slide. In addition, component 2 stores the firm's β, the strength of its network externality function.
To represent a network of firms, we connect all corresponding agents in a clique. Every Network Externalities Society consists of such disjoint cliques of agents. For each agent, the learning production function for state component 0 (firm output) implements the modified Newton's Method described in the previous slides. Changing the initial output values and Equilibrium modes of each agent eventually brings the society to the various equilibria predicted in "Network Externalities."
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